Any Mate At Any Number
by Oli Foster

Oli Foster leads an exciting double life as an underwriter by day and magic enthusiast the rest of the time. Ahem. When he's not pretending card stacks are work-related, he enjoys collecting old magic books and working out superfluous mental card routines, like the one you're about to read...

Effect: The magician asks a spectator to name a number under 40. She names the number 23. A deck of cards is spread face up and the spectator is asked to think of and remove any card she likes and to place it face down on the table. She removes the five of diamonds.

The magician now remarks that every card in the deck has a mate: a card which is identical in value and colour – for example the two black sixes. Somewhere in the deck (which the spectator is still holding) is the mate of the card she just selected and this matching card could now be at any position in the deck, depending on which card she chose.

However, what would be really strange is if the spectator somehow knew the exact location of this matching card and had, in fact known this before she even chose a card. The magician states that he will not touch the deck and asks the spectator to count twenty three cards off the top of the deck and to place the twenty third card next to the face down selection she removed earlier.

Under these conditions, it would take nothing short of a one-in-fifty-two coincidence for the two cards to match. Despite this, when the spectator turns the cards over, she finds that they do indeed match – the two red fives!

Uses a complete deck of fifty two cards, no memory work and no sleight of hand!

Set-up:
This trick uses a novel application of a cyclic stack, which bizarrely enables you to control the mate of a chosen card to a chosen position before the card is chosen. Remove thirteen matching pairs (ie twenty six cards) of a random selection of different values, so for each of the thirteen values you have two cards of the same colour. Decide on a sequence for these thirteen values and create two piles with a matching card in the same position in each pile. For example, the two piles might contain:

First Pile Second Pile
1) Six of Hearts 1) Six of Diamonds
2) Queen of Clubs 2) Queen of Spades
3) Five of Diamonds 3) Five of Hearts
4) Nine of Spades 4) Nine of Clubs
5) King of Hearts 5) King of Diamonds
6) Three of Clubs 6) Three of Spades
7) Ace of Diamonds 7) Ace of Hearts
8) Eight of Spades 8) Eight of Clubs
9) Jack of Clubs 9) Jack of Spades
10) Ten of Hearts 10) Ten of Diamonds
11) Two of Diamonds 11) Two of Hearts
12) Four of Clubs 12) Four of Spades
13) Seven of Hearts 13) Seven of Diamonds

The only thing you need to remember about these cycles is the value and colour of the first and last card, in this case the two red sevens on top (from the face) and the two red sixes at the bottom. (think of it as God, 7, above and Satan, 6 below - both red from a furious battle). Place the first pile on top of the second pile to form a pile of twenty six cards. You should have 26 indifferent cards left over. Place thirteen of these on top of the pile and thirteen on the face. The complete deck of fifty two cards therefore runs: 13 indifferent cards, followed by first cycle of thirteen cards, second cycle of thirteen cards, 13 indifferent cards.

Basic principle:
Look back at those two piles of thirteen cards. Imagine placing one pile on top of the other to create a single pile of twenty six cards and just forget about the rest of the deck for the moment. If you were to give this twenty-six-card-pile a single cut, you’d find that the thirteenth card in the pile would match whichever card you’d cut to the top. That’s a feature of a cycle – that each card is the same distance from a card of matching value - but here we stray a little.

Imagine that you didn’t want to find a matching card at the thirteenth position but preferred the fourteenth spot in the deck. All you would need to do to achieve this would be to place an indifferent card between the two cycles. This indifferent card would place one more card between whichever card you cut to the top and the second cycle that the matching card is found in. If you preferred fifteen, you would add another, likewise with sixteen etc. You’ll see that in this way, you can control the position of the mate of any card (in the cycle) before it is selected.

That’s the basic principle at work in this trick, which is disguised by the routine. Obviously there are restrictions to the choice of card and number: One of the thirteen cards in the cycle must be selected and the number chosen must be between thirteen and forty. However, you’ll see that both of these points are going to fly by.

Handling:
As above, you first need a number between thirteen and forty but, to make this sound less particular, start by asking a spectator to name “a two-digit number under forty”. Tell her that it’s really important that she remembers this number she’s chosen as you’ll use it for something later, so ask her to fix it in her mind by imagining she can see it projected on a small square screen in front of her. There are three reasons you ask her to do this that go beyond presentation. The first is that you genuinely don’t want her to forget the number.

The second is that you will later try to convince her that she “merely thought of” a number by reminding her of this visual image in her mind. And the third is that it buys you a second to do the only small piece of mental arithmetic that makes the trick work, as follows:

- If the spectator’s chosen number is lower than twenty six, subtract 13. They will later count the cards from the face of the deck.

