The Mathematics of Card Shuffling

Did you know there was such a field of study?  I didn't, and neither did I know that there's an expert in this field:

Their engineers assured them that the machine would sufficiently randomise a deck of cards with one pass through the device, reducing the time between hands while also beating card-counters and crooked dealers. But they needed to be sure that their machine properly shuffled the deck. They needed Persi Diaconis.

Diaconis, a magician-turned-mathematician at Stanford University, is regarded as the world's foremost expert on the mathematics of card shuffling. Throughout the surprisingly large scholarly literature on the topic, his name keeps popping up like the ace of spades in a magician's sleight-of-hand trick.

So, when the company executives contacted him and offered to let him see the inner workings of their machine – a literal "black box" – he couldn't believe his luck.

With his collaborator Susan Holmes, a statistician at Stanford, Diaconis travelled to the company’s Las Vegas showroom to examine a prototype of their new machine. The pair soon discovered a flaw. Although the mechanical shuffling action appeared random, the mathematicians noticed that the resulting deck still had rising and falling sequences, which meant that they could make predictions about the card order.

The field of probability was founded on gambling.  I guess some things never change :-) 

Read the whole thing, it's fascinating.