Diaconis says that he will have "seven shuffles suffice" carved on his tombstone. He is referring to his most famous realisation: that it takes seven "riffle shuffles" to sufficiently randomise a deck of cards. The riffle shuffle is the familiar technique, used by casinos and serious card players, in which the deck is cut in two and then thumbed together with a satisfying zip, often ending with a bridge finish that gathers the cards together into a neat pile.

The riffle shuffle is the unruly twin of the perfect shuffle. Instead of perfectly interleaving the two halves of the decks, the halves are mixed together in disorderly clumps, planting a seed of randomness that progressively mixes the cards with each shuffle.

After one or two riffle shuffles, some cards will remain in their original sequence. Even after four or five shuffles – far more than most casinos typically use – the deck will retain some trace of order. But once you shuffle the deck seven times, the cards become truly mixed, at least as far as most statistical tests can prove. Beyond that point, further mixing will not do much. "It's just as close to random as can be," Diaconis says.