- If the spectator’s chosen number is higher than twenty six, subtract twenty six. They will later count from the top of the deck.

The result of this subtraction gives you the number of cards you’ll need to place between the two stacks of thirteen cards in order to bring the mate of a card the spectator will later choose to the number they’ve just named. The idea of secretly controlling a particular number of cards to a particular position in the deck sounds very fiddly. In fact it isn’t and doesn’t even require any sleight of hand.

In this example, the spectator has named the number twenty three. As this number is lower than twenty six, we subtract thirteen, which means that we’ll now have to place ten cards between the two cycles to bring the mate of the spectator’s chosen card to the twenty third position.

These ten cards are counted off the face of the deck in the action of spreading the cards to show that they are all different and then to have one thought of and remembered. Hold the deck face up in your left hand and, as you start to spread the cards, thumb the top three overlapping cards from left to right, onto your right fingertips. Continue to spread the next three cards, mentally counting “three, six” and then the next three, “nine”, and one more is ten.

Counting the cards in groups of three as they’re spread is quick and natural, as you will only have to count a maximum of four groups of three. When you have spread off your desired number of cards, ten in this case, slightly right-jog this counted pile so that you can clearly see the next card beneath it. Note this card and leave it protruding slightly more than the others as you continue spreading to show “a complete deck of 52 different cards.”

The next key you’re looking for is the first red seven (God above), which in this case, will follow three cards later. When you reach this 7, slightly square up all of the cards above it so that none of the preceeding individual cards can really be distinguished, with the exception of the card you left protruding a moment ago. This 7 and the following twelve cards form the cycle from which the spectator will make her selection but you don’t need to count them. Continue to spread the cards from left to right, keeping your sighted card protruding and saying, “please just think of and remember any card you see here in the deck”.

Continue to spread the cards until you reach the first red 6 (Satan below) The range of cards for selection should appear very broad as you have carelessly spread half the deck before the spectator to have one thought of. When the spectator confirms that she is thinking of one of the cards she sees, casually cut off the packet above the card you left protruding. This packet contains ten cards in this example. The rest of the deck is not yet squared and, before you go to square it, insert the ten card packet beneath the red 6 at the back of the spread. It’s just a thoughtless cut that’s meaningless at this point because the spectator hasn’t chosen a card yet (other than simply thinking of it) but this single cut has just placed the mate of their thought-of selection at their predicted number.

Square up the deck and hand it to the spectator. Ask her to concentrate on her card and, to help her burn an image of the card in her mind, she is to run through the cards, cut her card to the face of the deck and stare at it for a few seconds against the deck, without showing anyone else. This is basically a pretext to have her cut the deck. When she’s done this, as an afterthought, ask her to “actually remove the card and place it face down on the table.”

Believe it or not, regardless of which card she’s just removed, it’s mate now rests at the named number in the deck without you having to go anywhere near it again. The trick is over but it appears to have only just begun. Explain to the spectator that the reason you asked her to think of a card and then remove it was because you wanted her to be absolutely sure that she had a completely free choice of card, rather than just blindly taking one from a face down deck.

Casually continue that the reason you are able to give her a free choice of card is that every card in the deck is the same in one respect: every card has a mate – one single other card of the same colour and value. Give an example of the two black sixes (as she can’t have chosen either of these). So regardless of what card she chose, a matching card is to be found somewhere in the deck.

Here you lie, although what you say sounds completely truthful and self-evident: “The position of this matching card will depend on the card you chose. For example, you might have chosen a card which is the mate of the top card of the deck, or one that matches the second card, or the fifty-second card – or the matching card might, in fact, rest at any of the fifty two positions in the deck, as it entirely depends on what card you chose – and we agree that the card you chose was a free choice.”

“But here’s the weird thing: What if I somehow knew the exact location of this matching card without looking? That might look like a trick so what if it wasn’t me who knew this random piece of information but you? And what if you’d known it all along? – before you even chose a card?...” Hopefully the audience will be ahead of you at this point and eagerly anticipate what is about to happen, the more so the better, as you have nothing left to do.

“Earlier on you thought of a number and visualised it in your mind before you chose a card. What number did you think of?“ By phrasing it like this, there’s a reasonable chance that the spectator might forget that she ever named the number as she “remembered it” in the same way as she later remembered a card. Distorting this memory creates an even stronger effect as you literally don’t appear to have had any opportunity to have manipulated the cards. “Wouldn’t it be strange if that number was the position of the matching card? Being a magician, if I could handle the cards, I might be able to make that the case. But here’s the thing: I don’t want to go anywhere near them!”

Now ask the spectator to count the cards face up either from the top or the face of the deck, depending on whether her number is higher or lower than twenty six respectively. Berglas it aint, but just a little piece of weird...

Oli Foster