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.
SIMPLY STEBBINS
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?