DERB

[TimM]

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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.

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This is way over simplified. The sums tend towards a normal distribution, and it could take a long time to approach the point where a normal distribution is a good approximation, especially at the extremes. Add in the possibility that the individual hands in groups of hand results from one player are not independent, and this reduces your effective sample size further. I know this is a lot of conjecture when I haven't worked with the numbers, but it's something to be considered.