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#1
10-18-2005, 02:06 PM
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Re: Theory again: Let\'s take a couple of steps back
One possible way to factor the blinds in indirectly would be to look at the standard deviation of stack sizes. I'm guessing that the smaller the blinds are, the larger the standard deviation should be.
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#2
10-18-2005, 02:09 PM
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Re: Theory again: Let\'s take a couple of steps back
[ QUOTE ]
One possible way to factor the blinds in indirectly would be to look at the standard deviation of stack sizes. I'm guessing that the smaller the blinds are, the larger the standard deviation should be. [/ QUOTE ] I'm not sure that is the right way to do it. If you have one tournament that has 3 hour levels and another that has minute levels the stack size standard deviation may well be more time based than blind based but per/hand blind level should still matter.
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#3
10-18-2005, 02:11 PM
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Re: Theory again: Let\'s take a couple of steps back
[ QUOTE ]
[ QUOTE ] One possible way to factor the blinds in indirectly would be to look at the standard deviation of stack sizes. I'm guessing that the smaller the blinds are, the larger the standard deviation should be. [/ QUOTE ] I'm not sure that is the right way to do it. If you have one tournament that has 3 hour levels and another that has minute levels the stack size standard deviation may well be more time based than blind based but per/hand blind level should still matter. [/ QUOTE ] Good point. So much for that idea.
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#4
10-18-2005, 04:01 PM
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Re: Theory again: Let\'s take a couple of steps back
[ QUOTE ]
One possible way to factor the blinds in indirectly would be to look at the standard deviation of stack sizes. I'm guessing that the smaller the blinds are, the larger the standard deviation should be. [/ QUOTE ] What about expressing stack size in terms of BB's? This would allow you to estimate "BB-EV", rather than cEV, which is probably the more meaningful number anyway, right? Or maybe expressing it in terms of M would be better? It doesn't seem to me that the number of chips in your stack is meaningful in isolation, ie without knowledge of blinds/antes. Keep up the good work, this is interesting.
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#5
10-18-2005, 04:33 PM
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Re: Theory again: Let\'s take a couple of steps back
[ QUOTE ]
[ QUOTE ] One possible way to factor the blinds in indirectly would be to look at the standard deviation of stack sizes. I'm guessing that the smaller the blinds are, the larger the standard deviation should be. [/ QUOTE ] What about expressing stack size in terms of BB's? This would allow you to estimate "BB-EV", rather than cEV, which is probably the more meaningful number anyway, right? Or maybe expressing it in terms of M would be better? It doesn't seem to me that the number of chips in your stack is meaningful in isolation, ie without knowledge of blinds/antes. [/ QUOTE ] I thought about that, but if you express your stack in terms of M, the ratio ends up having the same value, because the size of the opening pot ends up in both the numerator and denominator. So it just drops out. I've thought of adding the average M as a factor, which would model both blinds and antes, but I haven't figured out how to factor it in, yet.
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#6
10-18-2005, 01:53 PM
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Re: Theory again: Let\'s take a couple of steps back
The more I think about this, the more I think that the random walk solution is as good as it's gonna get. We really need a dataminer to test that.
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#7
10-18-2005, 02:04 PM
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Re: Theory again: Let\'s take a couple of steps back
[ QUOTE ]
The more I think about this, the more I think that the random walk solution is as good as it's gonna get. We really need a dataminer to test that. [/ QUOTE ] The random walk method should work if and only if everyone is equally skilled. If you make that assumption, I'm sure it works fine. I'm trying to move beyond that, though.
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#8
10-18-2005, 02:12 PM
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Re: Theory again: Let\'s take a couple of steps back
[ QUOTE ]
[ QUOTE ] The more I think about this, the more I think that the random walk solution is as good as it's gonna get. We really need a dataminer to test that. [/ QUOTE ] The random walk method should work if and only if everyone is equally skilled. If you make that assumption, I'm sure it works fine. I'm trying to move beyond that, though. [/ QUOTE ] I think the random walk still works if people aren't equally skilled. The difference is it isn't an equally balanced random walk but rather an upwardly biased random walk (like the stock market) for an above average skill player or a downwardly biased randome walk (like perfect non-counting blackjack strategy) for a below average player. The question, which I agree is worth investigating, is does the size of the bias and the size of the steps in the random walk change also with factors like blind size and stack size and if so how does this effect the random walk models. So I think you can still do a random walk model and account for everything you are looking at and may end up thinking in WTA chip value is constant, but also may not, depending on the details of your random walk model.
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#9
10-18-2005, 02:21 PM
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Re: Theory again: Let\'s take a couple of steps back
[ QUOTE ]
I think the random walk still works if people aren't equally skilled. The difference is it isn't an equally balanced random walk but rather an upwardly biased random walk (like the stock market) for an above average skill player or a downwardly biased randome walk (like perfect non-counting blackjack strategy) for a below average player. The question, which I agree is worth investigating, is does the size of the bias and the size of the steps in the random walk change also with factors like blind size and stack size and if so how does this effect the random walk models. So I think you can still do a random walk model and account for everything you are looking at and may end up thinking in WTA chip value is constant, but also may not, depending on the details of your random walk model. [/ QUOTE ] OK, I'll buy that.
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#10
10-18-2005, 02:19 PM
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Re: Theory again: Let\'s take a couple of steps back
[ QUOTE ]
[ QUOTE ] The more I think about this, the more I think that the random walk solution is as good as it's gonna get. We really need a dataminer to test that. [/ QUOTE ] The random walk method should work if and only if everyone is equally skilled. If you make that assumption, I'm sure it works fine. I'm trying to move beyond that, though. [/ QUOTE ] So why not modify this theory instead of looking for new ones? I can't imagine that a person's % chance of coming in a certain place wouldn't be proportional to the results the random walk method returns. I think what you really need to look for is the ordered set of coefficients that modify these numbers. The first place coefficient is probably just affected by the skill of the player and the blind sizes relative to the player's stack. Something like (1+sign(k)|kS/B|^(1/2)), where k represents a player's skill (0 for average player), S is stack size, and B is blinds seems reasonable.
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