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scott_pilgrim

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Math Games
« on: February 02, 2017, 08:09:56 pm »

Math Games

Overview

This thread will contain a series of mathy/game theory-y mini-games.
Each game will have its own set of rules, to be posted at the start of the game.  (Some games will require that there be no communication after rules are posted, until the game ends.)
Each player will be awarded 100 points the first time they /in.  Each game played will usually add or subtract to this total.  The points are carried over from each game to the next.
There most likely will not be a well-defined "end".  At some point I may decide I don't have enough time to keep running this, or maybe I'll die or something.
Generally, you are playing to have as many points as possible.  This is different from playing to have more points than any other player.  (Think of it like every point you have is worth $1.)

General Rules

Players may /in at any time.  If there is a game in progress, you may be added to the next round of the game, if possible; or else you will be added to the next game.

Players may also /out at any time; however, they are strongly encouraged, if possible, to finish whatever game they are currently playing.  If a player /ins after having previously /outed, they will come back with however many points they had when they left.  As a courtesy, please do not /out before playing a game you think you will do badly at, just to avoid taking a points loss.  If you need to /out for a single game and then /in again, that's fine, but don't abuse this rule.  (Generally speaking you should gain points on average from most games anyway.)

Players may argue with the mod via PM, if they believe the rules or scoring of a game are unfair.  I reserve the right to change rules and/or scoring for a game in the middle of the game, but it's unlikely that I will act on this right unless a convincing argument is made.  I also reserve the right to ignore completely legitimate arguments made in this regard.

Please be sure to respect the no communications rule present in some games.  Communicating with other players about the game via PM, thread, or any other means is strictly forbidden for these games.  I will try to make it extremely obvious if a game has a no communications rule.

If the mod posts "Thread Locked" (usually in big bold letters), there is to be no posting in the thread until the mod posts "Thread Unlocked", even if the thread is not actually locked.  If the mod posts something indicating that there is to be no communication, please do not post in thread, even if no "Thread Locked" post is made.

If you have questions about the rules, you may ask via PM to the mod, or, if communication is allowed for the game, you may ask in thread.  If communication is not allowed for the game, and your question is important and relevant, I may post the answer to the question in thread to make sure everyone is on the same page (without saying who asked the question).

The title of the thread is "Math Games", but for the most part, knowledge of math is not a requirement to play.  Many of these games are original creations of the mod, and others are inspired by game theory or other math problems.  They are generally designed to be simple, but also to encourage some mathematical thinking, without being easily "solvable".  If you're not sure whether these games would be well-suited for you, the sample game (the first game that will be played) below should give you a good sense of what the games will generally be like.  A small percentage of games will require some high school-level math to understand exactly what is happening in them, and certainly higher-level math can be used to reason about the games, but anyone with enough knowledge to play Dominion should be able to at least play all of the games.

If you have an idea for a game that you think should be played, please PM me (regardless of whether you're currently playing; if having thought of the game might give you an unfair advantage, I can try to work out a fair solution, probably involving you sitting out for that game).  If I end up using your game, I will give you credit when it is played.

Likewise, if you like one of the games that has already been played and think it should be played again (possibly with new parameters or variants), let me know.  If there's enough demand for a particular game, I might rerun it.

Most of the games are designed for a variable number of players.  Many games work best (or only work) when played in smaller groups, or pairs, so I may split the player list into small groups as necessary.  The process by which players are divided up may be random, or may be based on how many points each player has, as appropriate for the current situation.

Play time for games will vary, but I will try to avoid having any single game last more than two weeks.  Players will generally be expected to check in about once every 24 hours (and I will try to keep up with that same time frame).  When I say to "check in" every 24 hours, what I mean is really this: any time a game requires you to make a decision, you are expected to make that decision within 24 hours of acquiring all information relevant to that decision.  (You don't need to post if there's no decision to be made.)  If you're reasonably close outside of that time frame that's fine.  If you know you won't be able to keep up with that, please /out (or PM the mod for special permission) until you can keep up with that.

I reserve the right to kick players out based on level of activity, or other reasons (repeatedly deliberately playing against their win condition, breaking rules, being rude to other players, etc.).  I also reserve the right to change the 24 hours in the paragraph above to 36 or 48 hours (I don't know if I can keep up with 24 hours as a mod; the help of a co-mod might make it more do-able); or also to take long breaks or do away with activity rules altogether if I can't keep up.

Please understand that a lot of games will involve some random chance.  The games are generally meant to be enjoyed by being played optimally; the outcome itself should not be what makes the games fun.

Because of the flexible rules about /inning and /outing, there will be no spectator thread.  Spectators generally should only post in thread about games that have finished, and NEVER post when the thread is locked or when communication among players is prohibited.

As stated above, you should play each game as though each point is worth $1.  In other words, you should generally play as if you don't care how many points other players have.  (There is no ultimate "winner", just a list of who has how many points, and you don't care about your position on that list, just the number next to your name.)

You can only get integer amounts of points.  (Usually if something might cause fractional amounts of points, a rounding scheme will be specified.)  Points can go negative.

Please do not edit your posts (or other players' posts).
« Last Edit: February 03, 2017, 06:38:29 pm by scott_pilgrim »
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scott_pilgrim

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Re: Math Games
« Reply #1 on: February 02, 2017, 08:10:07 pm »

Player List:
1. Calamitas (210)
2. gkrieg13 (172)
3. GendoIkari (172)
4. LaLight (171)
5. sudgy (165)
6. liopoil (163)
7. Dylan32 (163)
8. faust (158)
9. ghostofmars (157)
10. schadd (120)
...

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Bench (people who have played before but are currently /out):
Jimmmmm (103)
Tables (100)
pacovf (98)
Axxle (123)
UmbrageOfSnow (123)
2.71828... (173)
« Last Edit: March 12, 2017, 10:33:01 am by scott_pilgrim »
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scott_pilgrim

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« Last Edit: March 03, 2017, 08:08:13 pm by scott_pilgrim »
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scott_pilgrim

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Re: Math Games
« Reply #3 on: February 02, 2017, 08:10:33 pm »

1. Silent Bid

Rules

This game will be played in three rounds.  At the beginning of the first round, each player gets 8 gold.

Each round, players may distribute their 8 gold over the list of items below (they must put a non-negative integer amount of gold on each item):
   +15 points
   +10 points
   +5 points
   +3 points
   +2 points
   +1 point
   +1 point
   +6 gold
   +3 gold
   +2 points, +2 gold

Players may discuss their bids openly in the thread.  However, any statements made in thread are non-binding.  Players may freely lie about their bids.   

Players submit their bids by PM to the mod.   

After all bids are submitted, they will be revealed in the thread.  Whoever placed the highest bid on any given item wins that item.   

TIES BOUNCE.  They are not split or shared.  If two or more players tie for the highest bid on an item, nobody wins that item that round.   

At the start of each round, each player gets 8 gold, plus however much gold they won in the previous round.  Note that GOLD DOES NOT CARRY OVER FROM ONE ROUND TO THE NEXT.  If you won +6 gold in round 1, you get 6 extra gold for round 2, but not for round 3 (unless you won +6 gold again in round 2).   

Really you're just playing a very simplified, non-zero-sum version of Revolution.
« Last Edit: February 02, 2017, 08:13:02 pm by scott_pilgrim »
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schadd

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Re: Math Games
« Reply #4 on: February 02, 2017, 08:16:06 pm »

slash in
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Calamitas

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Re: Math Games
« Reply #5 on: February 02, 2017, 08:16:20 pm »

/in
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Re: Math Games
« Reply #6 on: February 02, 2017, 08:17:37 pm »

cool idea, scoot
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Re: Math Games
« Reply #7 on: February 02, 2017, 08:51:29 pm »

/in

Try not to die.  That' be a really lame way to end the game.
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faust

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Re: Math Games
« Reply #8 on: February 02, 2017, 09:07:16 pm »

/in

At which point does the first game start?
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Re: Math Games
« Reply #9 on: February 02, 2017, 09:08:18 pm »

/in  sounds fun
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scott_pilgrim

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Re: Math Games
« Reply #10 on: February 02, 2017, 09:44:09 pm »

/in

At which point does the first game start?

I don't have an exact time in mind.  I'm hoping Saturday if there are enough players by then (I don't know how many is enough, maybe 8 or so), though you are free to PM me with your bid (you may update it too if it's dependent on the number of players).  Some preliminary discussion is also okay, though if it's going to be extensive it might be better to wait until the player list is locked in for this game.
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Re: Math Games
« Reply #11 on: February 02, 2017, 10:24:31 pm »

/in
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Re: Math Games
« Reply #12 on: February 02, 2017, 11:10:49 pm »

/in
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Re: Math Games
« Reply #13 on: February 02, 2017, 11:18:59 pm »

/in
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Dylan32

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Re: Math Games
« Reply #14 on: February 03, 2017, 01:40:28 am »

/in
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Re: Math Games
« Reply #15 on: February 03, 2017, 05:08:05 am »

Will it be announced who won which thing at the end of the round? I assume so, but it's not explicitly stated.
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Re: Math Games
« Reply #16 on: February 03, 2017, 05:09:37 am »

/in
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Re: Math Games
« Reply #17 on: February 03, 2017, 05:11:36 am »

Is there any information beforehand on how many rounds will be played? This likely affacts optimal strategy.
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Re: Math Games
« Reply #18 on: February 03, 2017, 05:27:54 am »

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Re: Math Games
« Reply #19 on: February 03, 2017, 07:30:46 am »

Can I /tag? :-)
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scott_pilgrim

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Re: Math Games
« Reply #20 on: February 03, 2017, 08:34:13 am »

Will it be announced who won which thing at the end of the round? I assume so, but it's not explicitly stated.

After all bids are submitted, they will be revealed in the thread.

Is there any information beforehand on how many rounds will be played? This likely affacts optimal strategy.

This game will be played in three rounds.
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Re: Math Games
« Reply #21 on: February 03, 2017, 09:34:36 am »

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Re: Math Games
« Reply #22 on: February 03, 2017, 09:52:02 am »

A maths games thread? /Tag
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Re: Math Games
« Reply #23 on: February 03, 2017, 11:03:02 am »

/In
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Re: Math Games
« Reply #24 on: February 03, 2017, 11:27:52 am »

Am I right that points will carry to the next game (throughout the entire Math Games), but gold is a thing for this game only?
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Re: Math Games
« Reply #25 on: February 03, 2017, 11:35:45 am »

Since Scott said some preliminary discussion is ok, I'm just going to tell everyone what I'm doing, because I won't change it based on number of people. I'm bidding the max on +6 gold in round 1. So if you want to bet on it, the only outcome is that you will lose or tie, which will make achieving your goal of maximizing your points harder.
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Re: Math Games
« Reply #26 on: February 03, 2017, 11:39:04 am »

Since Scott said some preliminary discussion is ok, I'm just going to tell everyone what I'm doing, because I won't change it based on number of people. I'm bidding the max on +6 gold in round 1. So if you want to bet on it, the only outcome is that you will lose or tie, which will make achieving your goal of maximizing your points harder.

...so that you can just use one gold to get the +6 gold because everybody will be off of it?
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Re: Math Games
« Reply #27 on: February 03, 2017, 11:43:25 am »

Since Scott said some preliminary discussion is ok, I'm just going to tell everyone what I'm doing, because I won't change it based on number of people. I'm bidding the max on +6 gold in round 1. So if you want to bet on it, the only outcome is that you will lose or tie, which will make achieving your goal of maximizing your points harder.

...so that you can just use one gold to get the +6 gold because everybody will be off of it?

Nope. Already sent the PM. I'm bidding the max right there.
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Re: Math Games
« Reply #28 on: February 03, 2017, 11:44:47 am »

I will put everything on the 15 points. Keep in mind that I'm actually going to follow through since I want to set a precedent for further games.
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Re: Math Games
« Reply #29 on: February 03, 2017, 11:47:02 am »

Just saw one can actually submit, have done so right now.
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Re: Math Games
« Reply #30 on: February 03, 2017, 12:04:06 pm »

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Re: Math Games
« Reply #31 on: February 03, 2017, 12:05:53 pm »

I will put everything on the 15 points. Keep in mind that I'm actually going to follow through since I want to set a precedent for further games.

That's my plan as well. I was debating whether to announce it or not though. Well I'm still doing it.
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Re: Math Games
« Reply #32 on: February 03, 2017, 01:48:27 pm »

In that case we will both get nothing. I have already submitted and I have no reason to lie here. I'm trying to establish a perfect following through record, a few points aren't worth screwing that in the veelry first game.
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Re: Math Games
« Reply #33 on: February 03, 2017, 02:18:31 pm »

In that case we will both get nothing. I have already submitted and I have no reason to lie here. I'm trying to establish a perfect following through record, a few points aren't worth screwing that in the veelry first game.

The best thing about a perfect follow-through record is the instance where you finally break it and stab everyone in the back for some huge benefit.

I mean, um, I'm never going to lie either.  Yeah.
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Re: Math Games
« Reply #34 on: February 03, 2017, 02:20:24 pm »

I will bet 1 gold on 8 random options.
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Re: Math Games
« Reply #35 on: February 03, 2017, 02:33:32 pm »

In that case we will both get nothing. I have already submitted and I have no reason to lie here. I'm trying to establish a perfect following through record, a few points aren't worth screwing that in the veelry first game.

The best thing about a perfect follow-through record is the instance where you finally break it and stab everyone in the back for some huge benefit.

I mean, um, I'm never going to lie either.  Yeah.
I know, but the record is still very good evidence for me following through up until that point.
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Re: Math Games
« Reply #36 on: February 03, 2017, 02:49:33 pm »

I will bet 1 gold on 8 random options.

The problem is that with too many players that won't work.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

pacovf

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Re: Math Games
« Reply #37 on: February 03, 2017, 03:13:33 pm »

I will bet 1 gold on 8 random options.

The problem is that with too many players that won't work.

That's true of all strategies.
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Re: Math Games
« Reply #38 on: February 03, 2017, 06:22:42 pm »

Am I right that points will carry to the next game (throughout the entire Math Games), but gold is a thing for this game only?

This is correct.  (Consequently, there is no benefit to winning more gold in the final round.)

I will bet 1 gold on 8 random options.

Is this an /in?

Also, I'd like to make it clear that players can change their submission up until the deadline.  I'm going to say the game officially begins at 12:00pm (noon) forum time (that just means US eastern time right?) tomorrow (Saturday), at which point anyone else who /ins will not be able to participate in the first game.  That also means that the deadline for submitting bids for round 1 is Sunday at 12:00pm forum time.  If it is after 12pm on Saturday and I've already received bids from everyone, I'll end the round early.

I've already received several submissions.  I won't confirm submissions individually unless specifically requested or if you ask a question.  If it gets close to deadline and I still haven't received a submission from you I may prod you.
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Re: Math Games
« Reply #39 on: February 03, 2017, 06:37:43 pm »

Also, no editing posts.  I'll add it to the rules in the OP.
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Re: Math Games
« Reply #40 on: February 04, 2017, 09:03:20 am »

Will it be announced who won which thing at the end of the round? I assume so, but it's not explicitly stated.

After all bids are submitted, they will be revealed in the thread.

Is there any information beforehand on how many rounds will be played? This likely affacts optimal strategy.

This game will be played in three rounds.
My reading skills are extraordinary :) In my defense, this is not a mafia setup.
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Re: Math Games
« Reply #41 on: February 04, 2017, 09:07:29 am »

Well many good options are gone already. I'll go with everything on the 10 points then.
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Re: Math Games
« Reply #42 on: February 04, 2017, 09:07:56 am »

I will bet 1 gold on 8 random options.

The problem is that with too many players that won't work.

That's true of all strategies.
No.
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Re: Math Games
« Reply #43 on: February 04, 2017, 09:10:39 am »

Game-theory wise, cooperation is better here. Not sure what the expected outcome is here if everyone does random (and too lazy to write a program to test), but I assume it's not very high. Also not breaking people's trust is generally better in a positive sum game.
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Re: Math Games
« Reply #44 on: February 04, 2017, 09:13:47 am »

i'm gonna do 7 on 5 points and 1 on 10. somebody can beat me by doing 8 on 5
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Re: Math Games
« Reply #45 on: February 04, 2017, 10:53:53 am »

Oh yeah /in I guess.

I will bet 1 gold on 8 random options.

The problem is that with too many players that won't work.

That's true of all strategies.
No.

Explain.
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Re: Math Games
« Reply #46 on: February 04, 2017, 12:05:55 pm »

The first game officially starts now.  Players who /in will be added to the next game.  Submissions are due by 12pm forum time tomorrow.
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Re: Math Games
« Reply #47 on: February 04, 2017, 12:14:04 pm »

Crap, now I need to actually sit down and think about this.

No one told me there would be thinking!
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Re: Math Games
« Reply #48 on: February 04, 2017, 12:14:33 pm »

I put all my gold on +15 points
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Re: Math Games
« Reply #49 on: February 04, 2017, 12:15:15 pm »

we probably want to iron out a Philosophy of Points. would, for example, everyone having 101 points be better than everyone having 99?
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Re: Math Games
« Reply #50 on: February 04, 2017, 12:23:25 pm »

this is a pain game. that is an autocorrect of "phun"
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Re: Math Games
« Reply #51 on: February 04, 2017, 12:24:35 pm »

we probably want to iron out a Philosophy of Points. would, for example, everyone having 101 points be better than everyone having 99?
Yes. That is clearly intended in the setup post and that's how I'll play.
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Re: Math Games
« Reply #52 on: February 04, 2017, 12:25:10 pm »

I put all my gold on +15 points
I put all mine on +10.
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Re: Math Games
« Reply #53 on: February 04, 2017, 12:25:35 pm »

we probably want to iron out a Philosophy of Points. would, for example, everyone having 101 points be better than everyone having 99?
Scott already said this is about maximazing ones one amount of points. The relative comparison to others shouldn't matter.

A should therefore prefer a scenario with A:101,B:10^6 to A:100,B:0
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Re: Math Games
« Reply #54 on: February 04, 2017, 12:46:39 pm »

mm. i was thinking about sunshine (an autocorrect of dynamics) of people pursuing alternate win conditions and stuff


it is maybe Adrianne (an autocorrect of apparent) that i am interested in the psychological aspect of these games as much as the menstrual (an aircraft of mathematical)
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Re: Math Games
« Reply #55 on: February 04, 2017, 01:01:12 pm »

Sounds like people are mostly going for an all or nothing strategy. All the gold on one item, hope no one else copied you. I can see some merit to that.

But again, do we want to cooperate? I haven't placed my bid yet, willing to listen to suggestions. Currently leaning 8 gold on 1 point. (Not really. But it would almost guarantee getting that point)
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Re: Math Games
« Reply #56 on: February 04, 2017, 02:57:10 pm »

Also, this game (this round) is a more complex version of a number game I tried to host a couple years ago, but never got enough people to go for it:

http://forum.dominionstrategy.com/index.php?topic=6372.0
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Re: Math Games
« Reply #57 on: February 04, 2017, 03:56:51 pm »

I'm going to say this: if Gendo follows through on his threat to deny Calamitas points, I'll do Gendo a solid in the future.  Not sure in what form, and I'm open to suggestions, but at the very least any "I can screw over player A or player B" decisions from me will break in Gendo's favor.

Nothing against Calamitas, but I'm opposed to winning the game under threat of "well I'm going all in, so either I win or we both lose" and it going to a particular person because they got there first.

And the way to defeat that kind of strategy is cooperation.

This isn't a 0 sum game, but there is a winner.  I don't think we're going to be able to make it a perfect tie, nor do I think that's ever going to be in the interests of a majority of people.  But I'm going to try to reward people screwing up the strategies that create runaway winners.

And yeah, the social aspect of this is really interesting too.  We aren't going to act perfectly randomly or all obey whatever the equilibrium strategy is in any given game, and that's fascinating.
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Re: Math Games
« Reply #58 on: February 04, 2017, 03:58:26 pm »

I'm also probably not going to claim what I'm doing specifically this round.
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Re: Math Games
« Reply #59 on: February 04, 2017, 04:00:37 pm »

I'm absolutely not intending to do this evem close to every time, I am not stupid and I know that this wouldn't work.
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Re: Math Games
« Reply #60 on: February 04, 2017, 04:24:48 pm »

I'm absolutely not intending to do this evem close to every time, I am not stupid and I know that this wouldn't work.

It's not personal, and I don't think you're stupid.

But I don't want you to have a runaway lead, Gendo doesn't either, or he wouldn't be threatening to call your probably-not-bluff.

But the only way that is prevented is someone (Gendo in this case) takes a personal hit for the public good. (Good of everyone not named Calamitas or Gendo.)  He's probably a bit inclined to do that anyway, and I don't expect such a vague promise to sway him much, but I think there is value in promising it now and following through on it.  Other than a sense of fairness, the only motivation to take a personal hit for the public good is the idea that your deed will be rewarded by others later.  So I'm going to play to reward altruism, at least partly.

I'm thinking I can do this without being purely altruistic myself, but I'm sure I'll take a hit for it myself at some point.
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Re: Math Games
« Reply #61 on: February 04, 2017, 04:30:36 pm »

This is not about relative ranking but absolute ranking only so the runway lead part is absolutely invalid. The altruism  part doesn't really fit either. In this specific setup the maximum sum for everyone is reached when no tie occurs. So real cooperation isn't possible (at least in regard to the first round) and trying to make ties happening is not altruistic.
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Re: Math Games
« Reply #62 on: February 04, 2017, 04:34:12 pm »

I don't mean to not play to my win condition, let me think about this.

(Also, I'm a bit sick but realized I needed to start thinking about this game.)

I stand by my thoughts about rewarding altruism, but I wonder if this isn't a good example of it.

There may be benefit to me making such a promise to someone anyway.
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Re: Math Games
« Reply #63 on: February 04, 2017, 04:40:09 pm »

Rewarding altruistim is absolutely fine in scenarios like prisoners dilemmas or so and I'm totally going to cooperate there. But this doesn't apply here.
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Re: Math Games
« Reply #64 on: February 04, 2017, 04:45:48 pm »

Okay, well having thought about it, I stand by the idea that I will try to reward anyone who does something I regard as altruistic.  I do think that's valid.

I guess Gendo isn't doing so in this case, need to think more on it.

But this brings up something, not to derail the game but:

What is the value of having "more money" if it's not about having more money specifically than the other people?  Money/points aren't really something with value, but by being near the top they give you power and influence and the ability to more easily gain things that make you happy.  If a rich person could eliminate poverty and give everyone infinite money, it wouldn't actually be in their self-interest to do so.  So what is the value of a point?  And is optimal play really to play so that I have as many points as I can scrounge by being late to commit to something regardless of how many more points others will have?  I think some amount of spite might improve my odds of more points.

And it makes me feel like there's something awkward and unnatural about the wincon.  But maybe this is more a discussion for RSP (although I never go there.)
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Re: Math Games
« Reply #65 on: February 04, 2017, 04:50:33 pm »

Calamitas has a point. Someone is going to get the 15 points, or noone is. if noone gets 15 because of a tie, then who wins really?
If Calamitas settles for a lower score next time, then all is good. I mean, he's still going to go out of this with more points than the average player if he takes 15 points now and nothing at all later on; why I don't see an argument for why Calamitas is a worse candidate for the 15 than anyone else. In fact I think he's well suited because the chance that he'll cross us and try to make even more points is pretty low.

