It is the story of an organization manufacuring precision card-shuffling machines for casinos — and a gang of hustlers who used a hidden video digital camera to movie the shuffler’s insides. “The pictures, transmitted to an confederate outdoors within the on line casino parking zone, had been performed again in gradual movement to determine the sequence of playing cards within the deck,” remembers the BBC, “which was then communicated again to the gamblers inside. The on line casino misplaced tens of millions of {dollars} earlier than the gang had been lastly caught.”
So the corporate turned for assist to a mathematician/magician:
The executives had been decided to not be hacked once more. They’d developed a prototype of a complicated new shuffling machine, this time enclosed in an opaque field. Their engineers assured them that the machine would sufficiently randomise a deck of playing cards with one go by the system, lowering the time between arms whereas additionally beating card-counters and crooked sellers. However they wanted to make sure that their machine correctly shuffled the deck. They wanted Persi Diaconis.
Diaconis, a magician-turned-mathematician at Stanford College, is thought to be the world’s foremost skilled on the arithmetic of card shuffling. All through the surprisingly giant scholarly literature on the subject, his identify retains popping up just like the ace of spades in a magician’s sleight-of-hand trick. So, when the corporate executives contacted him and supplied to let him see the inside workings of their machine — a literal “black field” — he could not consider his luck. Along with his collaborator Susan Holmes, a statistician at Stanford, Diaconis travelled to the corporate’s Las Vegas showroom to look at a prototype of their new machine.
The pair quickly found a flaw. Though the mechanical shuffling motion appeared random, the mathematicians observed that the ensuing deck nonetheless had rising and falling sequences, which meant that they may make predictions in regards to the card order. To show this to the corporate executives, Diaconis and Holmes devised a easy method for guessing which card can be turned over subsequent. If the primary card flipped was the 5 of hearts, say, they guessed that the subsequent card was the six of hearts, on the belief that the sequence was rising. If the subsequent card was really decrease — a 4 of hearts, as an illustration — this meant they had been in a falling sequence, and their subsequent guess was the three of hearts. With this straightforward technique, the mathematicians had been in a position to accurately guess 9 or 10 playing cards per deck — one-fifth of the full — sufficient to double or triple the benefit of a reliable card-counter….
The executives had been horrified. “We’re not happy along with your conclusions,” they wrote to Diaconis, “however we consider them and that is what we employed you for.” The corporate quietly shelved the prototype and switched to a distinct machine.
The article additionally explains why seven shuffles “is simply as near random as may be” — rendering additional shuffling largely ineffective.
