Are Winrates Normally Distributed?

[felson]

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i can't speak on math, but i know that people tend to play a lot when they're down and tend to leave when they're up

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Astro, that shouldn't matter since even if Josh leaves, his next session gets grouped in the stats (if I understand correctly). This would only matter if Josh tilts.

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It should matter. If you quit early to lock up a win, and "play through your downswings," then you're going to have a smaller winrate, and the center of your distribution will be more to the left than it could be.

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If Josh wins his first hand and quits immediately, then plays again later, then will the hands from his second session be put in the same block as his first hand?

If so, then it doesn't matter if Josh locks up his wins.

If Josh's one hand forms its own block, then that's different -- but I don't think that's what is happening.