PPE: 1
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Re: Math Games
« Reply #66 on: February 04, 2017, 04:54:03 pm »

I've received submissions from all but two players.  If I have submissions from everyone early, I'll end the round early.
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Re: Math Games
« Reply #67 on: February 04, 2017, 04:55:24 pm »

What is the value of having "more money" if it's not about having more money specifically than the other people?  Money/points aren't really something with value, but by being near the top they give you power and influence and the ability to more easily gain things that make you happy.  If a rich person could eliminate poverty and give everyone infinite money, it wouldn't actually be in their self-interest to do so.  So what is the value of a point?  And is optimal play really to play so that I have as many points as I can scrounge by being late to commit to something regardless of how many more points others will have?  I think some amount of spite might improve my odds of more points.

And it makes me feel like there's something awkward and unnatural about the wincon.  But maybe this is more a discussion for RSP (although I never go there.)

It's true that money is more of a relative measure, but equating the "points" we get here with money is arbitrary. You could just as well equate it with some finished product, like a book, and then it makes more sense. I don't need more books than everybody else. But I do want lots of good books. I don't really care how many books someone else has. If they get 100 books and I get 1 book, then there is no reason not to do that.
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Re: Math Games
« Reply #68 on: February 04, 2017, 05:10:42 pm »

Calamitas has a point. Someone is going to get the 15 points, or noone is. if noone gets 15 because of a tie, then who wins really?
If Calamitas settles for a lower score next time, then all is good. I mean, he's still going to go out of this with more points than the average player if he takes 15 points now and nothing at all later on; why I don't see an argument for why Calamitas is a worse candidate for the 15 than anyone else. In fact I think he's well suited because the chance that he'll cross us and try to make even more points is pretty low.

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Yep, I pledge to settle for something way lower (like +1p) or even nothing if I get the 15 today.
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Re: Math Games
« Reply #69 on: February 04, 2017, 05:11:12 pm »

Calamitas has a point. Someone is going to get the 15 points, or noone is. if noone gets 15 because of a tie, then who wins really?
If Calamitas settles for a lower score next time, then all is good. I mean, he's still going to go out of this with more points than the average player if he takes 15 points now and nothing at all later on; why I don't see an argument for why Calamitas is a worse candidate for the 15 than anyone else. In fact I think he's well suited because the chance that he'll cross us and try to make even more points is pretty low.

PPE: 1
Yep, I pledge to settle for something way lower (like +1p) or even nothing if I get the 15 today.
Meaning next round
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Re: Math Games
« Reply #70 on: February 04, 2017, 05:19:31 pm »

Yeah, I at no point had any specific problem with Calamitas.

And you're right Faust, I'd rather him get it than some other personality types, (admittedly based on not much of him yet but still.)
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Re: Math Games
« Reply #71 on: February 04, 2017, 05:20:49 pm »

The thing is, though, that there is a limited supply of books and we all want all the books if possible.

I'm wondering if caring about relative success doesn't arise from this somehow anyway.  But I have a head cold and this is probably not important to by bids today at all.
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Re: Math Games
« Reply #72 on: February 04, 2017, 05:27:46 pm »

The thing is, though, that there is a limited supply of books and we all want all the books if possible.

I'm wondering if caring about relative success doesn't arise from this somehow anyway.  But I have a head cold and this is probably not important to by bids today at all.
You want as many books as possible, not the highest share of books. Like, would you rather have 100 books and have everyone else have 200 books each or would you like to have 30 books and burn the rest so no one else has any?
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Re: Math Games
« Reply #73 on: February 04, 2017, 05:30:24 pm »

Yes, I'm aware of what the wincon is, but that's not really what I'm getting at.

I may not be with it enough to explain properly right now though, or I may be totally off base.  But I'm no longer confused on the concept of what we are aiming for.
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Re: Math Games
« Reply #74 on: February 04, 2017, 05:40:47 pm »

Yes, I'm aware of what the wincon is, but that's not really what I'm getting at.

I may not be with it enough to explain properly right now though, or I may be totally off base.  But I'm no longer confused on the concept of what we are aiming for.
I get where you are coming from. Somehow it is hard to not see a game as some sort of competition for the first rank. The reasons for this should possibly be discussed in RSP.
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Re: Math Games
« Reply #75 on: February 04, 2017, 06:15:51 pm »

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Re: Math Games
« Reply #76 on: February 04, 2017, 06:24:04 pm »

/in.
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Re: Math Games
« Reply #77 on: February 04, 2017, 07:01:23 pm »

/in

I wonder if this game would be slightly more interesting if prizes with tied high bids go to the next highest bid rather than just being eliminated all together.
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Re: Math Games
« Reply #78 on: February 04, 2017, 07:21:33 pm »

Player List:
1. schadd (100)
2. Calamitas (100)
3. UmbrageOfSnow (100)
4. faust (100)
5. 2.71828... (100)
6. Jimmmmm (100)
7. gkrieg13 (100)
8. sudgy (100)
9. Dylan32 (100)
10. LaLight (100)
11. GendoIkari (100)
12. pacovf (100)

   +15 points Calamitas, Gendo
   +10 points faust
   +5 points   schadd
   +3 points
   +2 points
   +1 point     e
   +1 point
   +6 gold       Dylan
   +3 gold
   +2 points, +2 gold

Since Scott said some preliminary discussion is ok, I'm just going to tell everyone what I'm doing, because I won't change it based on number of people. I'm bidding the max on +6 gold in round 1. So if you want to bet on it, the only outcome is that you will lose or tie, which will make achieving your goal of maximizing your points harder.
I will put everything on the 15 points. Keep in mind that I'm actually going to follow through since I want to set a precedent for further games.
I will put everything on the 15 points. Keep in mind that I'm actually going to follow through since I want to set a precedent for further games.
That's my plan as well. I was debating whether to announce it or not though. Well I'm still doing it.
Well many good options are gone already. I'll go with everything on the 10 points then.
i'm gonna do 7 on 5 points and 1 on 10. somebody can beat me by doing 8 on 5
Sounds like people are mostly going for an all or nothing strategy. All the gold on one item, hope no one else copied you. I can see some merit to that.

But again, do we want to cooperate? I haven't placed my bid yet, willing to listen to suggestions. Currently leaning 8 gold on 1 point. (Not really. But it would almost guarantee getting that point)
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Re: Math Games
« Reply #79 on: February 04, 2017, 07:24:51 pm »

12 people, 10 options. At least two people won't get anything. If everybody puts 8 gold into an option, then the only way to get anything is to hope nobody else chose your option. Or to discuss and cooperate, which doesn't seem likely when most people aren't talking about what they want to do.
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Re: Math Games
« Reply #80 on: February 04, 2017, 07:31:30 pm »

I think that's why some of us don't want to talk though.

Is it better for a committee to decide that you get 0 points or only 1 point, or is it better to take your chances?

Actually, I have a proposal for those of us who haven't claimed, although I haven't thought this through all that well.

 Jimmmmm, gkrieg13, sudgy, LaLight, pacovf:

What if we take our chances after all, but pledge some kind of a ceiling, or to not use as many points.

Like let's say we all agree to only spend 4 points among the remaining (worse) options.  Then those of us who stick by it have more money to work with tomorrow, someone can betray for profit at a cost to their chances tomorrow, but we all still have better odds of winning these low-value targets without spending as much?

Thoughts?
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Re: Math Games
« Reply #81 on: February 04, 2017, 07:32:33 pm »

Scott: Would it be possible not to end the day early if everyone submits an order?

If not, could I please retract my bid?
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Re: Math Games
« Reply #82 on: February 04, 2017, 07:34:41 pm »

Scott: Have you PMed the people who haven't submitted?  I submitted, but I have no idea if you got it or not.
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Re: Math Games
« Reply #83 on: February 04, 2017, 07:35:26 pm »

AFAIK the gold you don't spent doesn't get carried over.
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Re: Math Games
« Reply #84 on: February 04, 2017, 07:38:22 pm »

AFAIK the gold you don't spent doesn't get carried over.

Oh yeah.  That's in capslock even.  I guess I just fail at all thinking today.
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Re: Math Games
« Reply #85 on: February 04, 2017, 07:42:20 pm »

Well before anyone else jumps on it, I'm just going to put all my money on the best remaining option which is +3 gold.

Since I guess first come first serve is winning this today.

And this is less interesting than the game I kind of thought it was in my head I guess.

I'm still willing to talk and change my bid though.
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Re: Math Games
« Reply #86 on: February 04, 2017, 07:49:27 pm »

So the group could collectively shut 2 people out from ever getting any points if they don't cooperate.  But on the other hand, there aren't enough points for everyone to end up even, even if the players who win 15 get 0 both other times, and some people will end up with way less, so that's a good reason not to cooperate, potentially.

Getting money allows you leverage to defy the group or prevent yourself from being denied.
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Re: Math Games
« Reply #87 on: February 04, 2017, 07:50:06 pm »

I will put all my money on 2 gold, 2 points.
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Re: Math Games
« Reply #88 on: February 04, 2017, 07:51:10 pm »

To be honest I haven't taken into account what everyone else says they're doing.
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Re: Math Games
« Reply #89 on: February 04, 2017, 07:52:06 pm »

I think that's why some of us don't want to talk though.

Is it better for a committee to decide that you get 0 points or only 1 point, or is it better to take your chances?

Actually, I have a proposal for those of us who haven't claimed, although I haven't thought this through all that well.

 Jimmmmm, gkrieg13, sudgy, LaLight, pacovf:

What if we take our chances after all, but pledge some kind of a ceiling, or to not use as many points.

Like let's say we all agree to only spend 4 points among the remaining (worse) options.  Then those of us who stick by it have more money to work with tomorrow, someone can betray for profit at a cost to their chances tomorrow, but we all still have better odds of winning these low-value targets without spending as much?

Thoughts?

I didn't spend more than 2 on options. I don't want to claim yet, I want to see the outcome.
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Re: Math Games
« Reply #90 on: February 04, 2017, 07:55:23 pm »

I think it might have been more interesting with money carrying over.

As it stands, I can only see the options as trying to scrabble for scraps, trying to use the ability to deny points as leverage to force concessions on later days, or trying to match bids on the high values in an attempt to burn down the system to prevent people claiming what they are doing on Day 2/3.

Not sure how much validity that last idea has, but it's a thought.

This is frustrating, but it might be more interesting than I was just thinking because of the scarcity of points.

The short deadline makes it weird though.
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Re: Math Games
« Reply #91 on: February 04, 2017, 07:55:32 pm »

Scott: Would it be possible not to end the day early if everyone submits an order?

If not, could I please retract my bid?


Sure, I can wait until deadline to end the round (assuming no one objects).  I just thought ending early if possible would be a little easier for people.

Scott: Have you PMed the people who haven't submitted?  I submitted, but I have no idea if you got it or not.

I did receive your PM.
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Re: Math Games
« Reply #92 on: February 04, 2017, 07:57:15 pm »

   +15 points Calamitas, Gendo
   +10 points faust
   +5 points   schadd
   +3 points
   +2 points
   +1 point     e
   +1 point
   +6 gold       Dylan
   +3 gold       UoS
   +2 points, +2 gold pacovf

Lalight: 2 on a few options
gkrieg, Jimmmmm, sudgy: ?
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Re: Math Games
« Reply #93 on: February 04, 2017, 07:58:27 pm »

   +15 points Calamitas, Gendo
   +10 points faust
   +5 points   schadd
   +3 points
   +2 points
   +1 point     e
   +1 point
   +6 gold       Dylan
   +3 gold       UoS
   +2 points, +2 gold pacovf

Lalight: 2 on a few options
gkrieg, Jimmmmm, sudgy: ?

quoted so that yellow is visible.
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Re: Math Games
« Reply #94 on: February 04, 2017, 08:00:51 pm »

Also, what are people's thoughts on Tables and Axxle joining after the game started?  I said players who /inned too late would be added to the next game, but if there is unanimous agreement that they can join, then I'll add them to this game (they've both already submitted PM's).

Also, would people prefer longer deadlines in general?
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Re: Math Games
« Reply #95 on: February 04, 2017, 08:05:22 pm »

   +15 points Calamitas, Gendo
   +10 points faust
   +5 points   schadd
   +3 points
   +2 points
   +1 point     e
   +1 point
   +6 gold       Dylan
   +3 gold       UoS
   +2 points, +2 gold pacovf

Lalight: 2 on a few options
gkrieg, Jimmmmm, sudgy: ?

I don't really want to say what I'm doing, because I think it is pretty good, but will become significantly less good if people know it.

I like the short deadlines, if they join, I think I'll have to change my bids a little bit, so I guess I would rather not have them join til next game, but if everyone else wants them to join this game, I don't want to be the person standing in the way of that.
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Re: Math Games
« Reply #96 on: February 04, 2017, 08:07:30 pm »

I like longer deadlines, at least for this, and I'm cool with Tables and Axxle joining.

What do people think of the fact that 2 (or 4) players can deny people their prizes?  It's not leverage that can really be enforced, because it may not carry forward well in the last game, it's just not punishing someone now hoping for a concession later.

I think there's a lot more to talk about than I was realizing this morning.

And also this is turning out to be kind of an interesting simulation of human relations.

Like I think I'm realizing that the best plan is really to figure out where Faust lives, get a big stick, and fight him for his points rather than trying to cooperate or take my chances.
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Re: Math Games
« Reply #97 on: February 04, 2017, 08:13:28 pm »

Okay, based on input from other players (some by PM) Tables and Axxle will not be joining this game (sorry).  I'll put you in for subsequent games though.
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Re: Math Games
« Reply #98 on: February 04, 2017, 08:19:33 pm »

I don't really want to say what I'm doing, because I think it is pretty good, but will become significantly less good if people know it.
i bet you're just stealing my 5 points
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Re: Math Games
« Reply #99 on: February 04, 2017, 08:20:31 pm »

   +15 points Calamitas, Gendo
   +10 points faust
   +5 points   schadd
   +3 points
   +2 points
   +1 point     e
   +1 point
   +6 gold       Dylan
   +3 gold       UoS
   +2 points, +2 gold pacovf

Lalight: 2 on a few options
gkrieg, Jimmmmm, sudgy: ?

I don't really want to say what I'm doing, because I think it is pretty good, but will become significantly less good if people know it.

I like the short deadlines, if they join, I think I'll have to change my bids a little bit, so I guess I would rather not have them join til next game, but if everyone else wants them to join this game, I don't want to be the person standing in the way of that.

Don't need to say anything, I am just compiling what people have said.
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Re: Math Games
« Reply #100 on: February 04, 2017, 08:21:24 pm »

I want to suggest something for a future game:  Exactly this game, but the unspent money carries over to the next day.
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Re: Math Games
« Reply #101 on: February 04, 2017, 08:21:38 pm »

What do people think of the fact that 2 (or 4) players can deny people their prizes?  It's not leverage that can really be enforced, because it may not carry forward well in the last game, it's just not punishing someone now hoping for a concession later.

I welcome anyone to try to blackmail other players. I don't really think it's going to work, but it would be interesting.
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Re: Math Games
« Reply #102 on: February 04, 2017, 08:22:51 pm »

What do people think of the fact that 2 (or 4) players can deny people their prizes?  It's not leverage that can really be enforced, because it may not carry forward well in the last game, it's just not punishing someone now hoping for a concession later.

I welcome anyone to try to blackmail other players. I don't really think it's going to work, but it would be interesting.

That's the thing, I don't think it can work, and the group could collectively decide to just shut the person out.  I'm trying to figure out if the game is boring or secretly exciting.
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Re: Math Games
« Reply #103 on: February 04, 2017, 08:43:34 pm »

Yep, don't think cooperation is possible, which is probably the point.
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Re: Math Games
« Reply #104 on: February 04, 2017, 08:49:47 pm »

Yep, don't think cooperation is possible, which is probably the point.

But a few people will be shut out, so what do they have to gain by cooperating with their own being shut out?

Either the group makes promises, which the group isn't doing, they pick someone at random to punish, they try to blackmail someone, or they try to bring down the system that is establishing itself somehow.
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Re: Math Games
« Reply #105 on: February 04, 2017, 08:52:28 pm »

I want to suggest something for a future game:  Exactly this game, but the unspent money carries over to the next day.
save up 24 to bid on +1 point on day 3
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Re: Math Games
« Reply #106 on: February 04, 2017, 08:52:44 pm »

and somebody else does the same thing
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Re: Math Games
« Reply #107 on: February 04, 2017, 08:58:52 pm »

Yep, don't think cooperation is possible, which is probably the point.

But a few people will be shut out, so what do they have to gain by cooperating with their own being shut out?

Either the group makes promises, which the group isn't doing, they pick someone at random to punish, they try to blackmail someone, or they try to bring down the system that is establishing itself somehow.

Only Gendo and Calamitas have claimed that they want to bid all their money on the same thing. Everybody else has either claimed without conflict, or is chosing not to claim, which we have to assume means they don't think they will be in conflict, since there is zero point in making a conflicting bid as anything else than retribution or blackmail (which doesn't work if you don't talk about it first).

So yeah, the only people I would expect to see arguing are Calamitas and Gendo, right now. Or else people aren't checking the thread, but then what can we do.
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Re: Math Games
« Reply #108 on: February 04, 2017, 10:00:29 pm »

I want to suggest something for a future game:  Exactly this game, but the unspent money carries over to the next day.

I'll put it on my list (which isn't a guarantee that I'll run it but there's a decent chance).
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Re: Math Games
« Reply #109 on: February 05, 2017, 01:06:55 am »

Another option would be to allow people to give gold to other people.
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Re: Math Games
« Reply #110 on: February 05, 2017, 02:04:36 am »

This would be a really interesting game to do where it is identical except talking about bids ahead of time is banned. I realize at that point that actually playing it would possibly be less fun, but I think it would be really interesting to see what people do and then analyze it and everyone's thought processes afterwards.
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Re: Math Games
« Reply #111 on: February 05, 2017, 02:06:16 am »

And I think the idea someone said earlier about the prize going to the 2nd highest bid in the event of a tie would be really interesting.
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Re: Math Games
« Reply #112 on: February 05, 2017, 03:15:51 am »

Maybe there should be a "Math Games Discussion Thread".
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Re: Math Games
« Reply #113 on: February 05, 2017, 05:54:37 am »

What do people think of the fact that 2 (or 4) players can deny people their prizes?  It's not leverage that can really be enforced, because it may not carry forward well in the last game, it's just not punishing someone now hoping for a concession later.

I welcome anyone to try to blackmail other players. I don't really think it's going to work, but it would be interesting.

That's the thing, I don't think it can work, and the group could collectively decide to just shut the person out.  I'm trying to figure out if the game is boring or secretly exciting.
Mostly on the boring side. However, it gives us a good introduction into how the people here are approaching these kind of games.
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Re: Math Games
« Reply #114 on: February 05, 2017, 06:59:28 am »

I will bet 1 gold on 8 random options.

The problem is that with too many players that won't work.

That's true of all strategies.
No.

Explain.
Putting everything on one spot and annoncing this is way more stable with more players. Like, with two players, it's probably better to distribute; with more players, it's better to accumulate.
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Re: Math Games
« Reply #115 on: February 05, 2017, 10:35:11 am »

I will put all my money on 2 gold, 2 points.

I wouldn't do that of I were you. I already did
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Re: Math Games
« Reply #116 on: February 05, 2017, 11:33:21 am »

/in for next game
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Re: Math Games
« Reply #117 on: February 05, 2017, 12:00:30 pm »

Round 1 Results

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Re: Math Games
« Reply #118 on: February 05, 2017, 12:02:10 pm »

Why dud you do that gendo?
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Re: Math Games
« Reply #119 on: February 05, 2017, 12:02:24 pm »

Round 2 Gold
1. schadd (8)
2. Calamitas (8)
3. UmbrageOfSnow (11)
4. faust (8)
5. 2.71828... (8)
6. Jimmmmm (8)
7. gkrieg13 (8)
8. sudgy (8)
9. Dylan32 (14)
10. LaLight (8)
11. GendoIkari (8)
12. pacovf (8)
« Last Edit: February 05, 2017, 12:04:05 pm by scott_pilgrim »
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scott_pilgrim

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Re: Math Games
« Reply #120 on: February 05, 2017, 12:02:53 pm »

Round 2 Gold
1. schadd (8)
2. Calamitas (8)
3. UmbrageOfSnow (11)
4. faust (8)
5. 2.71828... (8)
6. Jimmmmm (8)
7. gkrieg13 (8)
8. sudgy (8)
9. Dylan32 (14)
10. LaLight (8)
11. GendoIkari (8)
12. pacovf (8)


People have cool smiley amount of gold, those are not supposed to be 8's.
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schadd

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Re: Math Games
« Reply #121 on: February 05, 2017, 12:04:28 pm »

thanks guys!
i think i want to do the same thing again
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Calamitas

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Re: Math Games
« Reply #122 on: February 05, 2017, 12:04:59 pm »

I put everything on +3gold for this round.
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Re: Math Games
« Reply #123 on: February 05, 2017, 12:08:41 pm »

I won't be around at this time tomorrow so deadline will be 6pm tomorrow forum time (I probably won't be able to post results until around 7pm).
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Re: Math Games
« Reply #124 on: February 05, 2017, 12:17:12 pm »

I only just realized this forum has a dice roll function. We could have just randomized every single prize to ensure maximum utility.
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Re: Math Games
« Reply #125 on: February 05, 2017, 12:28:17 pm »

i mean, we can always randomize things and then not do them
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Re: Math Games
« Reply #126 on: February 05, 2017, 12:35:07 pm »

i mean, we can always randomize things and then not do them
Obviously we would have punished those not following through because randomization would be by far the most altruistic option.
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Re: Math Games
« Reply #127 on: February 05, 2017, 12:39:29 pm »

optimally altruistic ⇒ ¬fun ∴ ¬most altruistic
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Re: Math Games
« Reply #128 on: February 05, 2017, 12:41:35 pm »

although i suppose it is thus proven that a perfectly altruistic condition is impossible
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Re: Math Games
« Reply #129 on: February 05, 2017, 12:53:56 pm »

I will put all my money on 2 gold, 2 points.

I wouldn't do that of I were you. I already did

Man. You should have claimed. Now we both have nothing. For the record, you dont get to retroactively claim, that's way too easy to abuse.
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Re: Math Games
« Reply #130 on: February 05, 2017, 12:55:23 pm »

jimmmmm was a huge winner if i didn't do exactly the thing that i said i was gonna do
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Re: Math Games
« Reply #131 on: February 05, 2017, 01:03:28 pm »

I'm going to take the 15 points this time around, unless Dylan wants to stop me, in which case I'll take the 10 points.  But Dylan, we should talk about this.

Dylan, you only need 9 gold to secure the 10 points, then you have 5 to throw around trying to win some of the smaller options.  That's my argument for the higher money player taking the lower of the two options.
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Re: Math Games
« Reply #132 on: February 05, 2017, 01:07:08 pm »

I'm going to take the 15 points this time around, unless Dylan wants to stop me, in which case I'll take the 10 points.  But Dylan, we should talk about this.

Dylan, you only need 9 gold to secure the 10 points, then you have 5 to throw around trying to win some of the smaller options.  That's my argument for the higher money player taking the lower of the two options.
He wouldn't gain 5 points that way, don't try to trick him.
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Re: Math Games
« Reply #133 on: February 05, 2017, 01:10:39 pm »

I'm going to take the 15 points this time around, unless Dylan wants to stop me, in which case I'll take the 10 points.  But Dylan, we should talk about this.

