Wednesday, July 15, 2015

A Good Guess

Persi Diaconis has been known to perform a card trick during his mathematical lectures. Five people choose cards from a deck that Diaconis never touches. Diaconis asks the people who have red cards to stand up. They do and Diaconis reveals the names of their cards. He then reveals the names of the remaining five cards. He described the trick in Magical Mathematics, an excellent book co-authored with Ron Graham.

The deck is stacked in what is known as a de Bruijn sequence. Magicians call these sequences, mistakenly says Diaconis, Gray codes. The key is the moment some people reveal they have red cards. Let’s say, three people stand up. The five people can now be seen as a sequence of red and black cards, for example, R, B, B, R, R. This is enough information to tell you which section of the stack you are in. And all the cards can be identified.

It does take some work to translate the red black sequence into the names of playing cards and Diaconis only describes a method that works with a 32 card deck leaving the reader to work out their own method for a 52 card deck. There is, however, a simpler way of achieving the effect. It has its own compromises, of course, but the trick is very easy to do and you might already have the skills to do it.

The stack used in this case is Si Stebbins. It’s a simple mathematical sequence. Each card in the stack has a value of 3 more than the previous card. A thirteen-card sequence of values looks like this:

3 6 9 Q 2 5 8 J A 4 7 10 K

Suits are arranged in familiar CHaSeD order.

Hand the deck to a spectator and have him give it a cut or two or three. He then takes the top card of the deck and passes the deck to the spectator next to him. She takes the new top card and passes the deck on. This is repeated until four spectators are each holding a card. The deck is placed aside. Apparently there is no way you can know anything about the chosen cards.

In fact you do know two things. First that there is one card of each suit among the four. Secondly that there is a court card or an Ace among the four. You use these two pieces of information as follows.

First you say, to everyone:

I get the impression that one of you is holding a heart. Is that right?

One spectator will either nod or otherwise indicate that they are holding a heart suit. From this you know the arrangement of suits that the spectators hold.

Next you say:

And I’m getting… a high card. A court card. Okay?

One of three things will happen:

  • The person with the heart card also holds a court card and thinks you are talking to them. They say yes.
  •  Someone else says yes.
  • No one says yes.

In the case of the first two answers, you now know there is a J, Q or K in play.  Because the four cards are in CHaSeD order you also know the suit. So announce that too.

From the spectators’ point of view you’ve made two good guesses so far. Let’s continue to divine the court card.

Announce that it’s a King. You’ll be right one out of three times. If they say you’re wrong, ask them for the name of the card. It can only be a Jack (looks similar) or Queen (nearest value card). Even when you’re wrong you’re pretty close. Make the most of a minor mistake that you hope the audience will forgive because you now have enough information to reveal all four cards.

Let’s assume no one says yes when you make your guess about there being a court card. If no one says yes, you know that the Ace is in play. In fact you now know all four cards because the only combination that features an Ace without a court card is A, 4, 7, 10.

But segue into this by correcting your previous guess about it being a court card by saying:

It’s definitely a high card…. An Ace… Ace of Spades

Naming the suit which you nailed without further prompting. You can also now reveal the rest of the cards. Do this in the most interesting way possible, going from one spectator to another.

That’s all there is to it. A miracle using a stack you already know. There are other strategies for working the trick if you prefer to use five selected cards instead of four. But, like Persi Diaconis, I will leave you to figure that out for yourself.

NOTES: Si Stebbins (William Henry Coffrin) sold his system to the public in a number of booklets from the 1880s onwards. He said it had been shown to him by a Syrian card manipulator, Selim Cid, who worked alongside him in a travelling magic store. Although Stebbins sold a system involving a 3-card progression, the one he used himself featured a 4-card progression and he published at a much later date in1935.

St Stebbins performed what is known as a ‘rube act’ with the Barnum & Bailey Circus. It was a kind of clown act, which, judging by his publicity photo, he was perfectly suited for! You can download one of Si Stebbins’ booklets here. Fans of Chan Canasta will be intrigued by Trick no 5. See how it pays to read to the end?