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Author Topic: Math Games  (Read 60461 times)

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scott_pilgrim

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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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Calamitas

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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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Dylan32

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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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Calamitas

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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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schadd

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Re: Math Games
« Reply #354 on: February 20, 2017, 06:36:35 pm »

c:
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schadd

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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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I thought you thought it was a slip because I said 'Jake's partners' instead of 'Roadrunner7671.'

schadd

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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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2.71828.....

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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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Calamitas

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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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Calamitas

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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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pacovf

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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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liopoil

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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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liopoil

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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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sudgy

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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

GendoIkari

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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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Calamitas

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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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Calamitas

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Re: Math Games
« Reply #366 on: February 21, 2017, 12:21:20 am »

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sudgy

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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

LaLight

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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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liopoil

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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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faust

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

MVPs (1): M84

liopoil

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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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GendoIkari

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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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faust

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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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