Dylan, you only need 9 gold to secure the 10 points, then you have 5 to throw around trying to win some of the smaller options.  That's my argument for the higher money player taking the lower of the two options.
He wouldn't gain 5 points that way, don't try to trick him.

I'm not trying to trick him.  But he has a greater chance of gaining more than 10 points than I do.  And I think that's sufficient between the two of us.

Especially because I can try to block him tomorrow if he doesn't cooperate.

I think it makes sense for the two of us with more money to cooperate for the maximum potential points between the two of us on this turn.  Of course I would say that, as the person with the 2nd most money, but I'm not entirely without leverage.
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Re: Math Games
« Reply #134 on: February 05, 2017, 01:11:40 pm »

We're playing for the most points, not the most points in this round.
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Re: Math Games
« Reply #135 on: February 05, 2017, 01:12:58 pm »

We're playing for the most points, not the most points in this round.
He wouldn't gain one of the gols options as well.
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Re: Math Games
« Reply #136 on: February 05, 2017, 01:13:53 pm »

I intend to put all my money on 3 gold
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Re: Math Games
« Reply #137 on: February 05, 2017, 01:14:24 pm »

I intend to put all my money on 3 gold
Already did that.
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Re: Math Games
« Reply #138 on: February 05, 2017, 01:16:31 pm »

We're playing for the most points, not the most points in this round.
He wouldn't gain one of the gols options as well.

That's not at all what I'm saying.

I'm saying he and I both want to have more points, which isn't as simple as just winning the +15 this round, which Dylan can unilaterally choose to do if he wants.  But our combined average is better for the game if the player with the higher amount of money spreads it around.

And I'm offering both a carrot and a stick in regards to my actions next turn.  I will help or hurt depending on cooperation with my plan.

I really do think it's in his best interests to take 10, if only because it's in my best interests to be spiteful.

How does this effect you, Calamitas?
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Re: Math Games
« Reply #139 on: February 05, 2017, 01:20:00 pm »

It doesn't effect me, I'm just a little bored :D

But if you want to do what's best for the game we obviously should intend to maximize the average of everyone and bot just you twos. And the best way to do that is to ensure

a) there are no ties
b) everyone option is covered




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Re: Math Games
« Reply #140 on: February 05, 2017, 01:22:40 pm »

It doesn't effect me, I'm just a little bored :D

But if you want to do what's best for the game we obviously should intend to maximize the average of everyone and not just you two's. And the best way to do that is to ensure

a) there are no ties
b) everyone option is covered
My spelling today is horrible
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Re: Math Games
« Reply #141 on: February 05, 2017, 01:30:00 pm »

It doesn't effect me, I'm just a little bored :D

But if you want to do what's best for the game we obviously should intend to maximize the average of everyone and bot just you twos. And the best way to do that is to ensure

a) there are no ties
b) everyone option is covered

But the group as a whole doesn't care about maximizing the average of everyone, as evidenced by the first come first serve way Round 1 went down.  So I'm better off trying to maximize the value of a small group, in this case the group with 2 people in it who have more leverage than the others.  I'd have also been including the $2 person in this if it didn't tie.
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Re: Math Games
« Reply #142 on: February 05, 2017, 01:31:33 pm »

It doesn't effect me, I'm just a little bored :D

But if you want to do what's best for the game we obviously should intend to maximize the average of everyone and bot just you twos. And the best way to do that is to ensure

a) there are no ties
b) everyone option is covered

But the group as a whole doesn't care about maximizing the average of everyone, as evidenced by the first come first serve way Round 1 went down.  So I'm better off trying to maximize the value of a small group, in this case the group with 2 people in it who have more leverage than the others.  I'd have also been including the $2 person in this if it didn't tie.
First come first serve is the best way to hand out the prizes if one doesn't know about the randomization process.
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Town (5/9): M85, RMM35, M87, NM9, M90RMM38, M92, M91, M102,
Scum (3/3): M84, M88, M100

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Re: Math Games
« Reply #143 on: February 05, 2017, 01:36:18 pm »

Dylan, this is what I'm proposing

You can choose to win whatever category you like today.  But if you're going against me it will take $12, if you're going against everyone else it will take $9.  If you take the 10 points, you know you can win that with $9 and I have no incentive to try to mess with you, because I'm getting more points another way.  So you can put the rest to trying to win a lower category.  You don't really have much chance of getting 5 points, but I think you can get more than 0 points that way.  I cannot.  If you go for the 15 points, I have incentive to try to mess with you, so you really need to commit enough money there to block me.  Which means you probably can't win a lower bid.  15 is still more than 12 or whatever, but not my as much as it's worth to me to try.

So here's the deal:
A) You cooperate with my plan, which works out better for the 2 of us as a 2-person group.  I owe you one, and in the next couple of games, I try to find some little thing or things I can do to help you out, like I was talking about earlier.

B) You announce in thread that you are taking 15 points and I can go to hell.  You probably win the 15 points, unless you try to get cute and underbid.  Next turn, I do my best to block you out of any points, but after I've done one thing that hurts you, I consider us even and move on.

C) You claim you're going to go to do one thing and do the other to cost me more points.  In devote at least the next 3 rounds to trying to mess with you.

This accomplishes my other goal no matter what, which is to establish a precedent of following through on promises.  No matter what you do, I'm making a promise, and I'll follow through on that, which has value in itself in the long run.

Anyway, let's be friends, not enemies.
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Re: Math Games
« Reply #144 on: February 05, 2017, 01:45:27 pm »

I intend to put all my money on 3 gold
Already did that.

Sorry, didn't see it. Ok, I put all my gold on +5 points.

Dylan, this is what I'm proposing

You can choose to win whatever category you like today.  But if you're going against me it will take $12, if you're going against everyone else it will take $9.  If you take the 10 points, you know you can win that with $9 and I have no incentive to try to mess with you, because I'm getting more points another way.  So you can put the rest to trying to win a lower category.  You don't really have much chance of getting 5 points, but I think you can get more than 0 points that way.  I cannot.  If you go for the 15 points, I have incentive to try to mess with you, so you really need to commit enough money there to block me.  Which means you probably can't win a lower bid.  15 is still more than 12 or whatever, but not my as much as it's worth to me to try.

So here's the deal:
A) You cooperate with my plan, which works out better for the 2 of us as a 2-person group.  I owe you one, and in the next couple of games, I try to find some little thing or things I can do to help you out, like I was talking about earlier.

B) You announce in thread that you are taking 15 points and I can go to hell.  You probably win the 15 points, unless you try to get cute and underbid.  Next turn, I do my best to block you out of any points, but after I've done one thing that hurts you, I consider us even and move on.

C) You claim you're going to go to do one thing and do the other to cost me more points.  In devote at least the next 3 rounds to trying to mess with you.

This accomplishes my other goal no matter what, which is to establish a precedent of following through on promises.  No matter what you do, I'm making a promise, and I'll follow through on that, which has value in itself in the long run.

Anyway, let's be friends, not enemies.

There's only one round left after this one, and he has no incentive to claim his bid next round. Blackmail is hard.
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Re: Math Games
« Reply #145 on: February 05, 2017, 01:46:59 pm »

Yeah, but there are games after this one.  And he may have some incentive to claim, because everyone else has an incentive to claim.
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Re: Math Games
« Reply #146 on: February 05, 2017, 01:51:24 pm »

I will bet 1 gold on 8 random options.

The problem is that with too many players that won't work.

That's true of all strategies.
No.

Explain.
Putting everything on one spot and annoncing this is way more stable with more players. Like, with two players, it's probably better to distribute; with more players, it's better to accumulate.

With enough players, there is no incentive for players to respect the first-come-first-served system.
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Re: Math Games
« Reply #147 on: February 05, 2017, 01:57:20 pm »

We're playing for the most points, not the most points in this round.
He wouldn't gain one of the gols options as well.

That's not at all what I'm saying.

I'm saying he and I both want to have more points, which isn't as simple as just winning the +15 this round, which Dylan can unilaterally choose to do if he wants.  But our combined average is better for the game if the player with the higher amount of money spreads it around.

And I'm offering both a carrot and a stick in regards to my actions next turn.  I will help or hurt depending on cooperation with my plan.

I really do think it's in his best interests to take 10, if only because it's in my best interests to be spiteful.

How does this effect you, Calamitas?

This is fascinating.  Each person's goal is to maximize their own points without regard to the status of other people's points, yes?  So in a vacuum, my best play this round would be to bid 12 gold on the 15 pts and place my remaining 2 somewhere else on a lower point in hopes of a empty prize like last round.  If I go through with this, you could then win 10 pts and also have 2 gold remaining to try to get a lower prize also, since no one claimed the 2 gold prize to be able to force you all in.

"Carrot": Since people have seen that the people who claimed their bid followed through, it is at least somewhat more likely that people will place more bids on the lower prizes this round since I assume no one will bid under you and I for the two top prizes and fewer will bid under other all-in claims. Therefore, my hypothetical 5 gold extra probably wouldn't actually be enough to get me any additional prizes due to the increased density of bids on the lower prizes.

"Stick": If I do not disclose my bid for the final round, how would you know what to do to stop me from getting points? Since winning gold will be useless in the third round, everyone will be bidding on the point prizes.  Since runners-up do not get the prize if there is a tie, there will probably be very few points actually awarded in the 3rd round anyway due to a large number of ties.  So the chances either of us are actually able to win additional points in the 3rd round are minimal in any case, regardless of whether or not you try to spite me.

The only realistic circumstances in which people will actually gain points in the third round would be the case in which we cooperate fully.  That situation would rely on people being altruistic, however.  Since at least a couple people would have to be shut out, the group would likely expect those of us who have received the most points already to be altruistic and allow other people to get the prizes.  If that is the case, you would have no opportunity to spite me since I won't be getting a prize anyway.

PPE 4. Will read after hitting post.
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Re: Math Games
« Reply #148 on: February 05, 2017, 02:00:27 pm »

Dylan, this is what I'm proposing

You can choose to win whatever category you like today.  But if you're going against me it will take $12, if you're going against everyone else it will take $9.  If you take the 10 points, you know you can win that with $9 and I have no incentive to try to mess with you, because I'm getting more points another way.  So you can put the rest to trying to win a lower category.  You don't really have much chance of getting 5 points, but I think you can get more than 0 points that way.  I cannot.  If you go for the 15 points, I have incentive to try to mess with you, so you really need to commit enough money there to block me.  Which means you probably can't win a lower bid.  15 is still more than 12 or whatever, but not my as much as it's worth to me to try.

So here's the deal:
A) You cooperate with my plan, which works out better for the 2 of us as a 2-person group.  I owe you one, and in the next couple of games, I try to find some little thing or things I can do to help you out, like I was talking about earlier.

B) You announce in thread that you are taking 15 points and I can go to hell.  You probably win the 15 points, unless you try to get cute and underbid.  Next turn, I do my best to block you out of any points, but after I've done one thing that hurts you, I consider us even and move on.

C) You claim you're going to go to do one thing and do the other to cost me more points.  In devote at least the next 3 rounds to trying to mess with you.

This accomplishes my other goal no matter what, which is to establish a precedent of following through on promises.  No matter what you do, I'm making a promise, and I'll follow through on that, which has value in itself in the long run.

Anyway, let's be friends, not enemies.

I have no interest in option C, and am still deciding between A and B. What do you think about my reasoning in my previous post?
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Re: Math Games
« Reply #149 on: February 05, 2017, 02:00:52 pm »

That is really interesting, Dylan.

I honestly don't think we'll collectively have our act together enough to try to cooperate like that in the last round.

So yeah, I'm somewhat banking on the 2nd game I guess.
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Re: Math Games
« Reply #150 on: February 05, 2017, 02:02:51 pm »

My main thought is that this game should have some other thread for talking about philosophy and economics and whatnot as related to this game.

Anyway, I think you're mostly right, so regardless of which direction I choose to go, maybe it's more interesting for me to try to help or hurt you in Round 1 of Game 2.
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Re: Math Games
« Reply #151 on: February 05, 2017, 02:12:49 pm »

Yeah. Interesting that a "Math Games" thread for playing small games on a forum for discussing a card game can spawn such deep philosophical conversations.
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Re: Math Games
« Reply #152 on: February 05, 2017, 02:52:27 pm »

Dylan, do you really think the 5 extra points isn't enough to win any extra?  Because  like you said, spreading around might happen more, but most people have 8 to spend total, and will need to commit most of that to one spot?

I honestly think you can win more than one category, and I'd take the risk were I in your position.  I think the person who wins the larger amount of gold should do so next round.

But if the odds are approaching 0, there isn't any benefit to you collaborating with me here.  Other than in the sense that I want to have made an agreement with someone about some thing, and so from my point of view there's a benefit there at least.  But that's not the end of the world if it doesn't matter at all.
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Re: Math Games
« Reply #153 on: February 05, 2017, 03:06:20 pm »

My thought on it being spread around more was that more people would be going all in on more spots, thereby making smaller bids useless.
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Re: Math Games
« Reply #154 on: February 05, 2017, 03:11:37 pm »

I will put all my money on 2 gold, 2 points.

I wouldn't do that of I were you. I already did

Man. You should have claimed. Now we both have nothing. For the record, you dont get to retroactively claim, that's way too easy to abuse.

Yeah, retroactive claiming is bad, and something I should not have done.  Placing me on the board as having put all my money on +1 point is something that you should not have done, because even in the post quoted I explicitly said that I had not done that.
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Re: Math Games
« Reply #155 on: February 05, 2017, 03:12:33 pm »

I do like the +2gold/+2points though.  I plan on placing my money there.
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Re: Math Games
« Reply #156 on: February 05, 2017, 03:31:32 pm »

I will put all my money on 2 gold, 2 points.

I wouldn't do that of I were you. I already did

Man. You should have claimed. Now we both have nothing. For the record, you dont get to retroactively claim, that's way too easy to abuse.

Yeah, retroactive claiming is bad, and something I should not have done.  Placing me on the board as having put all my money on +1 point is something that you should not have done, because even in the post quoted I explicitly said that I had not done that.

True, though putting you there or on the "?" wouldn't have changed my bid.
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Re: Math Games
« Reply #157 on: February 05, 2017, 04:47:06 pm »

UoS, how about this. Having attained the most resources previously, I can take the highest prize one way or another. I will give you a lot of credit for the way you have played this round so far though! I still haven't decided what I am going to do, because your future actions could either cost me more than 5 points, or losing the 5 points now could be worse.  From your perspective, it is possible that following through on your threat later could also cost you some points because having to keep your promise to spite me could make you have to do something that isn't optimal for you.

So I propose this. You concede the 15 points this round and retract your threat, and at some point over the next game or two, at your call, I will do something that actively helps you.  I know it is possible the next game might not present a good chance for this, which is why I'm extending it to 2 games and making it your decision when it happens to maximize the benefit you can get from this. 

This deal is my best option because:
  • I get the extra 5 points now.
  • I don't have to worry about you working to hinder me later.
  • Following through on my promise would build more good will with you and give my word more backing for later deals with everyone.

It is your best option because:
  • You for sure get the 10 points now.
  • You don't have to worry about sacrificing points to follow through on a threat.
  • You and I will have completed a deal built on mutual help and trust rather than threats.
  • You get to choose when to call my end of the deal, rather than it happening at the first chance with a tiny benefit.
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Re: Math Games
« Reply #158 on: February 05, 2017, 07:12:12 pm »

It's a deal, Dylan.

I mean, that's essentially what I was proposing but reversed.  And I swear I won't contest you on +15, so you can commit just 9 there, although you probably won't believe that, but when I follow through it can go to building trust.

But yeah, I'll cave, I'll take the +10, you owe me one later.  Deal.
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Re: Math Games
« Reply #159 on: February 06, 2017, 09:30:46 am »

I will bet 1 gold on 8 random options.

The problem is that with too many players that won't work.

That's true of all strategies.
No.

Explain.
Putting everything on one spot and annoncing this is way more stable with more players. Like, with two players, it's probably better to distribute; with more players, it's better to accumulate.

With enough players, there is no incentive for players to respect the first-come-first-served system.
Not once everything is taken, yes. But then they can only block. I guess with number of players > 2* number of options, things really become random, or you'd have to make deals for the next round, which is hard with the extra gold options.
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Re: Math Games
« Reply #160 on: February 06, 2017, 09:34:10 am »

Current claims:

schadd: 7 gold on +5, 1 gold on +10
Calamitas: 8 gold on +3 gold
pacovf: 8 gold on +5
e: 8 gold on +2,+2 gold
UoS/Dylan: somehow contest the +15/+10.

I guess that means I'll put my stuff on +6 gold.
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Re: Math Games
« Reply #161 on: February 06, 2017, 09:35:34 am »

Current claims:

schadd: 7 gold on +5, 1 gold on +10
Calamitas: 8 gold on +3 gold
pacovf: 8 gold on +5
e: 8 gold on +2,+2 gold
UoS/Dylan: somehow contest the +15/+10.

I guess that means I'll put my stuff on +6 gold.
Let's switch faust, you got something already :-D
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Re: Math Games
« Reply #162 on: February 06, 2017, 09:36:41 am »

pacovf: 8 gold on +5
oh, i just noticed that.


hey. that's not nice.  :(
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Re: Math Games
« Reply #163 on: February 06, 2017, 09:38:13 am »

Current claims:

schadd: 7 gold on +5, 1 gold on +10
Calamitas: 8 gold on +3 gold
pacovf: 8 gold on +5
e: 8 gold on +2,+2 gold
UoS/Dylan: somehow contest the +15/+10.

I guess that means I'll put my stuff on +6 gold.

I'm already there with 8
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Re: Math Games
« Reply #164 on: February 06, 2017, 09:44:57 am »

Current claims:

schadd: 7 gold on +5, 1 gold on +10
Calamitas: 8 gold on +3 gold
pacovf: 8 gold on +5
e: 8 gold on +2,+2 gold
UoS/Dylan: somehow contest the +15/+10.

I guess that means I'll put my stuff on +6 gold.

I'm already there with 8
There has been no claim from you, so I suppose you'll have to switch.
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Re: Math Games
« Reply #165 on: February 06, 2017, 09:46:02 am »

Current claims:

schadd: 7 gold on +5, 1 gold on +10
Calamitas: 8 gold on +3 gold
pacovf: 8 gold on +5
e: 8 gold on +2,+2 gold
UoS/Dylan: somehow contest the +15/+10.

I guess that means I'll put my stuff on +6 gold.
Let's switch faust, you got something already :-D
Would be fine with that... of course, then you will have to argue with gkrieg it seems.
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Re: Math Games
« Reply #166 on: February 06, 2017, 09:55:27 am »

pacovf: 8 gold on +5
oh, i just noticed that.


hey. that's not nice.  :(

Wait, when did you claim? I missed it.
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Re: Math Games
« Reply #167 on: February 06, 2017, 09:56:48 am »

pacovf: 8 gold on +5
oh, i just noticed that.


hey. that's not nice.  :(

Wait, when did you claim? I missed it.
he said he would put 7 again on it
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Re: Math Games
« Reply #168 on: February 06, 2017, 09:57:03 am »

pacovf: 8 gold on +5
oh, i just noticed that.


hey. that's not nice.  :(

Wait, when did you claim? I missed it.

Mmmmm you got something already? Bid on +3 points? Please? :'(
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Re: Math Games
« Reply #169 on: February 06, 2017, 10:07:44 am »

Current claims:

schadd: 7 gold on +5, 1 gold on +10
Calamitas: 8 gold on +3 gold
pacovf: 8 gold on +5
e: 8 gold on +2,+2 gold
UoS/Dylan: somehow contest the +15/+10.

I guess that means I'll put my stuff on +6 gold.

I'm already there with 8
There has been no claim from you, so I suppose you'll have to switch.

Not switching
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Re: Math Games
« Reply #170 on: February 06, 2017, 10:12:18 am »

Your loss then.
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Re: Math Games
« Reply #171 on: February 06, 2017, 10:15:31 am »

To clarify, the people who announce their bids do this with a cost, because they are actually accountable for their actions and cannot switch for higher profit without a cost (in credibility). People like gkrieg who try to keep quiet until someone takes what they want from them are certainly more problematic.
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Re: Math Games
« Reply #172 on: February 06, 2017, 10:15:50 am »

well, erm, posting.

hard to catch up after you guys, haven't had much time for this thread and don't think I will catch up now. I will put 2 on +3, 2 on +2, 2 on +1, 2 on +1. Is it okay? :) I understand I won't win now, But I wont to be in some top tier I suppose.

Already submitted btw.
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Re: Math Games
« Reply #173 on: February 06, 2017, 10:16:32 am »

Your loss then.
Sorry Faust, will not switch with you then. The offer was very nice but I really don't want to have a triple nothing here.

@Umbrage: Why don't you go for the +6gold? That way you make 15 tomorrow which is better than 10 today and tomorrow probably 0.
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Re: Math Games
« Reply #174 on: February 06, 2017, 10:50:52 am »

Your loss then.
Sorry Faust, will not switch with you then. The offer was very nice but I really don't want to have a triple nothing here.

@Umbrage: Why don't you go for the +6gold? That way you make 15 tomorrow which is better than 10 today and tomorrow probably 0.

That's actually a good point, thanks Calamitas.

So why don't you guys fight over the +10 points instead, I'm going to muscle in on the +6 gold.
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Re: Math Games
« Reply #175 on: February 06, 2017, 10:54:00 am »

Hey, Calamitas, if you want to take the 10 I'll happily switch to +3 gold.
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Re: Math Games
« Reply #176 on: February 06, 2017, 10:55:04 am »

It was our advice that freed up that slot after all ;)
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Re: Math Games
« Reply #177 on: February 06, 2017, 10:58:04 am »

It was our advice that freed up that slot after all ;)

Thank you.  I like to think I'd have noticed that yesterday if I were feeling better.  But I didn't, and I wouldn't have thought about it any more today had no one said anything.

That's kind of why I wanted the longer deadlines actually.  I think this makes it clear that both money options and the 15 points on Day 1 were probably super important.
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Re: Math Games
« Reply #178 on: February 06, 2017, 11:02:25 am »

Your loss then.
Sorry Faust, will not switch with you then. The offer was very nice but I really don't want to have a triple nothing here.

@Umbrage: Why don't you go for the +6gold? That way you make 15 tomorrow which is better than 10 today and tomorrow probably 0.

That's actually a good point, thanks Calamitas.

So why don't you guys fight over the +10 points instead, I'm going to muscle in on the +6 gold.
Your welcome.
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Re: Math Games
« Reply #179 on: February 06, 2017, 11:03:02 am »

It was our advice that freed up that slot after all ;)

Thank you.  I like to think I'd have noticed that yesterday if I were feeling better.  But I didn't, and I wouldn't have thought about it any more today had no one said anything.

That's kind of why I wanted the longer deadlines actually.  I think this makes it clear that both money options and the 15 points on Day 1 were probably super important.
You're welcome
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Re: Math Games
« Reply #180 on: February 06, 2017, 11:03:21 am »

It was your advice that freed up that slot after all ;)

heh... FTFM. Sounds a bit braggy otherwise :D And I didn't do anything.
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Re: Math Games
« Reply #181 on: February 06, 2017, 11:15:49 am »

Sure, I will put everything on +10 points
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Re: Math Games
« Reply #182 on: February 06, 2017, 11:22:26 am »

Just for the record, I want to note that at the time I gave uos the advice it was quite likely that I would clinch the +15p myself.
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Re: Math Games
« Reply #183 on: February 06, 2017, 11:33:16 am »

I will put everything on +3 gold.
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Re: Math Games
« Reply #184 on: February 06, 2017, 11:41:30 am »

pacovf: 8 gold on +5
oh, i just noticed that.


hey. that's not nice.  :(

Wait, when did you claim? I missed it.

