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> You need about 10000 (ten thousand) of them to shuffle an ordinary deck of 52 cards.

My source[0] says the lower bound for full overhand shuffle is number of cards squared, so less than 3000 shuffles for 52 cards. Upper bound around 5000.

Your source?

[0] https://arxiv.org/abs/math/0501401

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Well, it seems that his point still stands. Overhand shuffle is terrible for actually shuffling a deck of cards.

Assuming 4 shuffles per second, 3000 shuffles would take about 12.5 minutes, while 10000 shuffles would take more than 40 minutes. One of those sounds feasible during a break on a casual game night.

Of course, those numbers apply only if the shuffle is done literally—I personally try to mix individual cards by letting one hand’s batch cut in-between the other’s (and I think I’m not the only one)—but I’m still curious where did those 10000 come from.

Numberphile, the youtube channel https://www.youtube.com/watch?v=AxJubaijQbI

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