THERE’S not much Persi Diaconis can’t do with a deck of cards. As well as the usual tricks, he can perform many of his own devising, and without a hint of boastfulness he declares that when he shuffles a deck – even with only one hand – the cards interleave in perfect sequence. But unlike most magicians, Diaconis’s skills go beyond pulling the queen of hearts out of your ear. Thirty-one years ago he turned himself into a mathematician.
But he hasn’t abandoned his first love. Diaconis, now a professor at Stanford University in Palo Alto, California, has a penchant for translating mathematical problems into questions about cards. Ten years ago, along with David Bayer of Columbia, he made headlines for proving that it takes seven ordinary “riffle” shuffles to randomise a deck. So it was no surprise when he got a letter from a major manufacturer of card-shuffling machines asking his advice.
The company, whose identity Diaconis considerately shields, had produced a prototype for a new automated card shuffler, intended for the casinos of Las Vegas. But the engineers weren’t sure whether the machine truly randomised the deck. Could Diaconis help?
The company had good reason to be anxious. Not long before, it had discovered that a gang of hustlers were exploiting one of its other machines an elaborate six-deck shuffler with a glass window – by training a hidden video camera on the glass, then transmitting the pictures by radio to a car parked in the casino’s lot. Their partners outside would slow down the tape to figure out how the cards were falling and broadcast the sequence to the …