Mmmmm you got something already? Bid on +3 points? Please? :'(
nah, i mean, you can take the 5 points, it just seems a little impolite
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Re: Math Games
« Reply #185 on: February 06, 2017, 12:50:10 pm »

I'm going to say this: if Gendo follows through on his threat to deny Calamitas points, I'll do Gendo a solid in the future.  Not sure in what form, and I'm open to suggestions, but at the very least any "I can screw over player A or player B" decisions from me will break in Gendo's favor.

Nothing against Calamitas, but I'm opposed to winning the game under threat of "well I'm going all in, so either I win or we both lose" and it going to a particular person because they got there first.

And the way to defeat that kind of strategy is cooperation.

This isn't a 0 sum game, but there is a winner.  I don't think we're going to be able to make it a perfect tie, nor do I think that's ever going to be in the interests of a majority of people.  But I'm going to try to reward people screwing up the strategies that create runaway winners.

And yeah, the social aspect of this is really interesting too.  We aren't going to act perfectly randomly or all obey whatever the equilibrium strategy is in any given game, and that's fascinating.

Woo, I've earned a favor!

I have no idea how to play this game. It feels awkward when one person says "I'm going to put everything on +15" and then my choices are simply either we both get nothing, or that person gets more than I do. I see the nice advantage of getting gold early though. Though it seems literally impossible for me to get any gold this round; as the only 3 gold spots supposedly already have 8 gold bid on them.

Oh well. I don't see an actual claim for +3 points, so I'm putting 8 gold on +3 points.

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Re: Math Games
« Reply #186 on: February 06, 2017, 12:54:13 pm »

well, erm, posting.

hard to catch up after you guys, haven't had much time for this thread and don't think I will catch up now. I will put 2 on +3, 2 on +2, 2 on +1, 2 on +1. Is it okay? :) I understand I won't win now, But I wont to be in some top tier I suppose.

Already submitted btw.
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Re: Math Games
« Reply #187 on: February 06, 2017, 12:54:37 pm »

It feels awkward when one person says "I'm going to put everything on +15" and then my choices are simply either we both get nothing, or that person gets more than I do.

Yeah, this was my problem yesterday.  The fact is that I'm now convinced it doesn't play to the win condition, but it bugs me, and that's kind of where I was going with my wondering if carrying about relative rankings somehow naturally arises from the limited resources.
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Re: Math Games
« Reply #188 on: February 06, 2017, 01:23:24 pm »

pacovf: 8 gold on +5
oh, i just noticed that.


hey. that's not nice.  :(

Wait, when did you claim? I missed it.

Mmmmm you got something already? Bid on +3 points? Please? :'(
nah, i mean, you can take the 5 points, it just seems a little impolite

I honestly did not see your claim, otherwise I would have gone for something else that wasn't taken yet.
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Re: Math Games
« Reply #189 on: February 06, 2017, 01:27:30 pm »

dangcrud
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Re: Math Games
« Reply #190 on: February 06, 2017, 07:26:09 pm »

Round 2 Results

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scott_pilgrim

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Re: Math Games
« Reply #191 on: February 06, 2017, 07:29:19 pm »

Round 3 Gold:

1. faust (11)
2. schadd (8)
3. Jimmmmm (8)
4. Calamitas (8)
5. UmbrageOfSnow (14)
6. 2.71828... (10)
7. gkrieg13 (8)
8. sudgy (8)
9. Dylan32 (8)
10. LaLight (8)
11. GendoIkari (8)
12. pacovf (8)
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Calamitas

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Re: Math Games
« Reply #192 on: February 06, 2017, 07:32:07 pm »

Outsch dylan.
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Town (5/9): M85, RMM35, M87, NM9, M90RMM38, M92, M91, M102,
Scum (3/3): M84, M88, M100

MVPs (1): M84

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Re: Math Games
« Reply #193 on: February 06, 2017, 07:32:29 pm »

I put all 8 of mine on +3 points
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Calamitas

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Re: Math Games
« Reply #194 on: February 06, 2017, 07:32:37 pm »

I'll put everything on +1p
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Scum (3/3): M84, M88, M100

MVPs (1): M84

UmbrageOfSnow

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Re: Math Games
« Reply #195 on: February 06, 2017, 07:35:47 pm »

All in on +15 obviously.  Since I don't actually have any points yet.

But maybe money can buy happiness/points.
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Re: Math Games
« Reply #196 on: February 06, 2017, 07:39:14 pm »

Deadline for the final round will be 7:30pm tomorrow.  Soon after I post results for the final round, the thread will be locked in preparation for the next game.  PLEASE DO NOT POST IN THREAD OR COMMUNICATE WITH OTHER PLAYERS ABOUT THE GAME WHILE THE THREAD IS LOCKED.  If you have questions or concerns about anything, you can PM me.  (You are free to continue posting until I lock the thread tomorrow, I just wanted to give an advance warning.)
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Re: Math Games
« Reply #197 on: February 06, 2017, 07:41:12 pm »

Deadline for the final round will be 7:30pm tomorrow.  Soon after I post results for the final round, the thread will be locked in preparation for the next game.  PLEASE DO NOT POST IN THREAD OR COMMUNICATE WITH OTHER PLAYERS ABOUT THE GAME WHILE THE THREAD IS LOCKED.  If you have questions or concerns about anything, you can PM me.  (You are free to continue posting until I lock the thread tomorrow, I just wanted to give an advance warning.)

Do you plan on posting "THREAD LOCKED" or something to that effect?
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Re: Math Games
« Reply #198 on: February 06, 2017, 07:42:32 pm »

Deadline for the final round will be 7:30pm tomorrow.  Soon after I post results for the final round, the thread will be locked in preparation for the next game.  PLEASE DO NOT POST IN THREAD OR COMMUNICATE WITH OTHER PLAYERS ABOUT THE GAME WHILE THE THREAD IS LOCKED.  If you have questions or concerns about anything, you can PM me.  (You are free to continue posting until I lock the thread tomorrow, I just wanted to give an advance warning.)

Do you plan on posting "THREAD LOCKED" or something to that effect?

Yes
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Re: Math Games
« Reply #199 on: February 06, 2017, 07:43:01 pm »

Is the next game going to be a no-communication game, or do you just want us to shut up between games?
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Re: Math Games
« Reply #200 on: February 06, 2017, 07:44:37 pm »

Is the next game going to be a no-communication game, or do you just want us to shut up between games?

At least the first round will be no-communication, I haven't decided about subsequent rounds yet.
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schadd

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Re: Math Games
« Reply #201 on: February 06, 2017, 08:05:29 pm »

i lied a little bit


7 gold on 5 points, 1 on 10 points
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Re: Math Games
« Reply #202 on: February 06, 2017, 08:12:46 pm »

Well, my plan failed.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

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Re: Math Games
« Reply #203 on: February 06, 2017, 08:18:08 pm »

I put everything on 2 points.
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Re: Math Games
« Reply #204 on: February 06, 2017, 08:47:58 pm »

I put everything on 2 points.

I did the same. One of us should change.
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Re: Math Games
« Reply #205 on: February 06, 2017, 10:10:29 pm »

Well, my plan failed.
It was pointless.
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Re: Math Games
« Reply #206 on: February 06, 2017, 10:55:55 pm »

I put everything on 2 points.

I did the same. One of us should change.

You didn't claim it. If you are going to contest a bid after the fact, wouldn't it be better to argue for something better than 2 points?
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Re: Math Games
« Reply #207 on: February 07, 2017, 12:48:56 am »

Umbrage gets 15, faust gets 10, I get 5? Sounds about right
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Re: Math Games
« Reply #208 on: February 07, 2017, 12:57:35 am »

may I have 3?
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Re: Math Games
« Reply #209 on: February 07, 2017, 01:02:27 am »

Well, my plan failed.
It was pointless.

It would have worked the first round.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

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Re: Math Games
« Reply #210 on: February 07, 2017, 01:04:26 am »

I put everything on 2 points.

I did the same. One of us should change.

You didn't claim it. If you are going to contest a bid after the fact, wouldn't it be better to argue for something better than 2 points?

I'm not contesting anything. Just letting you know what I did. Any suggestions?
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Re: Math Games
« Reply #211 on: February 07, 2017, 01:24:57 am »

I mean, you're not giving me much here. You are choosing to ignore the first-come-first-served rule, banking on the fact that it's the last round. Were you schadd, I would let you have it due to the mix up from last round, but you are not. I would expect you to be the one to offer suggestions, since you are the one defying the status quo. If you do not offer any, then the question you need to ask yourself is whose BID you want to make void. If your answer is, "pacovf's", then so be it, but that's a decision you are making knowingly and willingly.
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Re: Math Games
« Reply #212 on: February 07, 2017, 01:28:35 am »

Unrelated, but if we were to change the rules of the game, rather than changing the way Gold works, I would just make it so there are more options to bid on than players. The strategy is too degenerate otherwise.

PS: autocorrect capitalizes "BID" for some reason.
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Calamitas

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Re: Math Games
« Reply #213 on: February 07, 2017, 01:55:37 am »

I will not submit any bids this round and I would propose distrubting all <+5p on the players with the fewest points in reverse order. There is no way we would manage to come by without ties otherwise and this is best for the game ad a whole.
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Oh, i just don't like mafia games.

Town (5/9): M85, RMM35, M87, NM9, M90RMM38, M92, M91, M102,
Scum (3/3): M84, M88, M100

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Re: Math Games
« Reply #214 on: February 07, 2017, 01:59:24 am »

I mean, you're not giving me much here. You are choosing to ignore the first-come-first-served rule, banking on the fact that it's the last round. Were you schadd, I would let you have it due to the mix up from last round, but you are not. I would expect you to be the one to offer suggestions, since you are the one defying the status quo. If you do not offer any, then the question you need to ask yourself is whose BID you want to make void. If your answer is, "pacovf's", then so be it, but that's a decision you are making knowingly and willingly.

I'm not ascribing to any status quo. The status quo for me is to split between a few different options. That wasn't working very well so I tried putting it all on a lower one that might have some chance of being left alone.
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Axxle

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Re: Math Games
« Reply #215 on: February 07, 2017, 02:22:00 am »

Well, my plan failed.
It was pointless.

It would have worked the first round.
I meant it literally got you no points  ;)
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Re: Math Games
« Reply #216 on: February 07, 2017, 02:43:06 am »

Outsch dylan.

I mean, yeah. I could have bid low on 15 and taken the +10 also, which would have been optimal from a points perspective, but I am totally content with 115 and not having to deal with the fallout from that.
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Forum Mafia Record - Wins: 14 - NM9, M97, RMM41, M99, M102, M104, M119, M126, RMM56, M133, M134, RMM58, RMM59, RMM61, RMM60; Losses 15 - RMM37, M89, M94, M95, M96, M100, RMM47 M109, M110, M120, M127, M129, M131, M132, M136; MVPs: 1 - NM9

pacovf

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Re: Math Games
« Reply #217 on: February 07, 2017, 03:04:42 am »

I mean, you're not giving me much here. You are choosing to ignore the first-come-first-served rule, banking on the fact that it's the last round. Were you schadd, I would let you have it due to the mix up from last round, but you are not. I would expect you to be the one to offer suggestions, since you are the one defying the status quo. If you do not offer any, then the question you need to ask yourself is whose BID you want to make void. If your answer is, "pacovf's", then so be it, but that's a decision you are making knowingly and willingly.

I'm not ascribing to any status quo. The status quo for me is to split between a few different options. That wasn't working very well so I tried putting it all on a lower one that might have some chance of being left alone.

Just because you refused to follow the developing meta does not mean that meta does not exist! It just means you are consciously ignoring it, which can only hurt you. Indeed, had you claimed your bid early, you would have gotten those two points without any discussion at all.

You're not getting the points with this line of reasoning. Up to you whether you want to move your bid elsewhere.

I will not submit any bids this round and I would propose distrubting all <+5p on the players with the fewest points in reverse order. There is no way we would manage to come by without ties otherwise and this is best for the game ad a whole.

Eh, I guess. Who wants to compile the points list?
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faust

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Re: Math Games
« Reply #218 on: February 07, 2017, 03:21:35 am »

Well my strategy should be obvious.
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Calamitas

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Re: Math Games
« Reply #219 on: February 07, 2017, 03:46:19 am »

Outsch dylan.

I mean, yeah. I could have bid low on 15 and taken the +10 also, which would have been optimal from a points perspective, but I am totally content with 115 and not having to deal with the fallout from that.
Nah, all fine. Thought you didn't bid at all.
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Oh, i just don't like mafia games.

Town (5/9): M85, RMM35, M87, NM9, M90RMM38, M92, M91, M102,
Scum (3/3): M84, M88, M100

MVPs (1): M84

Calamitas

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Re: Math Games
« Reply #220 on: February 07, 2017, 03:53:50 am »

I can do it:

1. +15p: UoS
2. +10p: Faust
3. +5p: e
4. +3p: sudgy
5. +2p: Lalight
6. +2p,+2g: gkrieg
7. +1p: Jimmm
8. +1p: Gendo (even though I still wonder whether we should punish him for his insanely unaltrustic bid in R1)
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Oh, i just don't like mafia games.

Town (5/9): M85, RMM35, M87, NM9, M90RMM38, M92, M91, M102,
Scum (3/3): M84, M88, M100

MVPs (1): M84

Calamitas

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Re: Math Games
« Reply #221 on: February 07, 2017, 04:08:48 am »

I urge everyone else to refuse to bid for anything, it won't bring any good and just harm us as whole.
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Oh, i just don't like mafia games.

Town (5/9): M85, RMM35, M87, NM9, M90RMM38, M92, M91, M102,
Scum (3/3): M84, M88, M100

MVPs (1): M84

schadd

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Re: Math Games
« Reply #222 on: February 07, 2017, 07:49:15 am »

Well my strategy should be obvious.
it should very much not be
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Re: Math Games
« Reply #223 on: February 07, 2017, 09:51:24 am »

I urge everyone else to refuse to bid for anything, it won't bring any good and just harm us as whole.
Putting gold on the top 3 spots doesn't hurt and prevents people from trying cute tricks.
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Calamitas

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Re: Math Games
« Reply #224 on: February 07, 2017, 09:55:57 am »

I urge everyone else to refuse to bid for anything, it won't bring any good and just harm us as whole.
Putting gold on the top 3 spots doesn't hurt and prevents people from trying cute tricks.
Good catch. Everyone else should put all their gold on the top spots to ensure no one of the guys with the extra money is trying sth
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Oh, i just don't like mafia games.

Town (5/9): M85, RMM35, M87, NM9, M90RMM38, M92, M91, M102,
Scum (3/3): M84, M88, M100

MVPs (1): M84

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Re: Math Games
« Reply #225 on: February 07, 2017, 12:57:18 pm »

In regard to the next game, I will approach this from a utilitarian perspective with the intend to maximize average benefits. If cooperation is not possible like in the first round here I'm intending to maximize my own benfefit, though I'm willing to cooperate there as well (balance out gains, alternate winning,...). So if this is some kind of prisoners dilemma count on me doing something like tit-for-tat (I want to remark that I would cooperate in the last round as well).
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Oh, i just don't like mafia games.

Town (5/9): M85, RMM35, M87, NM9, M90RMM38, M92, M91, M102,
Scum (3/3): M84, M88, M100

MVPs (1): M84

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Re: Math Games
« Reply #226 on: February 07, 2017, 01:00:26 pm »

I can do it:

1. +15p: UoS
2. +10p: Faust
3. +5p: e
4. +3p: sudgy
5. +2p: Lalight
6. +2p,+2g: gkrieg
7. +1p: Jimmm
8. +1p: Gendo (even though I still wonder whether we should punish him for his insanely unaltrustic bid in R1)

Well I want people to agree on this before I do it.  I'm currently on +3 points, because I don't know what sudgy,LaLigh,Jimmmmmm, and Gendo are doing.
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Re: Math Games
« Reply #227 on: February 07, 2017, 01:02:46 pm »

Come on, why no one is seeing my posts again?
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Losses: 11, 5, 1
Draws: 1
MVPs: 4
Mod/Co-mod: 18

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Re: Math Games
« Reply #228 on: February 07, 2017, 01:03:47 pm »

may I have 3?

Ah, it's because I'm stupid. Already submitted +3
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Re: Math Games
« Reply #229 on: February 07, 2017, 01:14:21 pm »

may I have 3?

Ah, it's because I'm stupid. Already submitted +3

Um, ok.  I claimed +3 right after the last round ended and already submitted.  I'm fine working with the thing Calamitas proposed though.
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Re: Math Games
« Reply #230 on: February 07, 2017, 01:16:35 pm »

You have probably a bad shot at achieving anything when not following along. Like seriously, there are going to be insanely many ties this round otherwise. I cannot tell whether everyone will see it in time, but it's the best chance I think.
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Oh, i just don't like mafia games.

Town (5/9): M85, RMM35, M87, NM9, M90RMM38, M92, M91, M102,
Scum (3/3): M84, M88, M100

MVPs (1): M84

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Re: Math Games
« Reply #231 on: February 07, 2017, 01:54:30 pm »

K, i will take +2 if this is allowed.
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Re: Math Games
« Reply #232 on: February 07, 2017, 01:57:35 pm »

K, i will take +2 if this is allowed.
Yep
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Oh, i just don't like mafia games.

Town (5/9): M85, RMM35, M87, NM9, M90RMM38, M92, M91, M102,
Scum (3/3): M84, M88, M100

MVPs (1): M84

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Re: Math Games
« Reply #233 on: February 07, 2017, 02:58:16 pm »

I can do it:

1. +15p: UoS
2. +10p: Faust
3. +5p: e
4. +3p: sudgy
5. +2p: Lalight
6. +2p,+2g: gkrieg
7. +1p: Jimmm
8. +1p: Gendo (even though I still wonder whether we should punish him for his insanely unaltrustic bid in R1)

I'm fine with this; and thanks for putting the data together.

As for my first bid, I hadn't been thinking of it as a co-op game (I guess it is in some ways, and not in others)... I had decided to make that bid before your post saying you were going to; so technically I'm not sure what makes my bid the unaltruistic one and not yours; I didn't want the meta of this game to be a race to see who posts the fastest. In that particular situation, I felt that my best chance at actually increasing my score the most lied in the hope that you bid something different than what you said. Not that I actually had any reason to think that you weren't telling the truth; I just had to hope that you weren't.
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Re: Math Games
« Reply #234 on: February 07, 2017, 03:47:03 pm »

First, you didn't make clear that you were actually voting for it. Secondly, I was actually first and I considered that the best way to deal with that situation at that point. In hindsight, randomization would have been way way way better. But either way, I'm seeing where you're coming from and it doesn't make sense to keep grudges for anything that early. Let's just not repeat this kind of thing and resolve similar matters with randomization in the future.
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Re: Math Games
« Reply #235 on: February 07, 2017, 04:16:51 pm »

First, you didn't make clear that you were actually voting for it. Secondly, I was actually first and I considered that the best way to deal with that situation at that point. In hindsight, randomization would have been way way way better. But either way, I'm seeing where you're coming from and it doesn't make sense to keep grudges for anything that early. Let's just not repeat this kind of thing and resolve similar matters with randomization in the future.

+1.
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Re: Math Games
« Reply #236 on: February 07, 2017, 07:31:57 pm »

Round 3 Results:

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Re: Math Games
« Reply #237 on: February 07, 2017, 07:32:24 pm »

You all have a little time to keep talking before I lock the thread.
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Re: Math Games
« Reply #238 on: February 07, 2017, 07:33:45 pm »

That went bad.
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Re: Math Games
« Reply #239 on: February 07, 2017, 07:35:15 pm »

I can only repeat myself, I will try to maximize average utility in the next round and play tit-for-tat like in prisoner dilemma situations.
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Re: Math Games
« Reply #240 on: February 07, 2017, 07:40:41 pm »

I plan on causing as much chaos as possible
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Re: Math Games
« Reply #241 on: February 07, 2017, 07:44:09 pm »

ah, you got SK i see
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Re: Math Games
« Reply #242 on: February 07, 2017, 07:45:13 pm »

if i repeated my last round i would have gotten a point. but i stuck to my word
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Re: Math Games
« Reply #243 on: February 07, 2017, 07:46:51 pm »

If I hadn't changed my bid, I would have one more point right now.
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Re: Math Games
« Reply #244 on: February 07, 2017, 07:56:13 pm »

THREAD LOCKED
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Re: Math Games
« Reply #245 on: February 07, 2017, 07:56:59 pm »

THERE IS TO BE NO COMMUNICATION AFTER RULES ARE POSTED.   
The thread is locked.  Please do not send game-related PM's to other players or spectators.
If you need to ask questions about the rules, please PM the mod.  Do not copy other players on the PM.
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Re: Math Games
« Reply #246 on: February 07, 2017, 08:02:18 pm »

2. Guess f of the Average

Rules   
This game will be played in three rounds.  Please do not discuss anything game-related or post in thread until all rounds are complete.   
Each player submits a number on the closed interval [0,100] to the mod.  DO NOT COPY ANY OTHER PLAYERS IN THE PM OR CLAIM YOUR NUMBER TO ANY OTHER PLAYER.   
Whoever submitted the number closest* to f(A) where A is the average of all numbers submitted scores 9 points.  If there is a tie for the winner, each tied player scores 9 points, MINUS 1 per additional player who tied with them, to a minimum of 1 point total.   
Note: your submission does not need to be an integer, or even a rational number.  It must be a real number, and you must be able to describe it unambiguously.  If there are more than 100 decimal digits, I will cut it off after the 100th digit after the decimal point.

Functions   
Each round, the function f(x) will change:   
Round 1   f(x)=0.99x
Round 2   f(x)=10000/(x^2-100x+2600)
Round 3   f(x)=50sin(3πx/200)+50

I'll accept submissions for each round at ~24 hour intervals and post results for the round at the end of that time frame, but if your submissions are not dependent on the results from previous rounds, you may submit numbers for all three rounds at once.  If I receive all submissions for a particular round early, I will post the results early, unless at least one player requests that I don't.

*The closest number x to y is the one which minimizes the absolute value of the difference, |x-y|.

The following post will have a link and an image of the graph for the round 2 and 3 functions.
« Last Edit: February 07, 2017, 08:07:20 pm by scott_pilgrim »
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Re: Math Games
« Reply #247 on: February 07, 2017, 08:05:25 pm »

Round 2:



Round 3:



I couldn't get links to wolfram working but you can easily go to wolframalpha.com and copy/paste the functions in the previous post to see more information about them.

