The Hillbilly, the Singing Midget, and the Mystery of Randomness / by William Poundstone

The life of William Coffren (1867-1950) was straight out of Harry Stephen Keeler's screwball fiction. Under the stage name "Si Stebbins" Coffren played a hillbilly bumpkin (The Rube) in Barnum and Bailey's circus. He was married to Dolly the Doll, who stood 32 inches high and performed in a "Singing Midgets" act. A 1944 Milwaukee Journal article painted this picture of their domestic life:

"Midgets whom you see in circuses have midget furniture; but a woman with a full-size husband who travels about and rents apartments must do with things as they are. What if she does have to stand on a chair to turn on the hot water and wash the dishes? What if she does have to drag the chair with her to get up and put the biscuits in the oven? It is all right as long as Si likes her cooking. And he does.…

"She has business notions and opinions regarding show affairs. 'And when Dolly puts her foot down,' says Si, 'I have just got to mind.'"

In real life Coffren was no fool. He anticipated, by half a century and more, some contemporary ideas about the psychology of randomness. Today he is remembered for popularizing the Si Stebbins deck, well known to magicians. Coffren realized that the Holy Grail of card magic would be a deck that looked random but isn't. It was this insight that launched Coffren into the apparently more lucrative world of vaudeville magic. 
It is an awkward fact that a properly shuffled deck may not look random to the audience. There will often be suspicious clusters, such as five face face cards in a row, or an unbroken string of red cards, or two adjacent aces. A statistician would expect such clustering, but average people don’t.

This isn't unique to cards. Many people are convinced that their music player's shuffle play feature isn't random. It plays too many A$AP Rocky songs in a row! The fact is that we have a wrong mental notion of randomness. We expect random sequences to be better "shuffled" than they are, to have little clustering.

With carnie shrewdness, Coffren gave the marks what they thought they wanted. The Si Stebbins deck is an arrangement of cards that looks more random than a truly random deck does. The four suits run in lockstep order (clubs-hearts-spades-diamonds: remember it as CHaSeD). Each value increases by three. For that reason no two adjacent cards share a color, suit, or value. There are no clusters of any kind.

You may think this strict pattern would stick out like a sore thumb. It doesn’t. Even the fact that it's black-red-black-red… doesn't register. To anyone except a magician, the deck just looks random.

The Stebbins arrangement is easily memorized, and that’s the point. A performer who glimpses the bottom card of a cut can instantly deduce the card below it… which becomes the top card of the restored and squared-up deck. He can, if desired, name that card and every other card in the deck.

As the arrangement is circular, it is preserved through any number of honest cuts. An honest shuffle destroys the Stebbins order, of course, but the expert practitioner may use a false shuffle if desired.

Coffren made a career out of this simple gimmick, and so did a number of rivals who stole the idea. Actually it's unclear whether Coffren came up with the idea himself. Essentially the same concept is described in magic publications going back hundreds of years. In or about 1898, however, Coffren revealed his secret in a pamphlet, Card Tricks and the Way They Are Performed. The pamphlet's many endorsements of a cigar brand suggests that he had found another way to monetize his gimmick. 

You can find a scan of Card Tricks and the Way They Are Performed online.