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Author Topic: [Discussion] DominionStrategy Qualifier for 2012 US National Championships  (Read 49349 times)

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timchen

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #75 on: June 25, 2012, 10:11:18 am »
0

Quote
points vs wins

Here's the best example I can see for a points system: 1-1-4-4 vs 1-2-2-2.  Maybe you think the second player here should advance: but note that under pretty much any system other than 4-3-2-1, the first player is going to advance no matter what.  Does everyone really think 1-2-2-2 is clearly superior to 1-1-4-4? 

I worry that if I implement that, the Day 2 results topic will be "omg kingmaking!".  Yeah, you play screwy when you're P4 and go for TMap x2, but you also play screwy when you realize the other person is gunning for second and will happily end it in a losing position.

Note also that neither player could have possibly qualified yesterday.
With all due respect, I still don't see why you think someone gunning for second (if they can!) is more likely being affected. Who can screw them up anyway? If you are playing for the first place? If so you have every right to screw everyone. If you are gunning for 2nd place yourself? Dunno why you want to do that, but if you do, I find it justified as well. If you are 3rd or 4th and just want to screw people? This problem is there already, and even more severe with winner-take-all.

Quote
3p v 4p

Maybe the best way to do this is to make sure 3p games don't happen, somehow.  It is unfair no matter what.  Either you basically can never advance out of a 3p pod, or you get a great chance of advancing.
I don't like the comment you say it is unfair no matter what. Specifically if you use 1 2/3 1/3 0 for 4 players and 1 1/2 0 for 3 players and 4 games for 4 players and 3 games for 3 players, the average score per game sounds like a fair standard. Sure you are more likely to get first place in a 3 player game; but you are also more likely to get last place, which is as damaging in this scoring system.
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theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #76 on: June 25, 2012, 10:15:01 am »
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Specifically if you use 1 2/3 1/3 0 for 4 players and 1 1/2 0 for 3 players and 4 games for 4 players and 3 games for 3 players, the average score per game sounds like a fair standard.

I like this a lot.  Let's go with the following system for Day 2, and give it a shot:

4p:

3 points for win
2 points for second
1 points for third
0 points for fourth

3p:

3 points for win
1.5 points for second
0 points for third
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #77 on: June 25, 2012, 10:15:58 am »
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Quote
3p v 4p

Maybe the best way to do this is to make sure 3p games don't happen, somehow.  It is unfair no matter what.  Either you basically can never advance out of a 3p pod, or you get a great chance of advancing.
I don't like the comment you say it is unfair no matter what. Specifically if you use 1 2/3 1/3 0 for 4 players and 1 1/2 0 for 3 players and 4 games for 4 players and 3 games for 3 players, the average score per game sounds like a fair standard. Sure you are more likely to get first place in a 3 player game; but you are also more likely to get last place, which is as damaging in this scoring system.

That's unfair because, as I keep trying to point out, a 3p win =/= 4p win.

I actually agree with theory. No one point system will be completely fair, because we all value different things and 3p and 4p are almost as different as 2p and 3p.
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theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #78 on: June 25, 2012, 10:17:25 am »
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The difference being, under this system, your expected value is the same regardless of which group you enter.  In other words, a priori, you would not choose to enter a 4p group or a 3p group.
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #79 on: June 25, 2012, 10:24:19 am »
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The odds of getting at least 20 points (an arbitrary number in the ballpark of what you should need to advance) in 3p is about 6.1%, while in 4p it's about 3.5%. So still, you're almost twice as likely to advance if you're in a 3p pod as opposed to a 4p pod if you assume equal ability. (Those numbers are 5 in 81 and 9 in 256 if anyone wants to check my math.)
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theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #80 on: June 25, 2012, 10:25:52 am »
+1

I'm confused.  Is this some probability thing I'm not getting?  Seems like you are expected to get exactly 1.5 points per game, and so you are therefore expected to get 1.5X points.
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theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #81 on: June 25, 2012, 10:30:49 am »
+2

Additional question: was the seat rotation that bothersome?  I.e., was it so terrible that the relative order remained fixed, such that we should try to explain and enforce:

A-B-C-D
D-C-B-A
B-A-D-C
C-D-A-B
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #82 on: June 25, 2012, 10:33:23 am »
+1

I'm confused.  Is this some probability thing I'm not getting?  Seems like you are expected to get exactly 1.5 points per game, and so you are therefore expected to get 1.5X points.

