PokerTracker Stats Convergence

[Sciolist]

Does anyone know how quickly PT stats converge? For example, VPIP or PFR. What kind of sample size do you need for specific confidence intervals? What's the SD/100 of these stats? I have a vague idea of how to calculate it, but I don't know how to do it in practice.

[bbartlog]

Generally speaking, a good approximation for the SD for count of infrequently occuring events is the square root of the expected number of occurences. So, for example, we expect to get dealt AA once every 221 hands. If we play 22100 hands, we should be dealt AA a hundred times, but the SD of the actual count will be approximately 10 (square root of 100). If our preflop raise percentage is 20%, the SD is 66.5 (of 4420 occurences) which translates to 0.3% - so our CI around 20% can be fairly narrow. As you can see the confidence intervals will be a lot tighter for things that occur with a reasonable frequency.

In my experience some things in poker tracker converge very quickly (for example VP$IP) while other would require a very large number of hands to converge, for example the return on playing 67 suited in no limit hold'em. The problem with the latter is that infrequent events weigh heavily on the average; e.g. you can expect to get stacked by a higher flush substantially less than 1% of the time you play this hand, but the number of those events is quite variable and at 100BB per each will presumably have a significant impact on the average return.

[Sciolist]

I want to be able to calculate my exact confidence in some statistics though. For example, if I have 100k hands on someone (e.g, me), I want to know how confident I can be that my VPIP is right, or my AGF, assuming I played the same through the whole sample.

This because much more useful when you have 10k hands on someone, or 1k, or 100. Then you can apply it to other factors, like folds to cbet, etc.