Your methodology for calculating win %

How are you calculating the win %? I'm assuming you wrote a program that calculates the pot equity given the board cards and hole cards. There may be an error with your program.

Having run similar experiments in the past, I feel like your earlier finding of SD = 14.2 to be extremely low. I'd have guessed a range of 8500 +- 3000 for an 80% interval after only 450 hands.

I think we need to clear something up

Whether or not he is making bad calls or bad all-ins doesn't change the analysis. Basically what he's doing is taking a situation like 8c8d vs. 7h6h on a flop like 8h9hAc. Say he's holding the 76 and he moves all-in on that board. In this situation with two cards to come, 88 will win 58% of the time and 76 will win 42%. So if the pot is $100 (excluding the amount of his all-in bet), he expects to win $42. If he's making poor choices in big pots or he bluffs too much, it should result in a higher than average SD.

In general, NL poker is a very high variance game and I'd expect the SD to be a multiple of mean. I track a different stat, the ratio of SD of hourly win-rate to average win-rate, and it is 24:1.

Oh, now it makes more sense

Can someone explain why you multiply the estimate of SD by the square root of the sample size?