This is incorrect. Each game, assuming equal ability, you have an equal chance of 6, 4, and 2 points in 4p and 6, 3, and 0 points in 3p. If you do all the permutations of those, you end up with 256(4 to the 4th) possible results in 4p and 81 (3 to the 4th). So first, you have a 1 in 256 chance in getting 24 points in 4p, and a 1 in 81 in 3p. You have a 4 in 256 chance of getting 22 points in 4p. You have a 4 in 81 chance of getting 21 points.You have a 4 in 81 chance of getting 20 points in 4p.

I can post all the permutations if you like, but it would be quite long. The point is that no, it's not quite that simple.

Just FYI, I'm currently in my final year as a math major and have taken two stats courses. I'm absolutely positive these are correct.

EDIT: This is actually incorrect. The actual difference is only .3 percentage points, as is noticed later on. I made an error in my haste. Sorry, and thanks timchen!
« Last Edit: June 25, 2012, 10:52:53 am by zxcvbn2 »
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nopawnsintended

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #83 on: June 25, 2012, 10:36:26 am »
0

Interesting discussion.

My view is that the 3p versus 4p is a bigger difference than whether winner take all or points is adopted. 

I don't have much to add to the discussion except that I think it would be fun if two of the qualifying days were points and two were winner take all.  On a practical level, everyone could participate in their favorite qualifying format before the semis.  As an added benefit, you could use the semifinals as a "test" for whether winner take all or points selects better (making sure that two wta players get matched with two points players in each pod).  Of course, the format of the semifinals would matter a lot for the outcome of the test.  To increase the power of the test, I'd be up for a longer series in the semifinals.
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timchen

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #84 on: June 25, 2012, 10:38:06 am »
+2

I think you miscalculated. with 20 points (6-4-2-0) as a threshold, there are actually 15 cases (6 of them being 2 first places and 2 second places) so the chance for 4p is 15/256. 15/256 and 5/81 are close enough to me.

This difference is caused by the quantization of the points. it does not give definite advantage to 3p or 4p however (depending on the threshold.)

Just to respond to someone says he's absolutely correct: in 4p the cases are
1-1-1-1 (1) 24 pts
1-1-1-2 (4) 22 pts
1-1-1-3 (4) 20 pts
1-1-2-2 (6) 20 pts

so this is 15/256.

in 3p
the cases are
1-1-1-1 (1) 24 pts
1-1-1-2 (4) 21 pts

this is 5/81.

Sorry if this sounds a bit harsh, but I usually find claim of correctness based on who you are kinda laughable.  ;)
« Last Edit: June 25, 2012, 10:42:54 am by timchen »
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nopawnsintended

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #85 on: June 25, 2012, 10:39:08 am »
0

Additional question: was the seat rotation that bothersome?  I.e., was it so terrible that the relative order remained fixed, such that we should try to explain and enforce:

A-B-C-D
D-C-B-A
B-A-D-C
C-D-A-B

I noticed the "fixed" seating order in our pod (may have made a difference in the last game).  I thought that the suggestion to mix up the seats was one of the better ones in the thread.
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theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #86 on: June 25, 2012, 10:39:53 am »
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I'm confused.  Is this some probability thing I'm not getting?  Seems like you are expected to get exactly 1.5 points per game, and so you are therefore expected to get 1.5X points.
Just FYI, I'm currently in my final year as a math major and have taken two stats courses. I'm absolutely positive these are correct.
I don't doubt you at all!  There is a reason why rrenaud does all the math stuff and I do all the writing stuff :)
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #87 on: June 25, 2012, 10:40:45 am »
+1

I think you miscalculated. with 20 points (6-4-2-0) as a threshold, there are actually 15 cases (6 of them being 2 first places and 2 second places) so the chance for 4p is 15/256. 15/256 and 5/81 are close enough to me.

This difference is caused by the quantization of the points. it does not give definite advantage to 3p or 4p however (depending on the threshold.)

