The 13 Card Trick
You deal the whole deck into piles, counting up to 13 each time. Somebody keeps any three piles. You gather the rest, look at two of the three, and name the value of the third card without turning it over.
Play it through
A real 52-card deck, shuffled fresh. The spectator deals, every time. As the spectator you turn the cards face up and count; as the magician you say the words that get them to do it, and see nothing but backs.
There is no setup, no sleight, and no memory work. The deck can be borrowed and shuffled by anybody for as long as they like. What makes this one worth knowing is that two separate quantities cancel out of the arithmetic, and you can watch both of them go.
Also called the 13 card magic trick, the thirteen card trick, or the 13th card trick. The number is the count you say out loud rather than the number of cards, and it is not the thirteenth card of anything — which is where most of the confusion about it comes from.
How to do the 13 card trick
They deal. You never touch the deck. That is the whole handling, and everything below is something you say rather than something you do.
- Hand them the deck and let them shuffle it as long as they like.
- Ask them to turn the top card face up where they can see it and you cannot, counting an ace as 1, a jack as 11, a queen as 12, and a king as 13.
- Ask them to deal cards face up on top of it, counting out loud from that value up to 13. A 7 gets "eight, nine, ten, jack, queen, king", so six cards. A king gets nothing and sits alone. An ace gets twelve.
- Ask them to turn the finished pile face down. This is the move that matters, and it looks like tidying. The card the pile started on was underneath everything, so turning the pile over puts it on top, face down.
- Repeat until they cannot finish a pile. Those leftover cards come to you, and you take them without looking.
- Ask them to point at any three piles. Gather every other pile into your hands.
- Ask them to turn over any two of their three. Add the two cards showing, add 10, and count that many cards off your hand.
- Count what is left. That is the value of the card on top of the third pile. Name it before they turn it over.
Counting up to 13 out loud is what sells it. It sounds like a rule you invented on the spot, and it is doing all of the work. The flip sells the rest: it is the reason you can say you never saw the card, and mean it.
Why it works
Start with one pile. A card worth v gets the cards from v + 1 up to 13 dealt on top, which is 13 − v cards, plus the card itself. So a pile holds 14 − v cards, and a pile is small exactly when its bottom card is large.
Now deal k piles from 52 cards, and call the sum of the bottom cards S. The piles use up 14k − S cards, so your hand holds what is left:
hand after dealing = 52 − 14k + S
Then you gather all but three piles. Those gathered piles held 14(k − 3) − (S − a − b − c) cards, writing a, b, and c for the three bottom cards still on the table. Add that back:
hand = (52 − 14k + S)
+ 14k − 42 − S
+ a + b + c
hand = 10 + a + b + c
Both cancel. k goes, so it does not matter how many piles you dealt. S goes, so it does not matter what any of the other cards were. Your hand is holding a number built from three cards that are still face down on the table.
So when you count off a + b + 10, what remains is c. You are not remembering anything and you are not calculating anything you could get wrong. You are reading a quantity that the dealing put in your hand several minutes earlier.
Do you see the card?
Yes, and it is worth being straight about that. To count a pile up to 13 you have to turn its first card face up and read it, so every card this trick can finish on has been in front of your eyes. About seven of them go past in a minute while you are talking.
What the arithmetic buys is that you do not have to remember any of them. The count left in your hand carries the answer, so a card can go by unnoticed and still be named at the end. That is the difference between this and a memory feat, and it is why the trick works when you are thinking about something else.
It also means the arithmetic can only ever give you the value. The suit is not in it, because nothing in the dealing rule ever looks at a suit. If you want the suit as well, you would have to remember which card you laid down at each place, and at that point you would know the card outright and would not need the count.
If you want it to be true that you never saw it, hand the deal over. The procedure is a rule rather than a skill, so a spectator can deal the piles themselves while you look away. They tell you two values at the end, you count off, and you name a card that has never been in your sight. That is the strongest way to perform this and it costs nothing.
Why it cannot run out
The obvious worry is counting off more cards than you are holding. It cannot happen. Your hand holds 10 + a + b + c, you count off a + b + 10, and the difference is c, which is at least 1 because the lowest card is an ace.
The demo above was checked against 200,000 random deals before it was written. The identity held in every one, and no deal ever produced fewer than three piles. The most piles seen in a single deal was 15, which happens when the deck runs high.
Where it comes from
No single inventor can be credited honestly, and this page will not guess at one. It is an old piece of the mathematical-trick literature, of the kind collected in Martin Gardner's Mathematics, Magic and Mystery in 1956. It is sometimes published under a name a particular writer gave it rather than the name it arrived with.
Questions people ask
What is the 13 card trick?
Deal a card face down and count up to 13 on top of it, so a 7 gets six more cards and a king sits alone. Keep building piles until you cannot finish one.
Gather all but three piles back into your hand, turn two of the three over, and count off their values plus ten. What is left in your hand is the value of the third card, which is still face down on the table.
How does the count to 13 card trick work?
A pile started with a card worth v holds 14 − v cards. Deal k piles from 52 and your hand holds 52 − 14k + S, where S is the sum of the pile bottoms.
Gather all but three and both k and S cancel, leaving exactly 10 plus the three remaining bottom cards. The number of piles does not matter and neither does any card you dealt. The full working is above.
Do you need to set the deck up for the 13 card trick?
No. The deck can be shuffled by anybody, as many times as they like, and it can be a borrowed deck. The trick works on whatever order it is handed.
What happens if you run out of cards mid-pile?
Those cards stay in your hand and the pile is abandoned. This is part of the method rather than a mistake, because the leftover count is exactly what the trick reads at the end.
Does the 13 card trick ever fail?
It cannot, if you deal correctly. Your hand always ends holding 10 plus the three bottom cards, and the lowest a card can be worth is 1, so there are always more cards in your hand than the number you have to count off.
The one thing that does break it is miscounting a pile, which is why the counting is done out loud.
More
This is one of the mathematical card tricks here, filed under the principle it runs on: a quantity that cancels. The other one built on that idea is Easy Location. All of them are on the self-working card tricks page.
Harrison Alley
Hobbyist · Writes Sleightless
A hobbyist, not a professional. I write up the self-working end of card magic, because it is the door I would point a beginner at, and every trainer here is played through and checked before it ships.