The Mathematics of . . . Shuffling

A magician turned mathematician saves the casinos' shirts

By Dana Mackenzie
Oct 1, 2002 5:00 AMJul 19, 2023 7:00 PM

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Persi Diaconis picks up an ordinary deck of cards, fresh from the box, and writes a word in Magic Marker on one side: RANDOM. He shuffles the deck once. The letters have re-formed themselves into six bizarre runes that still look vaguely like the letters R, A, and so on. Diaconis shuffles again, and the markings on the side become undecipherable. After two more shuffles, you can't even tell that there used to be six letters. The side of the pack looks just like the static on a television set. It didn't look random before, but it sure looks random now.

A seemingly random arrangement of cards in a deck is sometimes nothing but an illusion. Persi Diaconis, a Stanford mathematician and practiced magician, can restore a deck of cards to its original order with a series of perfect shuffles. The sleight of hand: Each time Diaconis cuts the cards, he interleaves exactly one card from the top half of the deck between each pair of cards from the bottom half.Photographs by Sian Kennedy

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