[pete fabrizio]

i'm too lazy to do this right and come up with a general formula for you, but i've calculated the standard deviations on winrates over a number of hand milestones (using my sd/100 of 90):

10k hands: 9
20k hands: 6.36
50k hands: 4.02
100k hands: 2.84
200k hands: 2.01
500k hands: 1.27
1m hands: .9

so a 95% confidence interval should be around +/- 2 * the number above. e.g. about 5% of 6bb/100 winners will run at 8bb/100 over a million hands. and just for you, gordo, the sd over 22k hands is 6.07 bb/100. so in theory, a 95% confidence interval would be +/- ~12bb/100, so there's still a decent chance that your "true" winrate is below 2bb/100. specifically, about 5% of 2bb/100 winners will have your winrate over a 22k hand sample.

while this is a good place to start, it doesn't actually create a confidence interval for *your* winrate, since when you have a high observed winrate it's much more likely that you're running good than that you're running bad (e.g., there's really no chance that your true winrate is 26 bb/100). this could be corrected for in theory, but you'd need a good model for the distribution of winrates over the general population of players and I have no idea about that.