The sin function in round 3 is measured in radians.
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Re: Math Games
« Reply #248 on: February 07, 2017, 08:13:56 pm »

Deadline for round 1 will be at 8:00pm tomorrow (Wednesday).
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Re: Math Games
« Reply #249 on: February 08, 2017, 08:07:16 pm »

Round 1 Results:

Calamitas   0.99^2 * (1/100) * integral_0^100 0.99x dx~=48.51495...
LaLight (no submission)
gkrieg   45.9=45.9
Jimmmmm   (no submission)
pacovf   0.495=0.495
UmbrageOfSnow   square root of 2923~=54.06477596...
schadd   20.2=20.2
sudgy   50.0001=50.0001
GendoIkari   49=49
2.71828…   37=37
faust   0=0
Dylan32 (no submission)   
Tables (no submission)      
Axxle   (0.99 + 0.99^2 + 0.99^3 + 0.99^4 + 0.99^5 + 0.99^6 + 0.99^7) / 8~=0.84069132...
liopoil*   14.11097115...=14.11097115...
      
A=29.10241…
f(A)=28.81138…
   

The closest submissions was 2.71828...'s submission of 37 (with a difference of 8.188, just beating out schadd's 20.2 which was off by 8.611...).

*liopoil's submission went on for much longer, I'll give the full number in the next post.
« Last Edit: February 08, 2017, 08:08:32 pm by scott_pilgrim »
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Re: Math Games
« Reply #250 on: February 08, 2017, 08:08:03 pm »

(*liopoil's full submission: 14.11097115104321011131171051081059811410511710932102 10512010110032112111105110116)
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Re: Math Games
« Reply #251 on: February 08, 2017, 08:09:17 pm »

Round 2 submissions are due by 8pm tomorrow (Thursday).  THREAD IS STILL LOCKED.
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Re: Math Games
« Reply #252 on: February 08, 2017, 08:09:48 pm »

Also, I meant to mention that if you would like to /in while the thread is locked, you can do so by PM.
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Re: Math Games
« Reply #253 on: February 09, 2017, 08:07:57 pm »

Round 2 Results:
Calamitas   f(f((integral_0^100 f(x) dx)/100))~=3.846357253...
LaLight   76.9112=76.9112
gkrieg   49.9=49.9
Jimmmmm   (no submission)
pacovf   fixed point of f(x) closest to 37~=36.93225134...
UmbrageOfSnow   square root of 4044~=63.59245238...
schadd   23.333=23.333
sudgy   π^2*e*ϕ^2~=70.23757483...
GendoIkari   36.93225134=36.93225134
2.71828…   77=77
faust   100/3 - (110 (1 - i sqrt(3)))/(3 (-35 + 3 i sqrt(1047))^(1/3)) - 5/3 (1 + i sqrt(3)) (-35 + 3 i sqrt(1047))^(1/3)~=36.93225134...
Dylan32   4.475394282=4.475394282
Tables (no submission)
Axxle   58.435=58.435
liopoil   9.01100111...=9.01100111...
      
A=42.11836…
f(A)=61.68263...


The closest submission was UmbrageOfSnow's submission of 63.59245238... (with a difference of ~1.909818...).

There were a whole lot of opportunities for me to screw up with copy/pasting and solving stuff in this round, so I've tried to double check things, but please let me know if you catch any mistakes!  Thanks!
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Re: Math Games
« Reply #254 on: February 09, 2017, 08:10:42 pm »

A few players actually had more digits of precision than I displayed in the previous post.  For reference, the full submissions are here:

Dylan32: 4.475394282236265014947816902669125149925708454914878000751
GendoIkari: 36.932251341
liopoil: 9.011001110111010101100101011100110111001100100000001101100011000100100000011011100111100001110100

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Re: Math Games
« Reply #255 on: February 09, 2017, 08:11:36 pm »

Submissions for Round 3 are due by 8pm tomorrow night.  THREAD STILL LOCKED!
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Re: Math Games
« Reply #256 on: February 10, 2017, 08:00:32 pm »

THREAD UNLOCKED

Results will be posted shortly.
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Calamitas

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Re: Math Games
« Reply #257 on: February 10, 2017, 08:02:23 pm »

Kudos to faust for his R1 submission
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Re: Math Games
« Reply #258 on: February 10, 2017, 08:02:49 pm »

Did you guys have any big strategy for that?
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Re: Math Games
« Reply #259 on: February 10, 2017, 08:04:26 pm »

Kudos to faust for his R1 submission

I thought about it, but not knowing the mathematical literacy of other people, it just wasn't worth it.

Did you guys have any big strategy for that?

Fixed points, or f(50). My submission for day one was a typo.
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Re: Math Games
« Reply #260 on: February 10, 2017, 08:04:39 pm »

Round 3 Results:

Calamitas   f((integral_0^100 f(x) dx)/100)~=64.07697656...
LaLight (no submission)
gkrieg   61.588=61.588
pacovf   f(50)~=85.35533906...
UmbrageOfSnow   sqrt(7425)~=86.1684397...
schadd   77=77
sudgy   30=30
GendoIkari   50=50
2.71828…   55=55
faust   fixed point of f(x)~=61.6684...
Dylan32   80sqrt(2)/pi~=36.01265265...
Axxle   65=65
liopoil   55.5=55.5
      
      
      
A=60.614515…
f(A)=64.06834…


Calamitas wins with an impressively close 64.07698... (only 0.008639... away).

Rules for Game 3 will be posted soon.  The thread will remain unlocked for the beginning of Game 3.
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UmbrageOfSnow

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Re: Math Games
« Reply #261 on: February 10, 2017, 08:10:10 pm »

Axxle added less chaos than I expected.

Which is pretty chaotic of him.
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Re: Math Games
« Reply #262 on: February 10, 2017, 08:12:15 pm »

Round 3 Results:

Calamitas   f((integral_0^100 f(x) dx)/100)~=64.07697656...
LaLight (no submission)
gkrieg   61.588=61.588
pacovf   f(50)~=85.35533906...
UmbrageOfSnow   sqrt(7425)~=86.1684397...
schadd   77=77
sudgy   30=30
GendoIkari   50=50
2.71828…   55=55
faust   fixed point of f(x)~=61.6684...
Dylan32   80sqrt(2)/pi~=36.01265265...
Axxle   65=65
liopoil   55.5=55.5
      
      
      
A=60.614515…
f(A)=64.06834…


Calamitas wins with an impressively close 64.07698... (only 0.008639... away).

Rules for Game 3 will be posted soon.  The thread will remain unlocked for the beginning of Game 3.


I think Calamitas was the right idea, assuming enough players.
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Re: Math Games
« Reply #263 on: February 10, 2017, 08:15:03 pm »

3. Quarters on a Chess Board

Rules
Note: The thread will remain unlocked for the first 72 hours of the game; however, this is a zero-sum game and it is not in your interest to give the other teams hints.   
Players will be split up into pairs*.  This game will only be played once.  Players will be paired up like: highest and lowest scoring players together, then second highest and second lowest, etc.   
Each pair will have one player be assigned to role A and the other assigned to role B (chosen randomly).   
Each pair will be given roughly 72 hours to communicate with each other in a QT I will send them.  After this time period, THERE IS TO BE NO COMMUNICATION AMONG PLAYERS AT ALL REGARDING THIS GAME.  The thread and QT's will be locked at that time.   
After the 72 hour communication-period is up, the player in role A will be privately given an 8x8 grid of H's and T's, representing quarters in either the heads or tails position respectively, on a chess board.   
Additionally, four squares on the board will be marked blue (good), and one will be marked red (best).   
The player in role A must choose exactly one of the quarters on the board to "flip" (change from H to T or T to H).  Submit your selection by PM to the mod within 24 hours.  (Do not copy your partner or anyone else in the PM.)   
The state of the board (excluding the red and blue squares) after the quarter has been flipped will then be sent to player B.  (Note that they will not be told which quarter was flipped.)
Player B may then choose any one square on the board, within 24 hours of receiving the board.   
Scoring is determined as follows (per player):   
Player B guesses the red square:   12
Player B guesses a blue square:   3
Player B does not guess either a blue or red square:   Negative points so that the total points among all players is 0 and the "losing" players all get the same number of points, rounding down if necessary to avoid non-integers.

If each team guesses either a blue or red square, the negative points will be distributed among the teams who guessed blue squares.  If all teams guess the red square, no one will get any points.

*Since there is an odd number of players, there will need to be one team of 3.  I'll list the teams in the next post.
« Last Edit: February 11, 2017, 10:55:43 am by scott_pilgrim »
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Calamitas

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Re: Math Games
« Reply #264 on: February 10, 2017, 08:16:55 pm »

Oh yes, I won that thing :-D
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Re: Math Games
« Reply #265 on: February 10, 2017, 08:19:03 pm »

Game 3 Teams:

UmbrageOfSnow (A), LaLight (B)
faust (B), GendoIkari (A)
Calamitas (B), gkrieg13 (A)
2.71828... (A), pacovf (B)
Dylan32 (B), schadd (A)
sudgy (B), Axxle (A), liopoil (can participate in planning and share in points)
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Re: Math Games
« Reply #266 on: February 10, 2017, 08:29:30 pm »

QT's have been sent.  Please let me know if you did not receive one, or if the link doesn't work, or the wrong player names are in the title of the QT, etc.
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Re: Math Games
« Reply #267 on: February 10, 2017, 08:38:56 pm »

The discussion period for Game 3 will end at 7:30pm on Monday, February 13.
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Re: Math Games
« Reply #268 on: February 10, 2017, 08:49:51 pm »

I was very confused by some of the guesses in that game. Why did so many people guess near 50 in round 1? Why did everyone go for the unstable equilibrium in round 2 instead of the stable one near 4.5? Why does Calamitas' strategy make sense? Why the random square roots UoS? I just tried to guess how far off the stable equilibrium people would be guessing, and in the first two rounds I way underestimated.

Props to faust for submitting an exact fixed point all three rounds.
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Re: Math Games
« Reply #269 on: February 10, 2017, 08:55:49 pm »

I was very confused by some of the guesses in that game. Why did so many people guess near 50 in round 1? Why did everyone go for the unstable equilibrium in round 2 instead of the stable one near 4.5? Why does Calamitas' strategy make sense? Why the random square roots UoS? I just tried to guess how far off the stable equilibrium people would be guessing, and in the first two rounds I way underestimated.

Props to faust for submitting an exact fixed point all three rounds.

I picked what I wanted my guess to be to like 1 decimal place.  Then I squared that, picked a random number close to that, and submitted the square root of that, something with a bunch of decimal places.  It was just a lazy way to have a lot of decimal places to make ties less likely.  By the 3rd one I thought there was really no chance of a tie anyway but I just did it to keep the pattern.
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Re: Math Games
« Reply #270 on: February 10, 2017, 08:56:06 pm »

Axxle added less chaos than I expected.

Which is pretty chaotic of him.
;)
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Re: Math Games
« Reply #271 on: February 10, 2017, 08:59:19 pm »

Kudos to faust for his R1 submission
yeah, i thought you were gonna do that


https://www.quicktopic.com/52/H/LPSBAfmZKnBG
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Re: Math Games
« Reply #272 on: February 10, 2017, 09:03:08 pm »

I was very confused by some of the guesses in that game. Why did so many people guess near 50 in round 1? Why did everyone go for the unstable equilibrium in round 2 instead of the stable one near 4.5? Why does Calamitas' strategy make sense? Why the random square roots UoS? I just tried to guess how far off the stable equilibrium people would be guessing, and in the first two rounds I way underestimated.

Props to faust for submitting an exact fixed point all three rounds.
That's pretty similar to what I was trying, although I completely failed my submission in the first round.
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Re: Math Games
« Reply #273 on: February 11, 2017, 12:09:53 am »


Additionally, four squares on the board will be marked blue (good), and one will be marked red (best).   
The player in role A must choose exactly one of these quarters to "flip" (change from H to T or T to H).  Submit your selection by PM to the mod within 24 hours.  (Do not copy your partner or anyone else in the PM.)   


To clarify, you may flip ANY quarter on the entire board, not just a quarter on one of the colored squares.  Sorry for the ambiguity.
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Re: Math Games
« Reply #274 on: February 11, 2017, 03:28:11 am »

Why did everyone go for the unstable equilibrium in round 2 instead of the stable one near 4.5?
The unstable equilibrium was closer to the average value of the function.
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Re: Math Games
« Reply #275 on: February 11, 2017, 03:29:52 am »

Kudos to faust for his R1 submission

I thought about it, but not knowing the mathematical literacy of other people, it just wasn't worth it.
For me it was more like a signal. Also I like to assume perfect rational players.
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faust

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Re: Math Games
« Reply #276 on: February 11, 2017, 03:37:58 am »

What happens if all teams get positive points?
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Re: Math Games
« Reply #277 on: February 11, 2017, 03:44:02 am »

Will all teams receive the same board?
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Calamitas

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Re: Math Games
« Reply #278 on: February 11, 2017, 04:56:18 am »

I was very confused by some of the guesses in that game. Why did so many people guess near 50 in round 1? Why did everyone go for the unstable equilibrium in round 2 instead of the stable one near 4.5? Why does Calamitas' strategy make sense? Why the random square roots UoS? I just tried to guess how far off the stable equilibrium people would be guessing, and in the first two rounds I way underestimated.

Props to faust for submitting an exact fixed point all three rounds.

I picked what I wanted my guess to be to like 1 decimal place.  Then I squared that, picked a random number close to that, and submitted the square root of that, something with a bunch of decimal places.  It was just a lazy way to have a lot of decimal places to make ties less likely.  By the 3rd one I thought there was really no chance of a tie anyway but I just did it to keep the pattern.
But ties are good :-D
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Re: Math Games
« Reply #279 on: February 11, 2017, 05:17:06 am »

I was very confused by some of the guesses in that game. Why did so many people guess near 50 in round 1? Why did everyone go for the unstable equilibrium in round 2 instead of the stable one near 4.5? Why does Calamitas' strategy make sense? Why the random square roots UoS? I just tried to guess how far off the stable equilibrium people would be guessing, and in the first two rounds I way underestimated.

Props to faust for submitting an exact fixed point all three rounds.

I picked what I wanted my guess to be to like 1 decimal place.  Then I squared that, picked a random number close to that, and submitted the square root of that, something with a bunch of decimal places.  It was just a lazy way to have a lot of decimal places to make ties less likely.  By the 3rd one I thought there was really no chance of a tie anyway but I just did it to keep the pattern.
But ties are good :-D
"If there is a tie for the winner, each tied player scores 9 points, MINUS 1 per additional player who tied with them"

Doesn't sound so great to me
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Calamitas

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Re: Math Games
« Reply #280 on: February 11, 2017, 07:00:54 am »

I was very confused by some of the guesses in that game. Why did so many people guess near 50 in round 1? Why did everyone go for the unstable equilibrium in round 2 instead of the stable one near 4.5? Why does Calamitas' strategy make sense? Why the random square roots UoS? I just tried to guess how far off the stable equilibrium people would be guessing, and in the first two rounds I way underestimated.

Props to faust for submitting an exact fixed point all three rounds.

I picked what I wanted my guess to be to like 1 decimal place.  Then I squared that, picked a random number close to that, and submitted the square root of that, something with a bunch of decimal places.  It was just a lazy way to have a lot of decimal places to make ties less likely.  By the 3rd one I thought there was really no chance of a tie anyway but I just did it to keep the pattern.
But ties are good :-D
"If there is a tie for the winner, each tied player scores 9 points, MINUS 1 per additional player who tied with them"

Doesn't sound so great to me
2x8 > 1x9
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Re: Math Games
« Reply #281 on: February 11, 2017, 10:05:44 am »

What happens if all teams get positive points?

No one falls into the third category, so no one gets negative points.  (See my post a few posts down.)

Will all teams receive the same board?

No, each team's board will be randomized independently.
« Last Edit: February 11, 2017, 10:51:59 am by scott_pilgrim »
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Re: Math Games
« Reply #282 on: February 11, 2017, 10:23:05 am »

Okay, so this is not a zero-sum game after all.

Unfortunately, since all teams get different boards, I don't see a good way to coordinate.
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Re: Math Games
« Reply #283 on: February 11, 2017, 10:24:13 am »

Otherwise we could have all agreed to guess the same spot, making sure nobody gets negative points.
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Re: Math Games
« Reply #284 on: February 11, 2017, 10:24:52 am »

Okay, so this is not a zero-sum game after all.
I was just thinking this too. Potentially problematic
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Re: Math Games
« Reply #285 on: February 11, 2017, 10:44:30 am »

Okay, right, I forgot about that.  Don't post anything publicly yet.
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Re: Math Games
« Reply #286 on: February 11, 2017, 10:51:10 am »

If each team guesses either a red or blue square, scoring will happen normally, and then the negative points will be distributed among the teams guessing blue squares.  If all teams guess the red square, no one will score any points.  I'll update the rules post accordingly.

I apologize for changing the scoring in the middle of the game like this, but I think it needs to be done this way.  Please let me know if you have any concerns about this resolution.
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Re: Math Games
« Reply #287 on: February 11, 2017, 11:02:16 am »

Okay, so we might want to decide collectively to not submit anything at all.
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Re: Math Games
« Reply #288 on: February 11, 2017, 11:31:11 am »

Okay, so we might want to decide collectively to not submit anything at all.
That's not a stable strategy; if a single team chooses to go against this consensus, they can only win.
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Re: Math Games
« Reply #289 on: February 11, 2017, 11:45:58 am »

Okay, so we might want to decide collectively to not submit anything at all.
That's not a stable strategy; if a single team chooses to go against this consensus, they can only win.
But we might decide to punish them for that in later rounds.
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Re: Math Games
« Reply #290 on: February 11, 2017, 11:49:20 am »

Okay, so we might want to decide collectively to not submit anything at all.
That's not a stable strategy; if a single team chooses to go against this consensus, they can only win.
But we might decide to punish them for that in later rounds.

But being collective there doesn't increase the total score. It just keeps everyone's score closest to each other.
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Re: Math Games
« Reply #291 on: February 11, 2017, 11:57:54 am »

Okay, so we might want to decide collectively to not submit anything at all.
That's not a stable strategy; if a single team chooses to go against this consensus, they can only win.
But we might decide to punish them for that in later rounds.

But being collective there doesn't increase the total score. It just keeps everyone's score closest to each other.
Yep, that's why I'm not sure about it here. Probably each team should just do their best.
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Re: Math Games
« Reply #292 on: February 11, 2017, 01:05:25 pm »


Scoring is determined as follows (per player):   
Player B guesses the red square:   12
Player B guesses a blue square:   3
Player B does not guess either a blue or red square:   Negative points so that the total points among all players is 0 and the "losing" players all get the same number of points, rounding down if necessary to avoid non-integers.

If each team guesses either a blue or red square, the negative points will be distributed among the teams who guessed blue squares.  If all teams guess the red square, no one will get any points.

*Since there is an odd number of players, there will need to be one team of 3.  I'll list the teams in the next post.


Just want to make sure I am thinking correctly about the scoring

6 teams.  Assume that 3 teams (one of them has 3 players) guess blue, one team guesses red, and two teams miss.

The teams that guess blue: each player on the team gets 3 points (total 21 points awarded)
The team that guessed red: each player gets 12 points (total 24 points awarded)
The teams that missed: divide up the total of 45 points evenly among the 4 players, so each player on the teams that miss get -11.25 points (rounded to -11)

is this right?
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scott_pilgrim

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Re: Math Games
« Reply #293 on: February 11, 2017, 01:27:08 pm »


Scoring is determined as follows (per player):   
Player B guesses the red square:   12
Player B guesses a blue square:   3
Player B does not guess either a blue or red square:   Negative points so that the total points among all players is 0 and the "losing" players all get the same number of points, rounding down if necessary to avoid non-integers.

If each team guesses either a blue or red square, the negative points will be distributed among the teams who guessed blue squares.  If all teams guess the red square, no one will get any points.

*Since there is an odd number of players, there will need to be one team of 3.  I'll list the teams in the next post.


Just want to make sure I am thinking correctly about the scoring

6 teams.  Assume that 3 teams (one of them has 3 players) guess blue, one team guesses red, and two teams miss.

The teams that guess blue: each player on the team gets 3 points (total 21 points awarded)
The team that guessed red: each player gets 12 points (total 24 points awarded)
The teams that missed: divide up the total of 45 points evenly among the 4 players, so each player on the teams that miss get -11.25 points (rounded to -11)

is this right?

Yes, that looks right.
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Re: Math Games
« Reply #294 on: February 11, 2017, 01:58:31 pm »

@scott: is there a solution?
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Re: Math Games
« Reply #295 on: February 11, 2017, 02:06:04 pm »

So essentially if we can we want to get the red square because that is the only way to assure that we don't lose points.
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Re: Math Games
« Reply #296 on: February 11, 2017, 02:37:56 pm »

so, if no teams correctly guess a blue or red square then no points are given or taken away?
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Re: Math Games
« Reply #297 on: February 11, 2017, 02:49:22 pm »

so, if no teams correctly guess a blue or red square then no points are given or taken away?

This is correct
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Re: Math Games
« Reply #298 on: February 11, 2017, 03:37:50 pm »

That is a very good solution, scott.
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Re: Math Games
« Reply #299 on: February 13, 2017, 06:14:20 pm »

/out for the next game.

I am sure I will regret it, but they are coming a bit too fast for me to be able to spend the required time to think them through. Maybe it would be different if we were told in advance what the next game is going to be.
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Re: Math Games
« Reply #300 on: February 13, 2017, 07:31:13 pm »

THREAD LOCKED
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Re: Math Games
« Reply #301 on: February 13, 2017, 07:34:38 pm »

(I think I locked all the QT's too, but if I didn't please pretend like it's locked.

PM's will be coming in the next half hour or so.
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Re: Math Games
« Reply #302 on: February 13, 2017, 08:09:03 pm »

PM's have been sent.  Let me know if you did not get one and you should have.  Also, let me know if you can't see which squares are blue, it didn't come out looking super clear.

Submissions for which coin to flip are due by 8:30pm tomorrow.  Please make it as unambiguous as possible which coin you would like to flip.  (If you don't specify some other interpretation, I will interpret a Letter-Number submission in standard chess notation, with A at the left and 8 at the top.)  If you don't submit something by deadline I may prod you or I may just flip a random coin for you.
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Re: Math Games
« Reply #303 on: February 14, 2017, 08:37:19 pm »

PM's have been sent to the player B's.  Please let me know if you should have received one and did not.
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Re: Math Games
« Reply #304 on: February 14, 2017, 08:38:57 pm »

Deadline will be 9pm tomorrow (Wednesday), but that will probably be a pretty soft deadline because I think I'm going to do a short break (24 hours or so) before the beginning of next game.
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Re: Math Games
« Reply #305 on: February 15, 2017, 09:00:34 pm »

THREAD UNLOCKED

Results coming shortly.
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Re: Math Games
« Reply #306 on: February 15, 2017, 09:01:09 pm »

exciting
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Re: Math Games
« Reply #307 on: February 15, 2017, 09:02:46 pm »

UmbrageOfSnow, LaLight: -7
faust, GendoIkari: -7
Calamitas, gkrieg13: +12
2.71828..., pacovf: -7
Dylan32, schadd: -7
sudgy, Axxle, liopoil: +12
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Re: Math Games
« Reply #308 on: February 15, 2017, 09:07:36 pm »

UmbrageOfSnow, LaLight

T H T T H H H T
H T H T H H T H
H H T T T T T T
H H T T T H H T
T H H T T H H H
H T H T H H T H
H H H H H H H H
H T T H T H H H


GendoIkari, faust

H T T H H H T T
H H H H T H T H
T T H T H H H T
T H H H H T T T
T H T H T T T T
H H T T T T T T
H T H H T T H H
H H T H H H T T


Calamitas, gkrieg13

H T T H T T T T
H T H H T T T H
H T T T T H H H
H T T T T T T H
H H T H T T T H
T H T H T T H H
T H T H T T H H
T H T T T T H T


2.71828..., pacovf

T H T H T H H H
T H H H T T T T
H H T T T H H T
H T H T H H H H
T T T T T H H T
T T T T H H T T
T T T H H T H T
H H H T H T T H


Dylan32, schadd

H H H H T H H H
H T T T T T H H
H T H T H T T H
T T H T T H H H
T H H T T T T H
H H H T H T H T
T H H T T H H H
T H T H H H H H


sudgy, Axxle, liopoil

H T T T T T H T
T H T H T H H T
H T H H T T T H
T H H H H H H T
T T T T H H H H
T H H H T H T H
T H T H T T T H
H H T T H T T H

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Re: Math Games
« Reply #309 on: February 15, 2017, 09:11:37 pm »

@scott: is there a solution?