Crap, got me. Maybe absolute positive was the wrong phrase XP. Those are within .3 percentage points. I suppose that's acceptable. Thanks.
« Last Edit: June 25, 2012, 10:48:02 am by zxcvbn2 »
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #88 on: June 25, 2012, 10:44:08 am »
+1

Quote
Sorry if this sounds a bit harsh, but I usually find claim of correctness based on who you are kinda laughable. 

You're right. I'm sorry, that was low.
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WanderingWinder

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #89 on: June 25, 2012, 10:58:22 am »
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First off, I want to say that when I advocate below for point-systems, it's a general advocacy, and not meant for this tournament. I believe that this tournament should be winner-take all, because Nats are WTA, and more importantly because that's how the rules were laid out from the beginning.
Furthermore, I don't discuss how things ARE set up, because this is a discussion (at least the one I want to have) of how they SHOULD be set up, and the way things are has extremely little to no relevance on that.

Having said that:
The first big difference I see in points vs WTA is in what kind of play they promote. WTA encourages you to take risks, because all that matters is getting first place or not. Points encourages you to play some system which is less risky and more consistent. Note that you probably still ought to take SOME risks, as is inherent in all forms of dominion, and the direct amount of risks you take is dependent on which point system you select. On the surface, these are just two different things, with neither being straight better than the other. It's a preference thing. However, I have a strong preference for points, and let me explain why.
So there's the cliched treasure map example, which has so much baggage that I'm going to step away from it. Here's another example. Opening something like fortune teller/potion when the cheapest potion-cost card on the board is golem. Now, assuming the other player doesn't attack you or mess with you or anything (which may not be the best assumption given that there's an attack, but this is a concept that makes sense anyway), your probability of spiking a golem on your first reshuffle is a hair's breath over 1/3. This probably makes it totally worth it under a WTA format, assuming it's a deck where golem can help you out a lot. But on average, this is a play that actually HURTS your deck quality, hurts your position. I don't particularly like encouraging this, first of all, but let's dig a little deeper. If this really is worth it, then everyone does it, yes? I mean, if they're playing well, making the 'right' decisions, they're all going to do this, yeah? But the point is, you now all have marginal chances of making that hit. Most probably, one of you gets this advantage, and the other three are way behind, and there's a HUGE spin toward that one guy - not that the game is totally over, but he has a MUCH larger chance of winning - based solely on how the shuffle fell, right off the bat. Basically what I'm saying is that WTA promotes strategies where, on a larger number of boards, a small amount of luck makes a large amount of difference. And especially for competitive environments, I don't like that.

Second, there's the issue of the number of games you have to play to get clear results. This is the direct result of having more information carry over from the point system than WTA. If you play 8 4-player games, you don't have a great idea as to who the best players are by your WTA metric. Probably nobody has more than 4 wins, and because of the high variance from a single game, we don't have that great an idea that mr. 4-win or mr. 5-win is really the best guy. However, if you play points matches, you have a much better idea, because you have more data. Now, of course, if you think winning is the only thing that matters, you reject this assessment, because you don't think the points metrics are meaningful; and this is mostly a logistical issue, really. But my point is that if you accept metric A, WTA, you need more games for results to have the same stability you get in fewer games from metric B, a points-based system. Because A has a higher inherent coefficient of variation than B does.

Finally, there's the kingmaking stuff. Which gets its own post.

rrenaud

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #90 on: June 25, 2012, 11:03:53 am »
+1

[Logs aren't updated from yesterday's matches on council room yet, I'll post it when they are.]
I don't know what went wrong, but I think the updates are progressing now.
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rrenaud

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #91 on: June 25, 2012, 11:09:37 am »
+1

Advancing in the tournament is not about expected value, it's about the chance of being near the max, and the chance that players win is not 1/N.  I am not sure if simple models will really help you or mislead you.

Of course, still the best answer is don't have 3p games.  Can we come up with a system using alternates or previously qualified players filling up the brackets?
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #92 on: June 25, 2012, 11:13:00 am »
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Quote
Advancing in the tournament is not about expected value, it's about the chance of being near the max, and the chance that players win is not 1/N.  I am not sure if simple models will really help you or mislead you.

