Theory again: Let's take a couple of steps back

[AtticusFinch]

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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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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.

[AtticusFinch]

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.

[SumZero]

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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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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.

[AtticusFinch]

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We really need a dataminer to test that.

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Yep. Specifically, I need data from successful players to see if this holds water. If my theory is correct, then an average player's results would still pretty much be a random walk, at least until the field thinned out to include mostly stronger players.

[AtticusFinch]

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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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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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Good point. So much for that idea.

[SumZero]

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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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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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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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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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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.

[AtticusFinch]

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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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OK, I'll buy that.

[AtticusFinch]

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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.


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I actually agree with this. In fact, this is exactly the sort of method I'd like to arrive at at the end of this effort. What I'm really trying to produce is a formula for weighting a random walk model, not an absolute estimate. But, one step at a time.

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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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Once again, we're thining along similar lines. I just think the Verhulst formula is a promising way of generating coefficients to use as weightings in a probabilistic model.

[PrayingMantis]

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I'd like to try to model the rate at which a person of a given skill can be expected to grow his stack over time.

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Atticus, "given skill" is an extremely vague factor. In other words, in order to get to any remotely reasonable model, you'll first need to accurately quantify skill for any specific player. You'll have an extrememly difficult time doing this. As you know, MTTs results come with a huge variance. For instance, there are quite a lot of MTT players on the big sites who are considered to be great players and big winners, while in fact they are losers or breaking-even players for the long run, or simply running hot for a short while. So you'll have to make sure the players whom their skill you're "quantifying" are sure winners in a big enough sample. This should actually be a huge sample in terms of MTTs played. That's a big problem.

Now, beside the technical problem, there's a logical loop here. Think about it, what will be your criteria for quantifying skill? surely, you'll have to base it upon ALL the past results of player X, who you are "measuring", that is, you'll have his entire hand-histories, and will know how he did in each MTT. However, that will mean that you already HAVE his "avergae cEV" for a hand (which is what you're after according to your post) since it is simply in the DATA you're using! So you don't need any complex theoretical model in order to calculate it... You just KNOW it as a fact.

(It is similar to creating a very complex model in order to determine how much the best winning players "should" win in a ring game, i.e, BBs for 100 hands or per hour, which is practically the same as your "average cEV". Now what sense is there in creating such a model when you in fact HAVE the actual information, coming from the winning players themselves? And of course, many winning players have different "average cEV", because each of them have a specific ability, and is better or worse than others. A "model" that is meant to predict all this will be pretty much meaningless.)

So this is moving in circles, if at all.