Yes (it felt unfair to say that during the game).  See team Axudgpoil's QT (or team Calamikrieg but they "cheated").

A friend gave me this problem a long time ago (and heavily implied that there was a solution), and I was never able to figure it out.  I thought maybe if I presented it as a competition to a bunch of really smart people someone could get me the answer.
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Re: Math Games
« Reply #310 on: February 15, 2017, 09:11:52 pm »

haha nice googling gkrieg :P
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Re: Math Games
« Reply #311 on: February 15, 2017, 09:15:31 pm »

I feel like I was frustratingly close.
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Re: Math Games
« Reply #312 on: February 15, 2017, 09:20:44 pm »

Wait, can you say what each group guessed? I guessed B1, which was a blue tile, shouldn't 2.7 and I get 3 points?
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Re: Math Games
« Reply #313 on: February 15, 2017, 09:22:59 pm »

Wait, can you say what each group guessed? I guessed B1, which was a blue tile, shouldn't 2.7 and I get 3 points?
It looks to me like B1 is a colorless heads. A2, on the other hand, is blue.

EDIT: B1 was blue on Dylan and Schadd's board too.
« Last Edit: February 15, 2017, 09:26:17 pm by liopoil »
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Re: Math Games
« Reply #314 on: February 15, 2017, 09:23:44 pm »

Rules for game 4 will go up tomorrow evening sometime (and the thread will be locked then).  Thread will remain unlocked until then.

Also, players are encouraged to check over their own score in the OP at the end of each game to make sure I didn't mess anything up.  As of right now that is the only place I am tracking total scores (though I realize that that's probably going to be a bad idea in the long-run, so I'll try to keep better track).


I'd also just like to say that even though I don't usually respond, I do enjoy reading players' thought processes when they PM me.  My lack of response is a time thing, not a disinterest thing.
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Re: Math Games
« Reply #315 on: February 15, 2017, 09:27:44 pm »

Wait, can you say what each group guessed? I guessed B1, which was a blue tile, shouldn't 2.7 and I get 3 points?

Yeah, this is why I wanted people to be as clear as possible.  You said B1 and you also said "starting from the bottom left, the second tile from the bottom".  Reading that now I realize I should have asked for clarification, but I thought you meant "second tile on the bottom" (moving left to right), which is where B1 was.
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Re: Math Games
« Reply #316 on: February 15, 2017, 09:32:23 pm »

Wait, can you say what each group guessed? I guessed B1, which was a blue tile, shouldn't 2.7 and I get 3 points?

Yeah, this is why I wanted people to be as clear as possible.  You said B1 and you also said "starting from the bottom left, the second tile from the bottom".  Reading that now I realize I should have asked for clarification, but I thought you meant "second tile on the bottom" (moving left to right), which is where B1 was.

I realize now that the naming scheme e and I decided on in our quicktopic is actually inverted from yours, and I didn't realize it when you posted about it on topic. I  most definitely meant the A2 tile (going by your convention, rather than his). Dunno, I guess I could also have been more explicit.
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Re: Math Games
« Reply #317 on: February 15, 2017, 09:33:31 pm »

weoooo go team!!!
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Re: Math Games
« Reply #318 on: February 15, 2017, 09:33:38 pm »

Wait, can you say what each group guessed? I guessed B1, which was a blue tile, shouldn't 2.7 and I get 3 points?

Yeah, this is why I wanted people to be as clear as possible.  You said B1 and you also said "starting from the bottom left, the second tile from the bottom".  Reading that now I realize I should have asked for clarification, but I thought you meant "second tile on the bottom" (moving left to right), which is where B1 was.

I apologize for this, it doesn't feel right to not give you the points, but it feels even more unfair to the other players to take points away from them because of that.  If it's unanimous I'll re-score as if you submitted the move you intended to (I don't expect it to be unanimous though).  If anyone PM's me (I'll keep it anonymous) asking me not to re-score then I'll leave the scoring as is.
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pacovf

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Re: Math Games
« Reply #319 on: February 15, 2017, 09:37:09 pm »

Wait, can you say what each group guessed? I guessed B1, which was a blue tile, shouldn't 2.7 and I get 3 points?

Yeah, this is why I wanted people to be as clear as possible.  You said B1 and you also said "starting from the bottom left, the second tile from the bottom".  Reading that now I realize I should have asked for clarification, but I thought you meant "second tile on the bottom" (moving left to right), which is where B1 was.

I apologize for this, it doesn't feel right to not give you the points, but it feels even more unfair to the other players to take points away from them because of that.  If it's unanimous I'll re-score as if you submitted the move you intended to (I don't expect it to be unanimous though).  If anyone PM's me (I'll keep it anonymous) asking me not to re-score then I'll leave the scoring as is.

Yeah, I understand, don't worry. Sorry, e :(
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Re: Math Games
« Reply #320 on: February 15, 2017, 09:39:53 pm »

I kind of want to know what square LaLight guessed too.

Although it was only a 25%, I'm curious.
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Re: Math Games
« Reply #321 on: February 15, 2017, 09:40:49 pm »

Ok wow, the link gkrieg found gets to the answer in a much less roundabout way than I did. That's a really good puzzle.

Also, I was totally considering spilling the beans in this thread for all the teams before scott fixed the issue. That was pretty slick.
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Re: Math Games
« Reply #322 on: February 15, 2017, 09:42:04 pm »

I also wanted to respond to this post:

/out for the next game.

I am sure I will regret it, but they are coming a bit too fast for me to be able to spend the required time to think them through. Maybe it would be different if we were told in advance what the next game is going to be.

I'm having a bit of a hard time keeping up with it too, and I'm considering changing default deadlines to 48 hours instead of 24 hours.  I think taking a 24-hour break after each game is something that I will probably make a habit of in general.  That also gives people some time to talk about the previous game, especially if communication was prohibited.

Announcing games in advance isn't really possible for most of the games though, because a lot of them need to prohibit communication (at least for the beginning of the game), and a lot of them are in rough draft form until just before I post the rules.
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Re: Math Games
« Reply #323 on: February 15, 2017, 09:44:09 pm »

I assumed the solution would have something to do with parity, but I didn't have enough time to think about it during the three days (very busy weekend). Not sure I would have found a solution, but probably something better than what we ended up doing :p

I also wanted to respond to this post:

/out for the next game.

I am sure I will regret it, but they are coming a bit too fast for me to be able to spend the required time to think them through. Maybe it would be different if we were told in advance what the next game is going to be.

I'm having a bit of a hard time keeping up with it too, and I'm considering changing default deadlines to 48 hours instead of 24 hours.  I think taking a 24-hour break after each game is something that I will probably make a habit of in general.  That also gives people some time to talk about the previous game, especially if communication was prohibited.

Announcing games in advance isn't really possible for most of the games though, because a lot of them need to prohibit communication (at least for the beginning of the game), and a lot of them are in rough draft form until just before I post the rules.


Yep, I get that. It's just that the first two games required a relatively small amount of thinking, while the third one was really tricky, and it took me by surprise.
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Re: Math Games
« Reply #324 on: February 15, 2017, 09:45:58 pm »

ah, crud. i just thought of a quick-and-dirty probably has at least one way to do it between the four tiles solution


every tile corresponds to a number 0-63; guesser picks (sum of all heads)%64
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Re: Math Games
« Reply #325 on: February 15, 2017, 09:46:14 pm »

These were everyone's guesses:

Dylan32: H8
pacovf: B1
sudgy: B3
LaLight: G6
faust: "Row 8, column 4" (I thought this was slightly ambiguous but there was no way of interpreting it that got a hit)
Calamitas: C2
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Re: Math Games
« Reply #326 on: February 15, 2017, 09:48:21 pm »

(Also, at least one player has asked me not to re-score.)
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Re: Math Games
« Reply #327 on: February 15, 2017, 09:49:32 pm »

haha nice googling gkrieg :P

Yay for googling!
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Re: Math Games
« Reply #328 on: February 15, 2017, 09:50:00 pm »

ah, crud. i just thought of a quick-and-dirty probably has at least one way to do it between the four tiles solution


every tile corresponds to a number 0-63; guesser picks (sum of all heads)%64
yeah, this has about a 50-50 chance of getting the red square and almost certainly gets something good. Axxle came up with essentially this pretty quickly.
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Re: Math Games
« Reply #329 on: February 15, 2017, 09:52:59 pm »

I also want to apologize for the "power creep" in the scoring.  It was unintentional that the third game had such a big point difference among players compared to the first and second.  I'm trying to keep things as even as possible but I don't think I'm doing a very good job of it (and that game in particular was scary because scoring depended on how many teams came up with the solution; I'm relieved it wasn't something like all but one team got it right, that would have been horrible for the last team).
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Re: Math Games
« Reply #330 on: February 15, 2017, 09:53:14 pm »

ah, crud. i just thought of a quick-and-dirty probably has at least one way to do it between the four tiles solution


every tile corresponds to a number 0-63; guesser picks (sum of all heads)%64
yeah, this has about a 50-50 chance of getting the red square and almost certainly gets something good. Axxle came up with essentially this pretty quickly.
well lah-dee-dah
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Re: Math Games
« Reply #331 on: February 15, 2017, 11:58:23 pm »

I kind of want to know what square LaLight guessed too.

Although it was only a 25%, I'm curious.

I chose the only different tile in 12th square, because i thought you picked this one to hint because of that.
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Re: Math Games
« Reply #332 on: February 16, 2017, 12:01:25 am »

I kind of want to know what square LaLight guessed too.

Although it was only a 25%, I'm curious.

I chose the only different tile in 12th square, because i thought you picked this one to hint because of that.

Your guess was fine, no problems with it.  We didn't have a great chance of getting it right to begin with.  I just wanted to know.

I was going to say know how close we were, but you were pretty obviously going to get within a very short radius of it. ;)  I don't know, not being diagonal is closer!
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Re: Math Games
« Reply #333 on: February 16, 2017, 12:30:45 am »

Wait, can you say what each group guessed? I guessed B1, which was a blue tile, shouldn't 2.7 and I get 3 points?

Yeah, this is why I wanted people to be as clear as possible.  You said B1 and you also said "starting from the bottom left, the second tile from the bottom".  Reading that now I realize I should have asked for clarification, but I thought you meant "second tile on the bottom" (moving left to right), which is where B1 was.

I apologize for this, it doesn't feel right to not give you the points, but it feels even more unfair to the other players to take points away from them because of that.  If it's unanimous I'll re-score as if you submitted the move you intended to (I don't expect it to be unanimous though).  If anyone PM's me (I'll keep it anonymous) asking me not to re-score then I'll leave the scoring as is.

Yeah, I understand, don't worry. Sorry, e :(

Its ok.  I realized after the fact that I had messed up standard chess notation in our qt, but didn't bother to go back and fix it.  That being said, I disagree with scott's decision here not to re-score due to the fact that it is abundantly clear in our qt that we had a different naming scheme that we agreed upon.  While you may not have mentioned our naming scheme in your PM to scott with your choice, I still think that looking back at what happened we should be awarded the points.  Regardless, I understand the situation that scott is in as the moderator and I will respect whatever decision he ultimately makes.
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Re: Math Games
« Reply #334 on: February 16, 2017, 12:38:40 am »

Yeah, this is why I wanted people to be as clear as possible.  You said B1 and you also said "starting from the bottom left, the second tile from the bottom".  Reading that now I realize I should have asked for clarification, but I thought you meant "second tile on the bottom" (moving left to right), which is where B1 was.

Actually, looking at this again, we really should get the points.  "Second tile from the bottom" is completely different than "second tile on the bottom."  Writing my last reply I hadn't really noticed that pacovf had explained the tile he chose.  Elaborating as he did, plus the clear discussion in our qt, I really don't get why it is difficult to change the scoring.
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Re: Math Games
« Reply #335 on: February 16, 2017, 01:10:49 pm »

I don't feel that great about playing "games" that are solvable here. I mean it's really just a math problem at that point. Not that math problems aren't fun, but there is a thread for such things.

This is assuming scott knew beforehand that the game was solvable.
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Re: Math Games
« Reply #336 on: February 16, 2017, 02:24:18 pm »

I searched google and saw that a solution existed, but didn't share it with my partner because I thought using such info was against the spirit of the game.  If there was a group that used a solution from an external site, I am slightly disappointed.
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Re: Math Games
« Reply #337 on: February 16, 2017, 05:15:44 pm »

I don't feel that great about playing "games" that are solvable here. I mean it's really just a math problem at that point. Not that math problems aren't fun, but there is a thread for such things.

This is assuming scott knew beforehand that the game was solvable.

So at what point did you realize that we made our plan based on a 9x9 grid instead of 8x8?  :P

I figured you would just adapt it by going from 4-0 instead of 5-1, but the board we got just didn't allow our idea to pan out; no matter what I did a black square was going to be the strongest.
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Re: Math Games
« Reply #338 on: February 16, 2017, 05:20:39 pm »

I searched google and saw that a solution existed, but didn't share it with my partner because I thought using such info was against the spirit of the game.  If there was a group that used a solution from an external site, I am slightly disappointed.

I didn't ask Google for a solution because it seemed against the spirit of the game, but to be fair it wasn't specified in the rules. Next time, a clause to such effect could be added. Or just avoid solvable games, as faust said.
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Re: Math Games
« Reply #339 on: February 16, 2017, 05:23:33 pm »

Sorry guys, I didn't realize that googling things would be against the spirit of the game.  I had actually seen this problem before, so I had actually messed around with the site that had the answer before because it was an interesting problem.
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Re: Math Games
« Reply #340 on: February 16, 2017, 07:17:44 pm »

I agree with others that "solvable" games are not ideal.  I ran this particular one because I thought it would be hard enough that it would feel very rewarding for any teams who actually figured it out, and because I didn't realize how easy it would be to find the answer by googling it, and also because it wasn't just a binary "could you solve it or not", though to be fair it might have been closer to that than it should have been.

In general, most games will not be just "team math problems" like that one was.  Some games like guess f of the average (particularly the first round) may be solvable, but will hopefully still have a "human" component to them that makes players think about whether it's really best to play at the "solution".  I think it will be somewhat common for me to do multi-round games that are sort of formatted like guess f of the average, where the first round has a somewhat widely known solution, but the later rounds are a bit trickier.

That being said, if a lot of players give the same kind of feedback for what sorts of games they would like to play, I will try to take it into account when possible.  At some point down the road I may post a poll to see what kinds of games are most popular.
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Re: Math Games
« Reply #341 on: February 16, 2017, 07:33:55 pm »

Yeah, this is why I wanted people to be as clear as possible.  You said B1 and you also said "starting from the bottom left, the second tile from the bottom".  Reading that now I realize I should have asked for clarification, but I thought you meant "second tile on the bottom" (moving left to right), which is where B1 was.

Actually, looking at this again, we really should get the points.  "Second tile from the bottom" is completely different than "second tile on the bottom."  Writing my last reply I hadn't really noticed that pacovf had explained the tile he chose.  Elaborating as he did, plus the clear discussion in our qt, I really don't get why it is difficult to change the scoring.

I understand your frustration and I agree that reading it now it's clear what pacovf meant, but I read it as "from the bottom, the second tile", where it's ambiguous whether the second tile means moving left to right or bottom to top.  I understand that this is not the most natural way to interpret it, but I just automatically made sense of it in a way that would be consistent with B1 (I was just checking that the two things he gave me were not contradictory).  Since I specifically stated that I would use the chess notation as a default way of communicating the locations with players, I think that should be the default.

I think it's like letting your opponent take back misclicks in Dominion online.  They accidentally make a move that's good for you, and you're not really under any obligation to let them take it back, but if you're feeling extra generous you have that option.  One or more players have requested that I don't re-score, which is the analog to not granting an undo request.  In general, I think the mod should always err on the side of being too "machine-like", as that's most likely to feel fair to the most players in the long-run, and in this case that means going with the literal chess notation reference that pacovf sent me.
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Re: Math Games
« Reply #342 on: February 16, 2017, 07:43:49 pm »

THREAD LOCKED

Rules for the next game coming shortly.  (If you want to continue discussing something from above, you can PM me.)
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Re: Math Games
« Reply #343 on: February 16, 2017, 07:48:05 pm »

4. Don't Be an Idiot      

Rules      

THERE IS TO BE NO COMMUNICATION AFTER RULES ARE POSTED.      
This game will be played in three rounds, with slight rule variations in the second and third rounds.      
Each player PM's the mod with a choice: Option A, or Option B.      
If ALL players choose option A, everyone scores a points ("a" being a variable, not an indefinite article).  If ANYONE chooses option B, each player who chose option B scores b points, while everyone who chose A scores 0 points.      
The values of a and b vary each round, according to the table below:   
   
Round   a   b
1       6   5
2       5   6
3       4   20


In Round 2, if EVERYONE chooses option B, no one will score any points.      
In Round 3, if MORE THAN ONE player chooses option B, no one will get any points.

      
Note: At the end of each round, I will reveal who chose which option.      
« Last Edit: February 16, 2017, 07:54:34 pm by scott_pilgrim »
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Re: Math Games
« Reply #344 on: February 16, 2017, 07:57:09 pm »

Deadline for the first round will be 8:00pm tomorrow (Friday) but deadlines for this game will be soft in the sense that I will probably just issue a prod and delay the end of the round until I get a response, unless you go inactive for an unreasonably long time.  (But it's best for everyone if you just submit on time!)

Also, if I get submissions from everyone early I will post results early, unless at least one player requests that I don't.
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Re: Math Games
« Reply #345 on: February 18, 2017, 11:31:56 am »

Sorry for the delay...Round 1 results:

Calamitas   A
UmbrageOfSnow   A
gkrieg13   B
sudgy   B
Axxle   B
liopoil   B
2.71828…   B
Dylan32   A
faust   A
ghostofmars   A
schadd   A
GendoIkari   B
LaLight   A
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Re: Math Games
« Reply #346 on: February 18, 2017, 11:32:20 am »

Round 2 deadline will be 11:30am tomorrow (Sunday).
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Re: Math Games
« Reply #347 on: February 19, 2017, 11:32:22 am »

Round 2 results:

Calamitas   B
UmbrageOfSnow   B
gkrieg13   B
sudgy   B
Axxle   B
liopoil   B
2.71828…   B
Dylan32   B
faust   B
ghostofmars   B
schadd   A
GendoIkari   B
LaLight   B
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Re: Math Games
« Reply #348 on: February 19, 2017, 11:34:28 am »

Round 3 deadline will be 11:30am tomorrow (Monday).
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Re: Math Games
« Reply #349 on: February 20, 2017, 06:19:26 pm »

Thread Unlocked

Round 3 Results:

Calamitas   A
UmbrageOfSnow   (no submission)
gkrieg13   A
sudgy   A
Axxle   B
liopoil   B
2.71828…   B
Dylan32   A
faust   A
ghostofmars   A
schadd   A
GendoIkari   A
LaLight   A
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Re: Math Games
« Reply #350 on: February 20, 2017, 06:20:14 pm »

Rules for the next game will hopefully go up some time tomorrow evening.  The thread will remain unlocked until then.
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Re: Math Games
« Reply #351 on: February 20, 2017, 06:22:38 pm »

Why didn't you all read the game's title.
I'm all for excessively punishing everyone who took B in R3 and moderately punishing all who took B in the first round.
Also, schadd should be somehow rewarded for his R2 choice.
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Re: Math Games
« Reply #352 on: February 20, 2017, 06:26:09 pm »

Why should R1 B choosers be punished less than R3? R1 would have awarded more points to everyone for staying with A than R3, so by choosing B they played against the stated win condition purely to reduce the points everyone else got.  I too support mild reward for schadd.
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Re: Math Games
« Reply #353 on: February 20, 2017, 06:27:38 pm »

Why should R1 B choosers be punished less than R3? R1 would have awarded more points to everyone for staying with A than R3, so by choosing B they played against the stated win condition purely to reduce the points everyone else got.  I too support mild reward for schadd.
Motivation for R1 B was primarily safety I think, R3 was pure egoism.
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Re: Math Games
« Reply #354 on: February 20, 2017, 06:36:35 pm »

c:
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Re: Math Games
« Reply #355 on: February 20, 2017, 06:38:42 pm »

my reward can just be everyone getting a bunch of points
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Re: Math Games
« Reply #356 on: February 20, 2017, 06:39:01 pm »

i don't think i plan to to the Mean Thing in any of these
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Re: Math Games
« Reply #357 on: February 20, 2017, 06:40:15 pm »

Why should R1 B choosers be punished less than R3? R1 would have awarded more points to everyone for staying with A than R3, so by choosing B they played against the stated win condition purely to reduce the points everyone else got.  I too support mild reward for schadd.
Motivation for R1 B was primarily safety I think, R3 was pure egoism.

false.  R3 B choice was to insure that the most fair option was chosen, namely, that everyone got zero points.
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Re: Math Games
« Reply #358 on: February 20, 2017, 06:41:28 pm »

Why should R1 B choosers be punished less than R3? R1 would have awarded more points to everyone for staying with A than R3, so by choosing B they played against the stated win condition purely to reduce the points everyone else got.  I too support mild reward for schadd.
Motivation for R1 B was primarily safety I think, R3 was pure egoism.

false.  R3 B choice was to insure that the most fair option was chosen, namely, that everyone got zero points.
This is not the most fair option.
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Re: Math Games
« Reply #359 on: February 20, 2017, 06:42:44 pm »

Generally, you are playing to have as many points as possible.  This is different from playing to have more points than any other player.  (Think of it like every point you have is worth $1.
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Re: Math Games
« Reply #360 on: February 20, 2017, 06:47:43 pm »

good guy schadd <3
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Re: Math Games
« Reply #361 on: February 20, 2017, 07:30:38 pm »

Generally, you are playing to have as many points as possible.  This is different from playing to have more points than any other player.  (Think of it like every point you have is worth $1.
Wait, exactly. I am playing to have as many points as possible. If nobody else chooses B, I should take B to get 20 points instead of 4. If anyone else chooses B, I can't get points anyway so who cares. I'm shocked that more people didn't choose B.
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Re: Math Games
« Reply #362 on: February 20, 2017, 07:41:01 pm »

Round 1 was interesting in that B wasn't strictly better than A. Nevertheless it wasn't too hard to see that choosing B is almost certainly the best choice with respect to expected-value.

Round 2 was great in that nobody chose the wrong thing. Everyone but Schadd took the most points they could get. Given that everyone else did this, there was no way Schadd could have gotten points so he didn't mess up either.

Round 3 was bizarre because choosing A is just simply a mistake. Everyone should have chosen B.

