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GILBREATH PRINCIPLE

The Gilbreath Principle is one of the most useful mathematical principles ever applied to magic. Norman Gilbreath first presented his now-famous principle in a trick called "Magnetic Colors", published in the July 1958 "Ring 21" Linking Ring Parade.

As originally presented in "Magnetic Colors" the principle was that if a deck was arranged with alternating black-red colors throughout, then cut in half (with opposite colors on the bottom of each half), and Riffle Shuffled together, every pair of cards from the top down (or bottom up) would have one red card and one black card. Each pair might be red- black order, or black-red, but there would be one of each color.

This original concept excited the magic world and produced a large number of variants. But some of the more mathematically sophisticated magicians came to realize that this was a special case of a more general situation. The reason it worked was that each half was a mirror image of the other: one black-red-black-red... from the top down, the other red- black-red-black… up. Couldn’t the sequence be not merely two cards - as in red-black - but any number at all? For example, suits: half the deck in C-H-S-D order from the top down, the other from the bottom up (throw out 1 set of 4 cards so you only have a 48 card deck). After shuffling the two halves together, each set of four cards from the top down will have one each of the four suits. As with the red-black stack, the order of the suits within each four card set will be unpredictable, but all four will be there.

Or perhaps values: half the deck stacked A-2-3-4-5-6-7-8-9-10-J-Q-K from the top down, the other half the same from the bottom up. Shuffled together, each set of thirteen cards from the top down, will have all thirteen values.

Norman Gilbreath was again the first to get this more generalized concept into print in his one-man Linking Ring Parade (June 1966), but it has been exploited extensively by many magicians in ways that seem far removed from the original concept.

Why does the Gilbreath Principle work? It’s not easy to see, but consider the situation where the stack is all the values from Ace to King. Since the other half is in the opposite order, if the King in the bottom half goes anywhere in the top thirteen cards, that means it shoves the King from

the first half out of the first thirteen into the next thirteen. If the Queen in turn is shuffled into the thirteen, it shoves the Queen out of the original thirteen into the next thirteen. And so on.

Usually magicians have to try this out themselves many times to convince themselves. One way that helps is to take a small sequence, say an A-2- 3-4-5 and lay them out in a face-up spread. Then spread a sequence of 5-4-3-2-A above them. Push the Five anywhere into the first stack, where it is obvious that it supplants the original Five in the first stack. Then the Four anywhere below the 5, and so on. This process is the same as a Riffle Shuffle.

You’ll find a mixture of tricks below exploiting both the original principle and the generalized principle.

THE HUSTLER

The presentation is given here in full to begin. Simply apply this to the method that follows.

EFFECT & PRESENTATION

While telling a story about a hustler you once met and an unusual wager he offered you, you take a deck of cards and mix half of them face-up with the other half face-down. A spectator now shuffles the deck further, then you take the deck behind your back (or below the table).

You invite the spectator to play your part in a re-enactment of the scenario. No money is actually wagered. You’ll be the hustler and he will be you - the sucker.

The wager is simple: You will bring cards from behind your back one pair at a time. Obviously each pair will consist of two possible situations. They will either both face the same way (match) - or one will be face-up and one face-down (no-match). The spectator is given a choice - match or no- match. He might say "match." You bring pairs round one at a time - for every matching pair, you owe the spectator a dollar. For every no-match he owes you a dollar. Remember, this is a re-enactment so no money is actually wagered.

You proceed to bring pairs round one by one and drop them on the table. Every pair is a "no-match." The spectator can stop you at any time. He might stop you after 10 pairs. He’s just lost $10. The terms of the wager are now reversed. For every "no-match" you produce, you owe the

spectator a dollar. You continue bringing round pairs and dropping them on the table. This time every pair is a "match." Again he can stop you at any time. Again he has lost every time (just like you did when you met the hustler).

This can be repeated, and every time the hustler wins. He can’t lose. Finally, you say, "At this point, I realized I was going to lose a lot of money, so I challenged the hustler to a final showdown - double or nothing. I demanded he bring round just two more pairs and unless both were matches I would win and owe him nothing."

At this, you bring round two more pairs, but they both match. You lost. But the hustler could not stop hustling and he offered a final and seemingly impossible wager. He said, "If you can guess what these 4 cards are I’ll give you back double all the money you lost!"

He didn’t know I was a magician and I waved my hand over these four cards and said, "That’s easy - these are the four Aces." He laughed and was about to walk away with all my money when he realized I was serious. And these are the four Aces that sent that hustler into early retirement." At that, you flip over the four cards revealing the four Aces.

This uses the Gilbreath Principle and is based on a Nick Trost idea using face-up and face-down cards that appeared in his 1964 booklet Card

Problems. Bob King used the concept more recently in Magician Foolers.

