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Maths

Variance in poker

The swing between short-run results and long-run expectation, why correct play still loses hands.

Variance is the gap between what should happen on average and what actually happens over a small number of hands.

Pocket aces beat pocket kings 81.9% of the time. Over four such confrontations, kings win at least once about half the time. Nothing has gone wrong when that happens; an 18% event occurring roughly one time in five is exactly the definition of an 18% event.

The practical consequence is that results are a terrible measure of decisions over short samples. Judge whether the expected value was positive. The results follow eventually, and there is no way to make them follow faster.

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