Re: Every [censored] time
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the probability of a bet or raise is also 30%
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I don't think you can do that. Bets and raises are distinct random variables. For example, the SD of two binomial with mean .15 is about 9% greater then the SD of one with mean .01 and one with mean .29 after 10K hands.
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that's true if we are taking the sum/average of two binomials. but if we select the result of one binomial distribution with probability 1/2 and the result of the other binomial distribution otherwise, then it's exactly the same as a single binomial with mean .15. this is obvious because the resulting distribution will simply correspond to selecting 1 with probability 1/2*.1+1/2*.29=.15 and selecting 0 otherwise. our case corresponds to this latter scenario since the definition of AF doesn't distinguish between bets or raises so all we care about is the probability that either a bet or a raise happens. the only thing is we don't know this probability exactly but whatever it is the standard deviation is clearly less than 5% in 100hands since 5% is the maximum possible sd for a binomial. but it's pretty close to 5% if that probability is around 30%.
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sqrt((5/30)^2+(5/30)^2)*(30/30)
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I see where the numbers come from but I'm not sure why your doing it. I guess you're saying that the SD of one binomial RV divided by another is the sqrt of (variance of the first plus the second) times the ratio of one to the other. Conceptually I have some concerns about this. Could you link me to something that talks about that?
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i studied this formula in one of my undergrad physics classes. it's not an exact expression for the sd of a ratio but it's a good approximation. it can be derived from taking F(A,B)=A/B where A and B are your two binomials and expanding dF=(dF/dA)*dA+(dF/dB)*dB = F*(dA/A - dB/B). the estimate gets more and more precise as the sample size increases because then dA and dB get smaller and smaller compared to A and B.
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of course a better, but slightly longer way of doing is is to examine data from pt for small samples of hands and see how AF fluctuates. or better yet, write an sql query.
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Well different AF are going to converge at different rates so this would be kind of hard. It's not impossible or statistically unsound though.
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i agree that this is statistically sound but disagree that this is hard. it doesn't matter that different AF converge at different rates. you just take any AF you care about (flop, turn, total, whatever), and examine how it fluctuates. it's not normally distributed of course but who cares if all we want to know is how good the estimate becomes after so and so hands. if i'm feeling not too lazy i might write an sql query to do that for me at some point.
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as for my 100th post calculation, what assumptions are you wondering about? if you mean the relationship between wtsd and fold to bet, i got it simply by looking at pahud stats various players. these variables are strongly correlated.
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While I believe you looked at it and saw a good correlation, these things have some complex dynamics. It's not as if fold to bet=1-WtSD.
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yes, of course, i never claimed otherwise. but this correlation is sufficient to derive an order of magnitude correction to the AF, which was my concern. with the limited number of hands we have on villains that's all we really care about.
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