DERB

[fnord_too]

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And what about the possibility that poker results do not follow a normal distribution, but rather something with fatter tails.

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It doesn't matter what distribution results for a single hand follow, if you are dealing with sums (or means) of sets of hands those sums or means will follow a normal distribution. (That's just the central limit theorem). So you can say for instance that results from 100 hand chunks will be normally distributed.