SMRTR Science & EngineeringJun 17, 2026Quanta Magazine

Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?

SMRTR summary

In 1992, mathematicians proved that seven perfect "riffle shuffles" fully randomize a deck of cards. But real-world shuffling is rarely perfect, so researchers have now explored how many messy, imprecise shuffles are needed to achieve the same result. The answer depends on how sloppy the shuffle is — with more randomness per shuffle potentially changing the number needed significantly.

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