|
Originally Posted by fishstick
first off, i will say that i am not a stat/math guy. i have a biostatistician friend looking at this and he's talking markov models to help determine sample size. markov models make my brain hurt. i'll be curious to see what he comes up with.
A Markov chain is a good way to model your bankroll, but it doesn't really address the issue at hand.
You still have to model the win rate as a random variable with a given mean and variance. Markov doesn't get around the fact that your mean win rate will be a small number compared to the variance of your win rate. Model a random walk with your mean and SD and see how easy it is to eyeball the slope of the line to see what I mean.
If you go with standard sample size calculations, where you replace the population standard deviation with the sample standard deviation, the results will be much smaller than I quoted earlier, but still quite large. For example, assume you wanted to be 95% sure that your win rate was within 1 BB of the sample mean given a standard deviation of 35. Then you would need (1.96*35/1)^2 = 4706 samples = 470,600 hands. If you wanted to be within 2BB, it would be about 1/4 of that, or 118,000 hands.
At 10,000 hands, if your mean and SD are still the same, you can be 95% sure that your win rate is greater than 1.
Originally Posted by fishstick
regarding standard deviation - my non-statistical mind says that the SD will NOT converge due to the nature of no limit holdem, and that we should be looking for a stabilization of the SD, while still continuing to show a profit.
am i way off base here?
If you mean that your SD may not decrease, I agree with that, but it should converge to a relatively small range (perhaps around 35, perhaps higher, perhaps lower).
|