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 exterior within the on line casino car parking zone, have been performed again in sluggish 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 have been lastly caught.”
So the corporate turned for assist to a mathematician/magician:
The executives have been decided to not be hacked once more. That they had 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 move by the system, lowering the time between fingers 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 professional 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 provided to let him see the interior workings of their machine — a literal “black field” — he could not imagine his luck. Together 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 concerning the card order. To show this to the corporate executives, Diaconis and Holmes devised a easy method for guessing which card could be turned over subsequent. If the primary card flipped was the 5 of hearts, say, they guessed that the following card was the six of hearts, on the belief that the sequence was rising. If the following card was really decrease — a 4 of hearts, as an illustration — this meant they have been in a falling sequence, and their subsequent guess was the three of hearts. With this easy technique, the mathematicians have been capable of accurately guess 9 or 10 playing cards per deck — one-fifth of the whole — sufficient to double or triple the benefit of a reliable card-counter….
The executives have been horrified. “We’re not happy along with your conclusions,” they wrote to Diaconis, “however we imagine them and that is what we employed you for.” The corporate quietly shelved the prototype and switched to a unique machine.
The article additionally explains why seven shuffles “is simply as near random as could be” — rendering additional shuffling largely ineffective.