That's true, but there's already so much variance in 3 and 4 player games. By the time you put together values for skill, turn order, shuffle luck, etc., in four games it's practically a roll of the dice anyway, at least in such a small sample size (which I realize we don't have time for a larger one).
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nopawnsintended

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #93 on: June 25, 2012, 11:26:08 am »
+2

Of course, still the best answer is don't have 3p games.  Can we come up with a system using alternates or previously qualified players filling up the brackets?

As one of the first round qualifiers, I'm happy to fill in if there are not enough alternates to fill a full set of 4p games.  Not sure how people feel about the strategic aspect of previously qualified players, but I still think my incentive is to play as well as I can.
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timchen

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #94 on: June 25, 2012, 11:27:15 am »
+1

Advancing in the tournament is not about expected value, it's about the chance of being near the max, and the chance that players win is not 1/N.  I am not sure if simple models will really help you or mislead you.

Of course, still the best answer is don't have 3p games.  Can we come up with a system using alternates or previously qualified players filling up the brackets?
I think it is a least requirement for a fair method to pass the test of a simple model. Beyond that it's harder to say. For a good player for example (suppose that means he always get to ranked #1 or #2), seems a 3p game will benefit him. But in that case the difference is not as large as to average players if we try to tilt the rules to compensate this. And anyway I have the belief we don't really have an idea who are the better players at 4p.

I don't like substitutes. By definition they can't win; do I still expect they are playing to win? Using qualified players may solve this problem, but then the field is probably stronger than it should be. 

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Polk5440

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #95 on: June 25, 2012, 11:32:31 am »
0

The tournament was organized so quickly at the last minute, people are bound to disagree with how it is set up. I am just happy that there was a tournament. It's been fun so far.  It would have been better to have these discussions about structure before the tournament since there seems to be a tradeoff between fairness and fun. The way it's set up now with four players, everyone gets to play, everyone has a chance to win, and there is no down time. It's fun! I think it would be a big mistake to change the rules of the tournament while it's in progress unless there is an obvious, glaring, easily-fixable issue --which there isn't.

However, for the future, it would be worth thinking about what the ideal tournament would look like. To me, something like the on-line Starcraft tournaments would be a good fit for Dominion.  For example, see: <http://www.ign.com/ipl/starcraft-2/ipl4/tournament>. Starcraft is a real time strategy game of 2 or more players, but is at its most fair/strategic with two players. In particular:
     1. Tournaments have a large selection of approved maps (picked for symmetry/fairness) among which the ones played are randomly selected.  Likewise in Dominion there would be "tournament approved cards/kingdoms."
     2. There are pods in which a round robin tournament is played. Usually there are 4 pods and members determined by seed to have equal strength across pods. Everyone plays 1 on 1, best of three for the "point." Two player games avoid the hassle of trying to decide how to interpret 2nd-, third-, fourth-, ... place finishes.
     3. Winners of each pod compete in a elimination-style bracket tournament to determine the winner. (Ties within pod are broken by most games won, then sudden-death playoff.)

Really it's like having a mini football season with conference play then a post-season playoff all in one tournament. The downside of this would be significant set-up costs for administrators and more downtime for participants. But it is on-line, so times for each set of 3 games in the round robin can be organized ahead of time.

Even with two players there are concerns about fairness in Dominion that are not present in Starcraft -- namely first player advantage. Here we could take a cue from tennis. The reason you must win by two in tennis is that the server has a distinct advantage and to win and prove you are the better player, you must "break" your opponent's serves. This is also why each tennis match is so long and has so many parts (points, games, sets) even though it is a bracket-based tournament. To adapt this to Dominion and the structure outlined above: make it "first to 4, win by 2, alternating who goes first" instead of "best of 3."

