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Great post Jax. And also along the lines of Pedigree's post, if playing 20k hands doesn't give you an idea of your winrate how many hands will?

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I think this is the hard part, as Jax mentions there is so much variance that it is very hard to know where your "true" winrate is from your empirical winrate.

Here is an exerpt from a post by MrWookie from a while back that I thought was really nice:

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My personal metric is, for play at a particular level, to know to within two standard errors (about 98% confidence) that I am a winning player. That is, that my win rate is twice or more as big as the uncertainty of my win rate. To compute the uncertainty of your win rate, take your standard deviation per 100 hands, usually about 15 BB/100, and divide it by the square root of the number of hands you’ve played divided by 100 (the number of 100 hand blocks you’ve played). Playing 20,000 hands with this standard deviation will yield an uncertainty in your win rate of 1.06 BB/100. Thus, you’d need a win rate of 2.12 BB/100 to know with 98% confidence that you were a winning player. Depending on your personal level of boldness or paranoia, you may be satisfied with 84% confidence (uncertainty = win rate) or 99.9% confidence (uncertainty = win rate / 3). Of note is that 20,000 hands at a win rate of 2.12 BB/100 will net you 424 BB, which, combined with the 300 BB you started with, gives you a bankroll sufficient to play at twice the current limit. An interesting side effect of this metric is that players who are truly crushing a particular level will advance more quickly, since they will need fewer hands to reduce their uncertainty to half (or whatever) their win rate, while players winning less are encouraged to stick around longer, hopefully learning new lessons that bring their win rate up along the way.

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