Are Winrates Normally Distributed?

[Justin A]

Nice work Max, thanks a lot.

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So if I play 20,000 hands and my BB/100 is 1.5, I know that the sampling distribution for samples of that size is normally distributed.

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Don't the numbers you posted indicate that this is not the case? Sampling distributions are going to approximate normal with n sufficiently large. What your numbers seem to show is that n=100 is not large enough.

Correct me if I'm wrong, but you've shown that the sampling distribution for bb/100 is decidedly not normal. What I want to know is how does this affect confidence intervals?