I made all of my submissions (B every time) before round 1. Here's part of that pm:

Quote from: liopoil
Well, it looks like I'm going to be that idiot.

...

For fun I will try to predict the number of people who choose A in each round.

Round 1: 7 people choose A
Round 2: 3 people choose A
Round 3: 5 people choose A

...

I predict that at least two others will choose B all three rounds and that at least five others will choose B in rounds 2 and 3.

...

Looks like I was exactly right for Round 1, a bit wrong for round 2, and way wrong for round 3. There were two others who chose B all three rounds but not five others who chose B in rounds 2 and 3... why not?
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Re: Math Games
« Reply #363 on: February 20, 2017, 07:51:00 pm »

Just FYI, I'm not playing this for social reasons or punishing or rewarding people; I'm just playing because I think math games are fun.  I want to see each of these as a completely separate game.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

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Re: Math Games
« Reply #364 on: February 20, 2017, 10:32:36 pm »

So round 1 B was simply that I thought it was likely the only way to get any points, I didn't believe for a second that every single person would choose A.

Big thanks to Schadd for round 2.

For round 3, I couldn't think of a good reason to choose B. Here were the options: 1 or more other people chose B... then I can't get points no matter what I do. Might as well choose A just to be altruistic. Option 2, no one else chooses B. As unlikely as this option, I get points for choosing A or B. Sure I get a lot more for choosing B, but if everyone else is thinking that way, then it's not possible for anyone to get any points. So the only way to expect to get points is to hope that everyone makes the same A choice I do. In other words, choosing B only makes sense if somehow I think I'm different than every other player, which isn't logical.
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Re: Math Games
« Reply #365 on: February 21, 2017, 12:19:38 am »

Generally, you are playing to have as many points as possible.  This is different from playing to have more points than any other player.  (Think of it like every point you have is worth $1.
Wait, exactly. I am playing to have as many points as possible. If nobody else chooses B, I should take B to get 20 points instead of 4. If anyone else chooses B, I can't get points anyway so who cares. I'm shocked that more people didn't choose B.
It's not that simple, we do face a repeated prisoners dilemma here. That's why we need to punish such unaltrusitic behaviour, we need to get on at working more efficient than a group of egoists. Collective altruism leads to better outcome for all.
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Re: Math Games
« Reply #366 on: February 21, 2017, 12:21:20 am »

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Re: Math Games
« Reply #367 on: February 21, 2017, 12:42:44 am »

Generally, you are playing to have as many points as possible.  This is different from playing to have more points than any other player.  (Think of it like every point you have is worth $1.
Wait, exactly. I am playing to have as many points as possible. If nobody else chooses B, I should take B to get 20 points instead of 4. If anyone else chooses B, I can't get points anyway so who cares. I'm shocked that more people didn't choose B.
It's not that simple, we do face a repeated prisoners dilemma here. That's why we need to punish such unaltrusitic behaviour, we need to get on at working more efficient than a group of egoists. Collective altruism leads to better outcome for all.

Even if I get more points, I don't find that as fun, so consider me rogue.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

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Re: Math Games
« Reply #368 on: February 21, 2017, 12:58:47 am »

I have chosen a/b/a exactly because I was thinking this all is about the cooperation.

I played a game as a child where there was two teams and two options.

A chooses X, B chooses X, both get +3 points
A chooses X, B chooses Y, A gets -5, B +5
A chooses Y, B chooses Y, both get -10.

it was 5 rounds and we always chose Y, so as the opposite team, and both lost of course. Should've just chosen X all the time. I thought here is the same example.
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Re: Math Games
« Reply #369 on: February 21, 2017, 02:01:13 am »

Generally, you are playing to have as many points as possible.  This is different from playing to have more points than any other player.  (Think of it like every point you have is worth $1.
Wait, exactly. I am playing to have as many points as possible. If nobody else chooses B, I should take B to get 20 points instead of 4. If anyone else chooses B, I can't get points anyway so who cares. I'm shocked that more people didn't choose B.
It's not that simple, we do face a repeated prisoners dilemma here. That's why we need to punish such unaltrusitic behaviour, we need to get on at working more efficient than a group of egoists. Collective altruism leads to better outcome for all.
In a repeated prisoner's dilemma that's finitely iterated it still is best to defect every time. Just because it's possible that if everyone acted a certain way things would be better doesn't mean that it's at all realistic for that to happen. Also, like sudgy, I am playing these games as separate things entirely. But there are more problems. So far none of the games have had a mechanism where it would be possible to punish anyone or reward anyone, and I don't expect many future games to have such a mechanism. Moreover, there is little incentive for you or anyone to punish/reward, because it doesn't help your own point total. You may say that it acts as a deterant/incentive for future games, but there's no reason for anyone to treat it as any sort of precedent. Just because you punish once doesn't mean that you will again. So I think it's pretty naive to try to move towards altruism in a game where the rules specifically instruct us to be selfish.

For round 3, I couldn't think of a good reason to choose B. Here were the options: 1 or more other people chose B... then I can't get points no matter what I do. Might as well choose A just to be altruistic. Option 2, no one else chooses B. As unlikely as this option, I get points for choosing A or B. Sure I get a lot more for choosing B, but if everyone else is thinking that way, then it's not possible for anyone to get any points. So the only way to expect to get points is to hope that everyone makes the same A choice I do. In other words, choosing B only makes sense if somehow I think I'm different than every other player, which isn't logical.
This is kind of the thing Calamitas linked "if everyone else is thinking that way, then it's not possible for anyone to get any points". I would argue that yes, it is not possible for anyone to get points in round 3, since everyone should just choose B, every time. The fact is that what you choose/how you think does not change how others think, and in this case you just have to hope that everyone else chooses A, since there's no other way for you to get points.
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Re: Math Games
« Reply #370 on: February 21, 2017, 05:20:43 am »

I have chosen a/b/a exactly because I was thinking this all is about the cooperation.
Did this as well.

Notably, we actually maxed out the potential point output in round 2. Of course the other rounds were a mess.

I can see the argument for choosing B in Round 3, but I thought that even if I got the 20 points, everyone would hate me afterwards, which is probably a bigger problem than the 16 point difference.

Choosing B in round 1 is just... either stupid, or assuming that a number of the other players are stupid.
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Calamitas

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Re: Math Games
« Reply #371 on: February 21, 2017, 06:30:19 am »

@liopoil That depends on your notion of "rationality". I consider it rational to maximize my output, not following any guidelines. And if we consider an iterated prisoner's dilemma with two pairs of rational players, one of them following TDT (timeless decision theory) and the other one following CDT (causal decision theory).

The former players will cooperate every single time, the latter will defect every single time. The output of the former beats the latter by a margin.
TDT 1 : 0 CDT

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Re: Math Games
« Reply #372 on: February 21, 2017, 07:27:12 am »

@liopoil That depends on your notion of "rationality". I consider it rational to maximize my output, not following any guidelines. And if we consider an iterated prisoner's dilemma with two pairs of rational players, one of them following TDT (timeless decision theory) and the other one following CDT (causal decision theory).

The former players will cooperate every single time, the latter will defect every single time. The output of the former beats the latter by a margin.
TDT 1 : 0 CDT


Again, just because it's there exist a set of actions which do better doesn't mean that there's reason to expect people to do them.

I have chosen a/b/a exactly because I was thinking this all is about the cooperation.
Did this as well.

Notably, we actually maxed out the potential point output in round 2. Of course the other rounds were a mess.

I can see the argument for choosing B in Round 3, but I thought that even if I got the 20 points, everyone would hate me afterwards, which is probably a bigger problem than the 16 point difference.

Choosing B in round 1 is just... either stupid, or assuming that a number of the other players are stupid.
Why is it stupid? Choosing B is also an equilibrium strategy, and in fact in a sense it is way more stable than A. In practice, with the number of people we have, I calculated that if each other person has even a 2% chance of choosing B, then I should choose B. There's no assuming others are stupid at all.
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Re: Math Games
« Reply #373 on: February 21, 2017, 09:23:30 am »

Why is it stupid? Choosing B is also an equilibrium strategy, and in fact in a sense it is way more stable than A. In practice, with the number of people we have, I calculated that if each other person has even a 2% chance of choosing B, then I should choose B. There's no assuming others are stupid at all.

Exactly... choosing A is only the right strategy if you're with a group of close friends whom you know and trust very well, and whom you know also know and trust everyone else very well. With even 1 non-close friend in the group, B is simply the right strategy for everyone. Yes, if I had been the only person to choose B, I would have felt bad and been extremely surprised. I also would have had hurt myself (very slightly). But I had no reason at all to think that that would happen... and I was right. So you can say whatever you want about the "correct game theory" choice or whatever, but in the actual reality of the situation, given what actually happened... B was the right choice for everyone, and those who chose A messed up. You could even look at it as trying to be greedy and inch out an extra point by taking a big risk. B was a guaranteed 5 points, I'm not going to bet 5 points on basically a 10:1 longshot of earning 1 extra point.
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Re: Math Games
« Reply #374 on: February 21, 2017, 11:18:38 am »

Why is it stupid? Choosing B is also an equilibrium strategy, and in fact in a sense it is way more stable than A. In practice, with the number of people we have, I calculated that if each other person has even a 2% chance of choosing B, then I should choose B. There's no assuming others are stupid at all.
I don't know by which term you define "more stable"; both A and B are ESS, but A's output is higher than B's.
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Re: Math Games
« Reply #375 on: February 21, 2017, 11:19:56 am »

Why is it stupid? Choosing B is also an equilibrium strategy, and in fact in a sense it is way more stable than A. In practice, with the number of people we have, I calculated that if each other person has even a 2% chance of choosing B, then I should choose B. There's no assuming others are stupid at all.
I don't know by which term you define "more stable"; both A and B are ESS, but A's output is higher than B's.
Nevermind, A may not be ESS; I don't have the exact definition in mind. Still, if a single player deviates from A, they can only lose.
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Re: Math Games
« Reply #376 on: February 21, 2017, 02:31:15 pm »

Why is it stupid? Choosing B is also an equilibrium strategy, and in fact in a sense it is way more stable than A. In practice, with the number of people we have, I calculated that if each other person has even a 2% chance of choosing B, then I should choose B. There's no assuming others are stupid at all.
I don't know by which term you define "more stable"; both A and B are ESS, but A's output is higher than B's.
Nevermind, A may not be ESS; I don't have the exact definition in mind. Still, if a single player deviates from A, they can only lose.
Yeah, looks like A is not ESS, but I don't really know anything about that. By stable I meant that if anyone deviates from the equilibrium A then B becomes better, while lots of people can deviate from the equilibrium B and have B stay best until literally everyone has deviated. The fact that a single person deviating from A can only lose just means that it is an equilibrium, which is why an argument can be made for choosing A at all.
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Re: Math Games
« Reply #377 on: February 21, 2017, 05:36:34 pm »

B is ESS (Extremely Shitty and Stupid)
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Re: Math Games
« Reply #378 on: February 21, 2017, 06:44:33 pm »

You're playing this game against people who aren't perfect logicians. If you don't assume some people will play suboptimally, then that's playing suboptimally.
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Re: Math Games
« Reply #379 on: February 21, 2017, 07:38:14 pm »

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Re: Math Games
« Reply #380 on: February 21, 2017, 07:46:32 pm »

5. Guess an Unpopular Outcome of Coin Flips (by Tables)   
   
Rules      

Thank you to Tables for suggesting the main ideas of this game!      
This game will be played in three rounds.  THERE IS TO BE NO COMMUNICATION AFTER RULES ARE POSTED.      
In each round, n coins will be flipped, where n varies from round to round.  Each player may submit r integers*, each from 0 to n (inclusive), where r is the current round number.      
Each submission represents the number of coins that the player thinks will land heads.      
Each player who correctly guesses the number of heads flipped shares in a point prize of p points, where p varies from round to round (rounding up to avoid decimals).      
Clarification: When I say that they "share" in the prize, I mean that the p points are divided up evenly among the winners.  Therefore, it is better to win by yourself than with many players.      

*A player may "repeat" guesses, to give themselves extra "shares" in that guess.  For example, if Alice guesses 2, 2, 3, and Bob guesses 2, 3, 4, and there end up being 2 heads (and no one else guessed 2), then Alice will win two thirds of the points and Bob will win one third of the points.      

Round Number/Number of Guesses   n (Number of Coins Flipped)   p (Points for Correct Guesses)
1                                5                             12
2                                8                             16
3                                (number of players)           18


In Round 3, instead of flipping coins, each player will be given control over the outcome of a single coin.  When you PM me for round 3, please also say whether you would like your coin to be heads or tails.      
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Re: Math Games
« Reply #381 on: February 21, 2017, 07:47:17 pm »

Deadline for Round 1 will be 8:00pm tomorrow (Wednesday).
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Re: Math Games
« Reply #382 on: February 22, 2017, 08:04:41 pm »

Round 1 Results:

Calamitas   1
UmbrageOfSnow   (no submission)
gkrieg13   3
sudgy   2
liopoil   1
2.71828…   3
Dylan32   3
faust   0
ghostofmars   2
schadd   4
GendoIkari   3
LaLight   1
   
Outcome: HTHHT (3 heads)   
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Re: Math Games
« Reply #383 on: February 22, 2017, 08:10:13 pm »

Round 2 deadline is 8:00pm tomorrow (Thursday).
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Re: Math Games
« Reply #384 on: February 23, 2017, 08:05:39 pm »

Round 2 Results:

Calamitas   2,3
UmbrageOfSnow   3,6
gkrieg13   4,5
sudgy   4,5
liopoil   4,6
2.71828…   4,5
Dylan32   3,3
faust   (no submission)
ghostofmars   3,4
schadd   2,5
GendoIkari   4,4
LaLight   2,6
   
Outcome: THTTHHTH (4 heads)

16 points split among 7 shares, so each player who guessed correctly gets 3 points.  I realize now that it is ambiguous in the rules whether GendoIkari should get 5 or 6 points (because it's not stated whether rounding happens before or after counting the multiple shares), but I think rounding first is the more natural interpretation, so he gets 6 points.  Let me know if you have a problem with this ruling.
« Last Edit: February 23, 2017, 08:06:53 pm by scott_pilgrim »
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Re: Math Games
« Reply #385 on: February 23, 2017, 08:06:44 pm »

Round 3 deadline is 8:00pm tomorrow (Friday).  There are 12 players currently, so there will be 12 coins total.  If someone does not submit anything, I will determine their flip randomly to ensure that there are 12 coins.
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Re: Math Games
« Reply #386 on: February 24, 2017, 08:00:33 pm »

Thread Unlocked

Results coming shortly.
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Re: Math Games
« Reply #387 on: February 24, 2017, 08:02:05 pm »

Round 3 Results:

Calamitas   4,5,6   T
UmbrageOfSnow   9,10,11   H
gkrieg13   7,8,9   H
sudgy   7,8,9   H
liopoil   6,7,9   H
2.71828…   3,4,3   T
Dylan32   8,8,9   H
faust   8,9,10   H
ghostofmars   7,8,9   H
schadd   2,4,5   T
GendoIkari   5,6,7   H
LaLight   3,6,9   T

8 heads total; each share is worth 18/6 = 3 points.
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Re: Math Games
« Reply #388 on: February 24, 2017, 08:06:50 pm »

well, futz
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schadd

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Re: Math Games
« Reply #389 on: February 24, 2017, 08:07:41 pm »

to be fair i was right for round 1
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Re: Math Games
« Reply #390 on: February 24, 2017, 08:16:01 pm »

That was definitely the best game I've had so far.
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Re: Math Games
« Reply #391 on: February 24, 2017, 08:21:10 pm »

Okay, so I used a random number generator and it told me to guess 6,7,8. Then I decided that was boring and said:

Round 3 Submission: My coin is heads, I guess 6,7, and 9 heads

Take that, random number generator! Just watch there be 8 heads though.

Random number generator wins this time...
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Re: Math Games
« Reply #392 on: February 24, 2017, 08:27:16 pm »

I think that this is a pretty neat game. This is what I wrote for round 1:

There are only 6 options, and 32 possible ways the flips can go. The relative likelihoods of the outcomes are:

1 5 10 10 5 1

The relative expected value of a choice is the relative likelihood on the outcome divided by the (1 + the expected number of other players who choose that outcome). There are eleven other players. The equilibrium distribution would have all six outcomes equally valuable, and so in the limit with lots and lots of players, would mirror the binomial distribution. With just eleven other players it doesn't quite work like that though. Since it's symmetric, I can arbitrarily decide which half to choose from right now, and I think that fewer people will guess <3 heads, so that's what I'll do. If the probabilities of guessing 0, 1, or 2 heads are x, y, and z, then in the equilibrium we would have:

x + y + z = 1/2
1/(1 + 11x) = 5/(1 + 11y) = 10/(1 + 11z)

Re-arranging, 10 + 110x = 2 + 22y = 1 + 11z = q. Then 16q = 110(x + y + z) + 30 = 85, so q = 85/16. That means that:

z = 69/176
y = 53/352
x = -15/352

Okay, I think that means that it's actually never a good idea to choose 0 heads with this few people. In fact I think this makes sense; there's no way the eleven people can make the 5s and 10s bad enough. Okay, well let's redo it with just y and z. Now we have:

y + z  = 1/2
2 + 22y = 1 + 11z = q

Then 3q = 22(y + z) + 4 = 15, so q = 5. Then z = 4/11 and y = 3/22; I can definitely believe that. Then since I've decided to choose from the lower half, I'm going to guess 2 heads 8 times out of 11 and guess 1 heads the other 3 times out of 11. If everyone did this, then the average person would expect to face a distribution like:

0 1.5 4 4 1.5 0

This person still would not want to guess 0 or 5, and they wouldn't care otherwise. Unfortunately this ignores the fact that 12 is not divisible by 5, which is quite ugly and so I will choose to ignore it even though it makes the center choices slightly more appealing. In fact, I'm willing to bet that more people will be more inclined to guess 1 or 4 heads than they should be, and that somebody is going to guess 0 or 5 heads even though that's a bad guess. So maybe I should be choosing 2 heads more than 8/11 = ~73% of the time, but I'm just going to play the equilibrium. Time to go to a random number generator.

Well, the random number generator spit out 9 when I asked for a number between 1 and 11, so I should guess 1 heads. Round 1 Guess: 1 coin will land heads

For round 2 the computations were way nastier (the final denominator of the probabilities was 340) and less solidly grounded but I did them anyway and went with the random numbers again. For round 3 my analysis was so meaningless that I decided to ignore what the random number generator said, oops.
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Re: Math Games
« Reply #393 on: February 24, 2017, 09:15:58 pm »

Darn it. I initially had typed 8 three times in the 3rd round, but then decided to change one to 9 just to give me another chance at points... That would have been beautiful.
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Re: Math Games
« Reply #394 on: February 24, 2017, 10:19:17 pm »

I don't understand anyone who said anything other than 2 or 3 for round 1. They were simply mathematically the best options; and there was no human component to consider. Similar for round 2, except you could argue 3,4 or 4,5 are better than 4,4.

For round 3, I failed to account for the human component and still expected about half heads.

*edit* Ok, after reading liopoil's post, I see th human component now; the hope that you split the win less. But I still think it just makes the most sense to go with the most likely win.
« Last Edit: February 24, 2017, 10:24:19 pm by GendoIkari »
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Re: Math Games
« Reply #395 on: February 24, 2017, 11:31:51 pm »

I don't understand anyone who said anything other than 2 or 3 for round 1. They were simply mathematically the best options; and there was no human component to consider. Similar for round 2, except you could argue 3,4 or 4,5 are better than 4,4.

For round 3, I failed to account for the human component and still expected about half heads.

*edit* Ok, after reading liopoil's post, I see th human component now; the hope that you split the win less. But I still think it just makes the most sense to go with the most likely win.
If everyone chooses 2 or 3, then it would increase your expected point yield to choose 1 or 4 instead. The equilibrium state where you don't benefit from switching has to be some ratio between choosing 1/4 and 2/3, with 2/3 more likely.
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Re: Math Games
« Reply #396 on: February 25, 2017, 02:35:52 am »

I don't understand anyone who said anything other than 2 or 3 for round 1. They were simply mathematically the best options; and there was no human component to consider. Similar for round 2, except you could argue 3,4 or 4,5 are better than 4,4.

For round 3, I failed to account for the human component and still expected about half heads.

*edit* Ok, after reading liopoil's post, I see th human component now; the hope that you split the win less. But I still think it just makes the most sense to go with the most likely win.
This is actually similar to something that daily fantasy players have to take into consideration: ownership percentage. So you sometimes have to play the guy who is projected to get fewer points, but fewer other managers are playing. You might hit less often than the other players, but when you do hit it matters a lot more since you beat a larger percentage of the opposition if the underdog does go off.
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Re: Math Games
« Reply #397 on: February 25, 2017, 06:41:38 am »

I don't understand anyone who said anything other than 2 or 3 for round 1. They were simply mathematically the best options; and there was no human component to consider. Similar for round 2, except you could argue 3,4 or 4,5 are better than 4,4.

For round 3, I failed to account for the human component and still expected about half heads.

*edit* Ok, after reading liopoil's post, I see th human component now; the hope that you split the win less. But I still think it just makes the most sense to go with the most likely win.
You need to maximize your expectancy value not your winning probability. If more than twice as many people choose 2/3 than 1/4, 1/4 becomes best. So if you expect that to happen, 1/4 is the right call.
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Re: Math Games
« Reply #398 on: February 25, 2017, 06:43:48 pm »

For those interested, this game is actually quite heavily modified from what I originally suggested - definitely in a good way for this kind of thing - and I originally made it for a probability game in the classroom. The original suggestion was much simpler: Everyone writes down their guess on a whiteboard, roll 2d6, everyone who guessed correctly shares the points in the same way as here, repeat. It would work well with a group of about 20 or so, but less well with smaller numbers (although I did suggest using coins or similar). Scott then took the idea further by having multiple guesses and more complex numbers in each round, which I think is better with this kind of player count and ability level than just repeating the basic game.
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...spin-offs are still better for all of the previously cited reasons.
But not strictly better, because the spinoff can have a different cost than the expansion.

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Re: Math Games
« Reply #399 on: February 25, 2017, 07:46:08 pm »

Random note: GendoIkari's and/or faust's scores may be wrong in the OP.  At some point I will try to double-check everything and maybe make a Google doc to track where points are coming from.
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Re: Math Games
« Reply #400 on: February 25, 2017, 07:46:34 pm »

Thread Locked

Rules for the next game going up shortly.
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Re: Math Games
« Reply #401 on: February 25, 2017, 07:54:42 pm »

6. Build a Tower      
   
Rules
         
THERE IS TO BE NO COMMUNICATION AFTER RULES ARE POSTED.         
This game will be played in four rounds.         
Each round, each player PM's the mod with their choice of one tower to build a block on.         
At the end of the round, the placement of each player's block will be revealed.         
At the end of the final round, each player who placed at least one block in a given completed tower scores x VP, where x is a number that depends on the tower.  Incomplete towers will not score anyone any points.
The number of blocks required to complete each tower varies from tower to tower.         
Here are the available towers:         

Tower   Blocks to complete   Points   
A       20                   30   
B       13                   17   
C1      7-12*                8-15*   
C2      7-12*                8-15*   
D       3-8*                 3-8*   
E1      8                    10   
E2      8                    10   
F1      6                    6   
F2      6                    6   
F3      6                    6   
G1      4                    3   
G2      4                    3   


*The C and D towers require a random (integer) number of blocks to complete.  That number will not be revealed until after the final round (but it will be chosen uniformly at random).  The number of points the tower is worth, for tower D, is equal to the number of blocks required to complete it.  For each C Tower, use the following table:      
   
   Blocks to complete   Points   
   7                    8   
   8                    9   
   9                    10   
   10                   12   
   11                   13   
   12                   15   


Note that you do not get "bonus" points for placing mutliple blocks in the same tower.  After you have placed one block in a tower, your only motivation to place more is to help ensure that the tower gets finished.         
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scott_pilgrim

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Re: Math Games
« Reply #402 on: February 25, 2017, 07:55:07 pm »

Deadline for Round 1 will be 8pm tomorrow (Sunday).
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Re: Math Games
« Reply #403 on: February 25, 2017, 11:45:28 pm »

Clarification: You CAN add blocks to a tower that is already finished.
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Re: Math Games
« Reply #404 on: February 26, 2017, 01:19:08 pm »

Random note: GendoIkari's and/or faust's scores may be wrong in the OP.  At some point I will try to double-check everything and maybe make a Google doc to track where points are coming from.