The problem with both of these tricks (and many other such tricks) was that you had to deal the complete deck into two piles before proceeding with the routine. In this routine you are ready to get going immediately after the spectator has shuffled the deck.

The only preparation is to secretly remove the four Aces and stick them under your belt at the back, or under your watchband. If you are seated at a table have them in your lap.

WORKING

1. To begin, split the deck into two equal halves of twenty-four cards, then turn one half over and Faro the sections together. This alternates the cards face-up and face-down. Alternatively, you can hold one half in each hand and mix them into a pile dealing from each hand alternately. However, the Faro is superior and if you miss it’s easy to spread through and correct the errors as you spread the cards to show them.

Place the deck on the table and ask a spectator to give it a few straight cuts. Now reach forward and cut the deck into two roughly equal halves - make sure there is a face-up card on one half and a face-down card on the other (Fig.1). He now Riffle Shuffles the cards together and squares the deck.

2. Pick up the deck and take it behind your back, or if you are seated, take it below the table. Remove the four Aces from under your belt and place them on the bottom of the deck but keep them injogged for an inch or so (Fig.2). Nobody sees the deck so you don’t need to worry. You now follow the presentation as outlined

above. Here’s how you make it work:

For a "no-match" you simply push off the top two cards and bring them round. For a "match" you flip over the top card of the deck and push off two cards then bring them round.

When you come to the final wager, bring two Aces round face-down, followed by the other two Aces face-down. "Two matches." Bring the rest of the deck round and discard it.

Finally flip them over revealing them to be the Aces.

DIRE STRAIGHTS

You place a King, Queen, Jack, Ten and Nine on the table. This is a target hand for anyone to try to match. A spectator shuffles the deck and ultimately finds a better hand consisting of Ace, King, Queen, Jack and Ten.

The inspiration was Roy Walton’s "A Straight Shuffle" (The Complete

Walton, Vol.2, Davenports, 1986).

The set-up is only ten cards, as follows:

WORKING

1. Begin by giving the deck a couple of Overhand Shuffles retaining the top stock. Then give it one more as follows:

a) Undercut half the deck - injog the first card as you shuffle the rest on top.

b) Undercut below the injog - run five cards - throw the rest on top.

This leaves one set of A-K-Q-J-10 on top, and the other set in the middle but in reverse order, 10-J-Q-K-A.

2. Run through the deck and toss out a King, Queen, Jack, Ten and Nine of mixed suits, but do not remove any cards from your little stacks. As you close the spread, catch a break beneath the five-card stack in the middle.

Leave the cards you removed in a face- up spread on the table, saying, "You’ll

notice this is a King, Queen, Jack, Ten, Nine straight, a very good hand to have in Poker. I’ll leave it here on the table. This will be a target that I want one of you to try and equal."

3. Turn your left hand palm down and deposit all the cards below the break on the table (Fig.1) then place the other half on the table beside it, so both sections are in position for a Riffle Shuffle. There is now a stack on top of each half.

Invite a spectator to carry out the Riffle Shuffle and then square the deck. 4. Tell him to pick up the deck and start dealing five hands of cards in the usual manner. Once he’s dealt a few rounds, stop him and tell him to distribute the remainder of the deck randomly across the five piles, "to

speed things up." In fact only the first five cards he deals are important,

Point out the random nature of the five piles, and then turn over the top card of every pile, leaving each card on top of its pile (Fig.2). If these five cards make up a better hand than the Straight on the table, quit now and take a bow! However, this is highly unlikely, so we will proceed as planned.

5. Ask the spectator to gather the five piles together in any order, then to give the reformed deck a complete cut to lose the top face-up card, saying, "We’ll

use these face-up cards as ‘helper’ cards and see if they can find a better poker hand for you."

6. Spread the deck across the table and slide out each face-up card along with the card directly above it (Fig.3). Now push the rest of the deck to one side. Next, gather up the five face-up "helper" cards and toss them to one side too.

This leaves the five face-down cards. Pick these up and hold them with the faces towards you.

Pull out the King and place it face-up on the table below the target hand, saying, "OK, you got a King. That’s a promising start." Pull out the Queen, saying, "And you got a Queen too. It’s looking better." Continue with the Jack and the Ten. Only one card remains. Act as if you’re about to place this card below the Ten to complete the Straight, then pause, and say, "But, unfortunately you failed to equal the target hand...in fact

Turn over the Ace and place it behind the King to form an A-K-Q-J-10 Straight.

THE PARANORMALIST

A spectator gives the deck a shuffle while you turn your back. He now turns over the cards in pairs and stops when he arrives at a pair of the same color. You ask him to concentrate on the highest value and to try to send it to you telepathically. He succeeds and you correctly name the card. This is repeated as he continues through the shuffled deck. Sometimes you ask him to think of the lowest value - it doesn’t matter, you always name it. To finish the demonstration off you predict the highest card in the final pair before he even reaches it.

