A deck of 52 cards can be put in order in about 8 followed by 67 zeros ways, so many that a properly shuffled deck is almost certainly in an order no deck has ever been in before. The catch is the word properly. In 1992 Dave Bayer and Persi Diaconis, a mathematician who had left home at fourteen to travel with a card magician, worked out how many ordinary riffle shuffles it takes to get there. Their answer was seven. The surprising part is how it arrives: after four or five shuffles the deck still keeps a lot of its old order, then around six and seven it gives way almost at once. Most of us stop at three, which feels like plenty. Thoroughness turns out not to be a dial you can turn halfway; for a while nothing much happens, and then suddenly it’s done.