Erica Klarreich in Quanta [h/t: Jennifer Ouellette] (image Skip Sterling):
Diaconis’ career as a professional magician began more than five decades ago, when he ran away from home at age 14 to go on the road with the sleight-of-hand virtuoso Dai Vernon. But unlike most magicians, Diaconis eventually found his way into academia, lured by an even more powerful siren song: mathematics. At 24, he started taking college classes to try to learn how to calculate the probabilities behind various gambling games. A few years later he was admitted to Harvard University’s graduate statistics program on the strength of a recommendation letter from the famed mathematics writer Martin Gardner that said, more or less, “This kid invented two of the best ten card tricks in the last decade, so you should give him a chance.”
Now a professor of mathematics and statistics at Stanford University, Diaconis has employed his intuition about cards, which he calls “the poetry of magic,” in a wide range of settings. Once, for example, he helped decode messages passed between inmates at a California state prison by using small random “shuffles” to gradually improve a decryption key. He has also analyzed Bose-Einstein condensation — in which a collection of ultra-cold atoms coalesces into a single “superatom” — by envisioning the atoms as rows of cards moving around. This makes them “friendly,” said Diaconis, whose speech still carries the inflections of his native New York City. “We all have our own basic images that we translate things into, and for me cards were where I started.”
In 1992, Diaconis famously proved — along with the mathematician Dave Bayer of Columbia University — that it takes about seven ordinary riffle shuffles to randomize a deck. Over the years, Diaconis and his students and colleagues have successfully analyzed the effectiveness of almost every type of shuffle people use in ordinary life.
All except one: “smooshing.”
This toddler-level technique involves spreading the cards out on a table, swishing them around with your hands, and then gathering them up. Smooshing is used in poker tournaments and in baccarat games in Monte Carlo, but no one actually knows how long you need to smoosh a deck to randomize it. “Smooshing is a completely different mechanism from the other shuffles, and my usual techniques don’t fit into that,” Diaconis said. The problem has tantalized him for decades.