This evolved out of Paul Curry’s "The Red and the Black" (Paul Curry

Presents, 1974), in which Curry offers an intriguing angle on the

Gilbreath Principle. Also see Karl Fulves’ "Incorporated Color Control" (More Self-Working Card Tricks, 1984), for a later use.

As with Curry and Fulves, the following effect uses a full stack and so should be switched in. It may be suitable as a feature mind-reading item as, despite the set-up, it is a very direct trick!

SET-UP

Remove all the Aces, Twos, Threes, Fours, Queens and Kings. Set the deck in two sections as follows:

(SECTION A - alternating red/black triplets – 24 cards in total)

Black [2-KC-3] - Red [4-AD-3] - Black [Q-2C-A] Red [K-4H-A] Black [3-QS-4] - Red [K-3D-Q] - Black [K-4S-A] - Red [2-QH-2]

(SECTION B)

The remaining 28 cards are simply alternating red/black/red/black throughout - red on top. Give the face card of this section a crimp, then place it on top of A.

WORKING

1. While you are talking you can give the deck a few short Overhand Shuffles by running odd numbers of cards then throwing the balance below them each time. This maintains the alternating arrangement of the upper section.

Now cut off the upper section at the crimp and place both halves face- down on the table. Invite a spectator to Riffle Shuffle the halves together while you turn your back.

2. He now turns over pairs of cards and stops when he hits two of the same color. He will only arrive at eight such pairs. Using the cue card you tell him the highest or lowest card in each pair, for example, when he stops at the first matching pair, say, "OK. I want you to think of the one

with the highest value and try to send that to me telepathically."

You glance at your cue card which says the highest is the KC. Name it. 3. Continue through all the pairs - asking him to think of the highest or lowest card as printed on the cue card. Stop after seven pairs. You need an applause cue to finish on.

4. Now take up a pad and pen, saying, "Your telepathic powers have been

outstanding. Now I’d like to try to predict the future." Write the final card

- Queen of Hearts - on the pad and hold it up with the blank side to the audience, saying, "Continue turning over pairs and I feel that you will

only hit one more pair of the same color in the deck." This turns out to be

true. When he hits the final pair ask him to shout out the name of the highest card. It will be the Queen of Hearts. Slowly turn round the pad revealing that very card.

THE POWER OF LOVE

This effect requires a full deck set-up and at least four spectators. It is a further variation on Paul Curry’s "The Red and the Black" (Paul Curry

Presents, 1974).

Remove the 4 Kings and Queens then set the deck as follows:

RBR-B(KC)B-R(KH)R-BRB-RBR-B(KS)B-R(KD)R-BRB-(QD)-

followed by the rest of the deck in alternating order: B-R-B-R-B-etc. Finally position the remaining three Queens anywhere below the Queen of Diamonds in Clubs, Hearts, Spades order, working up from the face.

WORKING

1. Ask for four spectators to help, then say that you’re going to put a special card in front of each of them, but they won’t get to see them until the end. Go through the deck with the spread facing you and remove the four Queens and place one face-down in front of each of the four spectators in C-H-S-D order from left to right. As you remove the Queens, downjog the card behind the Queen of Diamonds.

2. Turn the deck face-down and cut it into two piles by lifting on the injog. Have someone shuffle the cards together. Pick up the shuffled deck, turn it face-up and spread it as you explain that some pairs of cards are of opposite colors - show such a pair - some of the same color - again show such a pair. Turn the deck back face-down, without changing the order, saying that you're only interested in the ones that match in color. 3. Turn toward the leftmost spectator and show him the top two cards, asking if they match in color. If so, tell him to keep them and don't show them to anyone else. If not, discard the pair face-up on the table so everyone can see as the trick proceeds that they are really mixed red- black pairs. Continue with each spectator as you move to the right. At the end, you'll have a spread of mixed-color cards and each of the four spectators will have a pair of the same color.

4. Now say "Let's limit this further. You keep the highest card of your pair

- Kings are high, Aces low - and give me the other one." You discard

those cards face-up on the tabled pile. They will be random.

card in front of them - that is, the card you placed face-down in front of them at the start (Fig.1). Finally ask them each to turn over their face- down card. Every King will be with the matching Queen (Fig.2).

"Was it merely chance that brought these couples together? Or was it the power of love?"

HOURS OF MAGIC

A card location using the Gilbreath Principle.

The concept of the automatic pseudo-duplicate seems to have been first used by Nick Trost in "Repeat Six Card Test" (ESP Session, 1971, Hades). Stewart James also exploited the principle in an effect that required thirteen sets of actual duplicate cards. The following uses the idea to gain