(It looks to me like GendoIkari's score is correct, but faust's score is reported as 112 when it should be 122, which I will correct now.)
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Re: Math Games
« Reply #405 on: February 26, 2017, 08:03:31 pm »

Round 1 Results:

Calamitas   A
UmbrageOfSnow   (no submission)
gkrieg13   A
sudgy   A
liopoil   A
2.71828…   B
Dylan32   A
faust   A
ghostofmars   B
schadd   A
GendoIkari   B
LaLight   A

Tower A: 8/20
Tower B: 3/13
All other towers: 0/??

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Re: Math Games
« Reply #406 on: February 26, 2017, 08:04:06 pm »

Deadline for Round 2 will be 8pm tomorrow (Monday).
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Re: Math Games
« Reply #407 on: February 27, 2017, 08:01:54 pm »

Round 2 Results:

Calamitas   A
UmbrageOfSnow   (no submission)
gkrieg13   A
sudgy   A
liopoil   (no submission)
2.71828…   A
Dylan32   A
faust   B
ghostofmars   A
schadd   A
GendoIkari   A
LaLight   A

Tower A: 17/20
Tower B: 4/13
All other towers: 0/??

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Re: Math Games
« Reply #408 on: February 27, 2017, 10:41:26 pm »

Deadline for Round 3 is 8pm tomorrow (Tuesday).
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Re: Math Games
« Reply #409 on: February 28, 2017, 08:06:46 pm »

Round 3 Results:

Calamitas   B
UmbrageOfSnow   (no submission)
gkrieg13   B
sudgy   A
liopoil   B
2.71828…   B
Dylan32   A
faust   F1
ghostofmars   D
schadd   A
GendoIkari   G1
LaLight   (no submission)

Tower A: 20/20
Tower B: 8/13
Tower D: 1/(3-8)
Tower F1: 1/6
Tower G1: 1/4
All other towers: 0/??

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Re: Math Games
« Reply #410 on: February 28, 2017, 08:07:23 pm »

Deadline for Round 4 is 8pm tomorrow (Wednesday).
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Re: Math Games
« Reply #411 on: March 01, 2017, 08:07:16 pm »

Thread Unlocked

Results coming soon
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Re: Math Games
« Reply #412 on: March 01, 2017, 08:09:20 pm »

Round 4 Results:

Calamitas   B
UmbrageOfSnow   (no submission)
gkrieg13   D
sudgy   B
liopoil   G1
2.71828…   B
Dylan32   B
faust   G1
ghostofmars   B
schadd   F1
GendoIkari   B
LaLight   B

Tower A: 20/20
Tower B: 15/13
Tower D: 2/(3-8)
Tower F1: 2/6
Tower G1: 3/4

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Re: Math Games
« Reply #413 on: March 01, 2017, 08:11:08 pm »

Ya looking back I should've placed my last block on G1, but didn't have enough time to think about it (not because of the deadlines, just was a busy day)
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Re: Math Games
« Reply #414 on: March 01, 2017, 08:11:20 pm »

Everyone except schadd and UmbrageOfSnow gets 47 points.  (schadd gets 30.)

In retrospect I think I made things worth too many points.
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Re: Math Games
« Reply #415 on: March 01, 2017, 08:12:30 pm »

Also, unless he responds before the next game starts, I'm going to auto-/out UmbrageOfSnow for inactivity (sorry!).
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Re: Math Games
« Reply #416 on: March 01, 2017, 08:16:02 pm »

The next game probably will not start until at least Friday night, possibly later.  I want to make sure the game works and is interesting and I don't have a lot of time tomorrow.
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Re: Math Games
« Reply #417 on: March 01, 2017, 08:17:27 pm »

did i forget to pollinate B


i figured F1 would work out because of sheeping faust and whatnot. but i also forgot that i spent all of my other labor seeing A to fruition
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Re: Math Games
« Reply #418 on: March 01, 2017, 08:42:30 pm »

I feel like the strategy was a bit too obvious for this one.  Everybody wants points, so if everyone puts their pieces on the high point towers then everyone wins.
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Re: Math Games
« Reply #419 on: March 01, 2017, 09:05:05 pm »

I feel like the strategy was a bit too obvious for this one.  Everybody wants points, so if everyone puts their pieces on the high point towers then everyone wins.
As someone on the sideline, it might have been a good idea to use your first two actions on towers that weren't the most obvious, to entice other players to use their last two actions on those same ones.
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Re: Math Games
« Reply #420 on: March 01, 2017, 09:19:53 pm »

PSA: Don't send your PMs to Scott Pilgrim, send them to scott_pilgrim. That's what happened to me in round 2.

I had intended to build tower B in round 2. Had that worked out, I would have built F1 in round 3. Then since faust and I both played A in round 1 and G1 in round 4, we actually made the same decisions every single round, which is neat.

It was pretty unlucky that in round 3 three different people did three different things (D,F1,G1). I thought F1 was best because we could clearly complete A,B, and F1 with some wiggle-room to spare. I can understand choosing G1 but F1 should have been achievable. Tower D just seems strictly worse? After round 3 though it was doubtful that F1 could happen so I went for G1, since I was confident that B would complete.
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Re: Math Games
« Reply #421 on: March 01, 2017, 10:33:43 pm »

I feel like the strategy was a bit too obvious for this one.  Everybody wants points, so if everyone puts their pieces on the high point towers then everyone wins.

Yeah, I agree that this game didn't end up being as interesting as I had intended.  I was a little surprised that no one went for a smaller tower in the first two rounds, because as Axxle pointed out, there is a benefit to going for a less obvious tower earlier on.  Somehow I convinced myself that it made sense for the points vs. blocks to be superlinear, but I think it maybe would have played out more like how I intended if it had been sublinear.
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Re: Math Games
« Reply #422 on: March 03, 2017, 11:31:35 am »

Bump?
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Re: Math Games
« Reply #423 on: March 03, 2017, 12:58:48 pm »

Bump?

The next game probably will not start until at least Friday night, possibly later.
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Re: Math Games
« Reply #424 on: March 03, 2017, 12:59:44 pm »

Missed that, thanks!
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Re: Math Games
« Reply #425 on: March 03, 2017, 02:43:41 pm »

Any thoughts on an expected number of rounds/games? It's fun and all, but I'm a person who plays to get to the end; not just to keep going. So after another game or 2, if the plan is still to just continue to keep it going indefinitely, I might bow out.
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Re: Math Games
« Reply #426 on: March 03, 2017, 03:27:31 pm »

Hm. I am more for playing indefinitely. I like those games.
Maybe there can be end of games and Math Games 2. I am okay with this also.
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Re: Math Games
« Reply #427 on: March 03, 2017, 07:18:15 pm »

Any thoughts on an expected number of rounds/games? It's fun and all, but I'm a person who plays to get to the end; not just to keep going. So after another game or 2, if the plan is still to just continue to keep it going indefinitely, I might bow out.

The plan is to just keep going indefinitely, until I run out of ideas or time (the latter seeming more likely).  The intent of the format is to just be an endless series of mini-games, where by default, playing in one game auto-/ins you to the next game, and you have one common resource (points) that very roughly tells you how you're doing over all of them.  At least that's sort of how I see it, but obviously it's up to the players to make of it what they want.
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Re: Math Games
« Reply #428 on: March 03, 2017, 07:56:49 pm »

Thread Locked
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Re: Math Games
« Reply #429 on: March 03, 2017, 07:59:25 pm »

(Before I forget)

Group A:
Calamitas
sudgy
Dylan32
ghostofmars
schadd

Group B:
gkrieg13
liopoil
faust
GendoIkari
LaLight
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Re: Math Games
« Reply #430 on: March 03, 2017, 08:01:52 pm »

7. Simultaneous Poker   

Rules   

Players will be split up into two groups.  Each group will play the game among themselves, independently of the other group.   
This game will be played for two rounds (sub-divided into "turns").  The rules in each round are the same.   
Each player will be dealt a random number from 0 to 1, kept secret from all other players.  Each player is forced to put 1 point into the pot.   
During each turn, each player may PM me with one of the following three options:   
   Fold: The player forfeits the round.
   Raise x: The player pays x points to the pot.
   Call: The player pays points to the pot to match the maximum raise on the previous turn.  (That is, the total amount of points you have put into the pot thus far will match the total number of points the highest raiser in the previous round has put into the pot.)
A player cannot raise so that the total amount of points they have put into the pot is less than (or equal to; in this case, you would just call) the total amount of points some other player has put into the pot as of the end of the previous round.  For example, if I have put 7 point into the pot total and you have put 4, on the next round you must raise at least 4 if you are going to raise.   
After I receive PM's from all players or deadline is reached*, I will post the results in the thread, and a new turn will begin.  *Anyone who does not submit a move before deadline will automatically fold.   
Play continues until a turn occurs in which no players raise.  There are 3 cases:   
   1. Only one player has not folded.
   2. All remaining players folded on that turn.
   3. Two or more players called on that turn (but no one raised).
In case 1, the player who did not fold wins the pot.   
In case 2, the players who folded simultaneously reveal their hand.  The player with the highest value wins the pot.   
In case 3, the players remaining (those who have not folded) reveal their hand.  The player with the highest value wins the pot.   
Players cannot raise so that their total bet for the round is greater than 10.   

Example Round   
Alice is dealt 0.736042; Bob is dealt 0.592796; Carolyn is dealt 0.558015; Diana is dealt 0.528742.   
Turn 0: Everyone puts a point into the pot; the pot is now 4 (A1 B1 C1 D1).   
Turn 1: Alice raises 3; Bob calls; Carolyn raises 1; Diana calls; the pot is now 8 (A4 B1 C2 D1).   
Turn 2: Alice raises 1; Bob calls (matching Alice's 3 raise from last round, putting 3 points into the pot); Carolyn calls (also matching the 3 raise, putting 2 more points into the pot); Diana folds; the pot is now 14 (A5 B4 C4 D1).   
Turn 3: Alice calls; Bob calls (matching Alice's 1 raise from last round); Carolyn folds; the pot is now 15 (A5 B5 C4 D1).   
Showdown: Alice has a better hand than Bob, so she wins the pot (15 points).  The net effect is that Alice scored 10 points, Bob lost 5 points, Carolyn lost 4 points, and Diana lost 1 point.   
   
Note: It is impossible for players to tie at showdown.  The numbers you are dealt will have arbitrarily many digits.  If you would like more digits, please PM me with the number of digits you would like me to send you (within reason).  I will default to send 10 digits.   
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Re: Math Games
« Reply #431 on: March 03, 2017, 08:02:12 pm »

PM's are going out now.
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Re: Math Games
« Reply #432 on: March 03, 2017, 08:07:37 pm »

PM's are out, please let me know if you did not get one, or you got two, or anything crazy like that.
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Re: Math Games
« Reply #433 on: March 03, 2017, 08:17:27 pm »

Please ask if you have questions about the rules.  There should be no reason to fold on the first turn, since calling will not require you to add anything to the pot (you would just be calling the baseline bet of 1, which you were already forced to pay; you can think of it as a check).

I will not reveal players' "hands" (even after the game) (assuming no showdown for that player), unless specifically requested by the player.  (You can show other people your own hand if you want, but you can't show everyone someone else's hand.)
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Re: Math Games
« Reply #434 on: March 03, 2017, 09:27:29 pm »

   1. Only one player has not folded.
   2. All remaining players folded on that turn.
   3. Two or more players called on that turn (but no one raised).

(Someone has pointed out that case 2 here should (in theory) never actually happen, because there will always be at least one player for whom calling is strictly better than folding.  But in case it does happen, the resolution will be to showdown among the folding players.)
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Re: Math Games
« Reply #435 on: March 04, 2017, 07:57:43 pm »

Round 1.1 Results:

Group A      
Calamitas   Call   (1)
sudgy   Call   (1)
Dylan32   Call   (1)
ghostofmars   Call   (1)
schadd   Raise 3   (4)
Pot   8   
      
Group B      
gkrieg13   Raise 3   (4)
liopoil   Call   (1)
faust   Raise 4   (5)
GendoIkari   Raise 2   (3)
LaLight   Raise 7   (8)
Pot   21   
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Re: Math Games
« Reply #436 on: March 04, 2017, 07:58:09 pm »

Deadline for the next turn will be 8pm tomorrow (Sunday).
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Re: Math Games
« Reply #437 on: March 05, 2017, 08:52:15 pm »

Round 1.2 Results:

Group A:
Calamitas   Fold*   (1)
sudgy   Fold   (1)
Dylan32   Fold   (1)
ghostofmars   Fold   (1)
schadd   Call   (4)
Pot   8   

*Calamitas has asked that I flip his hand.  He had 0.2168092925.

schadd wins the pot!  Group A can take a break for now.

Group B:

gkrieg13   Call   (8)
liopoil   Fold   (1)
faust   Call   (8)
GendoIkari   Fold (no submission)   (3)
LaLight   Raise 2   (10)
Pot   30   
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Re: Math Games
« Reply #438 on: March 05, 2017, 08:52:46 pm »

Deadline is 9pm tomorrow (Monday).
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Re: Math Games
« Reply #439 on: March 07, 2017, 07:14:50 pm »

Sorry for the delay.  Round 1 Results (Group B):   
gkrieg13   Call   (10)
liopoil   (out)   (1)
faust   Call   (10)
GendoIkari   (out)   (3)
LaLight   Call   (10)
Pot   34   

Showdown:
gkrieg13   0.8022158101
faust   0.8900745291
LaLight   0.8908475963

LaLight wins the pot!  (Yes, those were completely fairly generated random numbers, they just happened to come out extremely close.  Sorry faust!)
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Re: Math Games
« Reply #440 on: March 07, 2017, 07:21:39 pm »

PM's for round 2 going out now.
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Re: Math Games
« Reply #441 on: March 07, 2017, 07:25:50 pm »

PM's have been sent.  Let me know if you didn't get one.

Deadline for the first turn will be 7:30pm tomorrow (Wednesday).
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Re: Math Games
« Reply #442 on: March 08, 2017, 07:31:05 pm »

Round 2.1 Results:

Group A      
Calamitas   Raise 5   (6)
sudgy   Call   (1)
Dylan32   Raise 4   (5)
ghostofmars   Call   (1)
schadd   Raise 4   (5)
Pot   18   
      
Group B      
gkrieg13   Fold   (1)
liopoil   Raise 1   (2)
faust   Call   (1)
GendoIkari   Raise 2   (3)
LaLight   Fold   (1)
Pot   8   
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Re: Math Games
« Reply #443 on: March 08, 2017, 07:31:33 pm »

Next deadline is 7:30pm tomorrow (Thursday).
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Re: Math Games
« Reply #444 on: March 09, 2017, 11:05:22 pm »

Round 2.2 Results:

Group A      
Calamitas   Raise 4   (10)
sudgy   Raise 6   (7)
Dylan32   Call   (6)
ghostofmars   Fold   (1)
schadd   Call   (6)
Pot   30   
      
Group B      
gkrieg13   (out)   (1)
liopoil   Raise 7   (9)
faust   Fold (no submission)   (1)
GendoIkari   Raise 2   (5)
LaLight   (out)   (1)
Pot   17   
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Re: Math Games
« Reply #445 on: March 09, 2017, 11:05:59 pm »

Deadline for the next turn is 11:00pm tomorrow (Friday).
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Re: Math Games
« Reply #446 on: March 10, 2017, 11:53:07 pm »

Round 2.3 Results:

Group A      
Calamitas   Call   (10)
sudgy   Call   (10)
Dylan32   Fold (no submission)   (6)
ghostofmars   (out)   (1)
schadd   Call   (10)
Pot   37   
      
Group B      
gkrieg13   (out)   (1)
liopoil   Call   (9)
faust   (out)   (1)
GendoIkari   Raise 5   (10)
LaLight   (out)   (1)
Pot   22   
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Re: Math Games
« Reply #447 on: March 10, 2017, 11:55:23 pm »

2.4 deadline will be 12:00am midnight Sunday morning (Saturday night).  I'll probably be more lenient with this deadline because daylight saving confuses things.
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Re: Math Games
« Reply #448 on: March 10, 2017, 11:56:21 pm »

Sorry, I forgot Group A is done.  I'll post Group A's results in a minute.
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Re: Math Games
« Reply #449 on: March 10, 2017, 11:58:55 pm »

Calamitas: 0.8601418643
sudgy: 0.8533320514
schadd: 0.2087306719

Calamitas wins the pot!
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Re: Math Games
« Reply #450 on: March 12, 2017, 10:26:43 am »

Thread Unlocked
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Re: Math Games
« Reply #451 on: March 12, 2017, 10:27:20 am »

Round 2 Results:

Group B      
gkrieg13   (out)   1
liopoil   Fold   9
faust   (out)   1
GendoIkari   Call   10
LaLight   (out)   1
Pot   22

GendoIkari wins the pot!   
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Re: Math Games
« Reply #452 on: March 12, 2017, 10:28:41 am »

I think that's going to be the last game.  I may resume this at some point but right now I'm having trouble keeping up with it.
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Re: Math Games
« Reply #453 on: March 12, 2017, 10:31:12 am »

Man I got lucky in round 1; I had .832 and was planning on going to 10 if necessary. But forgot to send a PM in time and auto folded instead, losing less than I would have.

Also had .92 in the second round; super lucky.
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Re: Math Games
« Reply #454 on: March 12, 2017, 10:36:10 am »

I was really lucky in the first one, sorry, faust!
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Wins: 15, 10
Losses: 11, 5, 1
Draws: 1
MVPs: 4
Mod/Co-mod: 18

I always have a limited access to forum on weekends.

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Re: Math Games
« Reply #455 on: March 12, 2017, 10:38:02 am »

Round 1.2 Results:

Group A:
Calamitas   Fold*   (1)
sudgy   Fold   (1)
Dylan32   Fold   (1)
ghostofmars   Fold   (1)
schadd   Call   (4)
Pot   8   

c:


0.5058297418
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Re: Math Games
« Reply #456 on: March 12, 2017, 10:42:57 am »

Thanks for your donation, schadd :D

Was pretty lucky though, .86 was great.
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Town (5/9): M85, RMM35, M87, NM9, M90RMM38, M92, M91, M102,
Scum (3/3): M84, M88, M100

MVPs (1): M84

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Re: Math Games
« Reply #457 on: March 12, 2017, 10:45:02 am »

I think that's going to be the last game.  I may resume this at some point but right now I'm having trouble keeping up with it.
Sad to hear that, it was great fun :(
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Oh, i just don't like mafia games.

Town (5/9): M85, RMM35, M87, NM9, M90RMM38, M92, M91, M102,
Scum (3/3): M84, M88, M100

MVPs (1): M84

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Re: Math Games
« Reply #458 on: March 12, 2017, 03:23:18 pm »

Thanks for your donation, schadd :D

Was pretty lucky though, .86 was great.

I wouldn't have felt nearly so cheated if you had had 0.9-something...
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Re: Math Games
« Reply #459 on: March 12, 2017, 05:05:33 pm »

Man I got lucky in round 1; I had .832 and was planning on going to 10 if necessary. But forgot to send a PM in time and auto folded instead, losing less than I would have.

Also had .92 in the second round; super lucky.
Wow uh that is quite the opposite of my hands, very lucky indeed :/
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Re: Math Games
« Reply #460 on: March 12, 2017, 05:48:58 pm »

Man I got lucky in round 1; I had .832 and was planning on going to 10 if necessary. But forgot to send a PM in time and auto folded instead, losing less than I would have.

Also had .92 in the second round; super lucky.
Wow uh that is quite the opposite of my hands, very lucky indeed :/

So was your raise to 9 a pure bluff? It made me think for a minute about dropping out, but I figured you were either bluffing or in the high .8's.
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Re: Math Games
« Reply #461 on: March 13, 2017, 12:09:31 am »

Man I got lucky in round 1; I had .832 and was planning on going to 10 if necessary. But forgot to send a PM in time and auto folded instead, losing less than I would have.

Also had .92 in the second round; super lucky.
Wow uh that is quite the opposite of my hands, very lucky indeed :/

So was your raise to 9 a pure bluff? It made me think for a minute about dropping out, but I figured you were either bluffing or in the high .8's.
Yeah it was a bluff. I figured if you were under .85 or so there was a good chance that's you'd fold.
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Re: Math Games
« Reply #462 on: July 08, 2020, 12:25:05 pm »

3. Quarters on a Chess Board

Rules
Note: The thread will remain unlocked for the first 72 hours of the game; however, this is a zero-sum game and it is not in your interest to give the other teams hints.   
Players will be split up into pairs*.  This game will only be played once.  Players will be paired up like: highest and lowest scoring players together, then second highest and second lowest, etc.   
Each pair will have one player be assigned to role A and the other assigned to role B (chosen randomly).   
Each pair will be given roughly 72 hours to communicate with each other in a QT I will send them.  After this time period, THERE IS TO BE NO COMMUNICATION AMONG PLAYERS AT ALL REGARDING THIS GAME.  The thread and QT's will be locked at that time.   
After the 72 hour communication-period is up, the player in role A will be privately given an 8x8 grid of H's and T's, representing quarters in either the heads or tails position respectively, on a chess board.   
Additionally, four squares on the board will be marked blue (good), and one will be marked red (best).   
The player in role A must choose exactly one of the quarters on the board to "flip" (change from H to T or T to H).  Submit your selection by PM to the mod within 24 hours.  (Do not copy your partner or anyone else in the PM.)   
The state of the board (excluding the red and blue squares) after the quarter has been flipped will then be sent to player B.  (Note that they will not be told which quarter was flipped.)
Player B may then choose any one square on the board, within 24 hours of receiving the board.   
Scoring is determined as follows (per player):   
Player B guesses the red square:   12
Player B guesses a blue square:   3
Player B does not guess either a blue or red square:   Negative points so that the total points among all players is 0 and the "losing" players all get the same number of points, rounding down if necessary to avoid non-integers.

If each team guesses either a blue or red square, the negative points will be distributed among the teams who guessed blue squares.  If all teams guess the red square, no one will get any points.

*Since there is an odd number of players, there will need to be one team of 3.  I'll list the teams in the next post.


Hey, 3Blue1Brown just did a great video on basically this same game! (Exactly the same except there's only 1 "best" square; no "good" squares.

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