The downside here is that it adds significantly to the number of games played.
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WanderingWinder

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #96 on: June 25, 2012, 11:35:54 am »
0

So, kingmaking stuff.
I think there are two problems here. One is the actual kingmaking, a la collusion. This can happen in any format, and you can't truly stop it in one as opposed to another. You can, of course, incentivize or disincentivize it, to an extent. So what the WTA people are worried about here is that I will 'prematurely' end the game because player B is ahead overall, and I need him to do poorly. Now, this is somewhat of a valid point, I will grant you. But typically, you're more interested in your own advancement, because you're playing against 4 other people, not just one. Furthermore, WTA doesn't really fix this. If wins are all that matter, and I'm in first, I'm liable to end the game WHENEVER my closest challenger isn't winning, regardless of how I'm doing. I mean, I can seriously just build a big engine that has really no way of getting victory points, but can pile things out relatively at will. This is a huge distortion of the game, of course. And you don't get it in points-based systems as much, because getting last, as you probably will doing this, hurts you more than just getting not-1st.
But I think the thing is with multiplayer games, you have to play not only the board, but also the other players. And that means that you have to react to what they're doing, to adjust the tempo vs staying power of your deck, to be able to deal with the different situations they present you with. Right? That's a huge multiplayer skill, and a big reason that multiplayer is a higher-variance game is that the more opponents you have, the less you can perfectly adjust to them.
How this deals with this, is the second post. The real important thing is to be able to have some ability to predict what your opponents will do. The best way to have this, is to have people to have dogs in the fight, i.e. they need to have something to play for. And in the WTA scenario, people who are way behind have to play only for other people's orderings. In the points-based scenario, they have their own ranking to play for. So people are much more predictable in the points-based scenario, because they have much more to play for. And that's what you really want. What you don't want is seemingly random 'it-doesn't-really-matter-what-I-do-at-this-point-for-myself' things that you get more often in WTA, because there's no way to improve your outcome more often in WTA.

WanderingWinder

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #97 on: June 25, 2012, 11:38:52 am »
+1

I'm confused.  Is this some probability thing I'm not getting?  Seems like you are expected to get exactly 1.5 points per game, and so you are therefore expected to get 1.5X points.
But as rrenaud says, expected value isn't important. Getting in the middle, or somewhat above average, doesn't matter. What matters is whether or not you get at or near the top. And as it's a LOT easier to win a 3-player than a 4-player, you have a significantly better chance of being able to qualify from the 3-player. I would a priori take the 3-player every time.
The other issue is that they're just such different games, 3p and 4p, that it's somewhat inherently unfair to try to compare them.

zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #98 on: June 25, 2012, 11:41:23 am »
0

potential tourney format

The problem we have isn't that we have a lack of tournament experience. We know how to set up two-player tournaments (or at least have a general idea about what's fair and what's not). We've already set up several tournaments with the DS finals earlier this year, several IsoDoms, and a couple of one day tournaments.

The trouble is that we're dealing with a type of tournament that we've largely avoided. We were forced to play 3-4 player matches, as to maintain a similar format to nationals/ world championships. This is something that we're pretty unfamiliar with, and we had a very short time to put it together. I think theory did a tremendous job in setting this up when we had so little time to discuss the semantics in a tournament that most here (including me) are a lot more unfamiliar with. I'm sure if we do a similar (multiplayer) tournament in the future, most players will be much happier with the format, because we'll have experience and more time to set it up.
« Last Edit: June 25, 2012, 11:43:46 am by zxcvbn2 »
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WanderingWinder

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #99 on: June 25, 2012, 11:42:16 am »
0

I think you miscalculated. with 20 points (6-4-2-0) as a threshold, there are actually 15 cases (6 of them being 2 first places and 2 second places) so the chance for 4p is 15/256. 15/256 and 5/81 are close enough to me.

This difference is caused by the quantization of the points. it does not give definite advantage to 3p or 4p however (depending on the threshold.)

Just to respond to someone says he's absolutely correct: in 4p the cases are
1-1-1-1 (1) 24 pts
1-1-1-2 (4) 22 pts
1-1-1-3 (4) 20 pts
1-1-2-2 (6) 20 pts

so this is 15/256.

in 3p
the cases are
1-1-1-1 (1) 24 pts
1-1-1-2 (4) 21 pts

this is 5/81.

Sorry if this sounds a bit harsh, but I usually find claim of correctness based on who you are kinda laughable.  ;)
Yeah, but this is still a problematic way of looking at it. There are this many ways of getting qualified, of course, but it is simply easier to get these cases form the 3p.
Importantly, it's not about getting to a point threshhold, it's about beating the other guys. The 3p are much more likely to produce a point total that is in the top X, as opposed to the 4p.
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