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, which nobody has seen.
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.
A real 52-card deck, shuffled fresh. As the spectator you watch it dealt, with the count said out loud on every pile. As the magician you deal it yourself, one card at a time, and decide when each pile is finished. No face is looked at until the end.
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.
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.
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.
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.
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 nobody has seen.
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.
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.
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.
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.
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.