How to do the count-to-thirteen card trick

A spectator deals the whole deck into piles that each “count up to thirteen”, then picks three. You turn over two of them, deal some cards away, and the number of cards left in your hand tells you the card on top of the third pile. It’s self-working, it runs on simple arithmetic, and it works with any shuffled deck.

What does the audience see?

A spectator shuffles an ordinary deck and, with your back turned, deals it into several face-down piles. You turn round and ask them to choose any three piles. The rest of the cards are gathered up. Two of the chosen piles are turned over and some cards are dealt away. Then, without touching the third pile, you name the value of its top card. They turn it over, and you’re right.

Like the down-under deal and the 21-card trick, there is no sleight of hand at all. The spectator shuffles and builds the piles themselves, so they know the deck isn’t set up.

How are the piles made?

Every card has a value: ace is 1, number cards are their number, jack is 11, queen is 12 and king is 13. To make one pile:

1. Deal one card face up. Its value is the starting number.
2. Count up to thirteen. Deal more cards face up onto it, counting from the next number until you reach 13. A 7 gets six more cards (“8, 9, 10, 11, 12, 13”). A king needs no extra cards. An ace gets twelve more.
3. Start the next pile. Deal a new card beside it and repeat until the deck runs out.
4. Set aside the leftovers. If there aren’t enough cards to finish the last pile, those cards go to one side.
5. Turn every pile face down. The card that started each pile is now on top.

Even the biggest pile (one that starts with an ace) holds only 13 cards, so a 52-card deck always gives at least four piles. You will always have enough for the trick.

How do you do the trick?

1. Have three piles chosen. Turn round and ask the spectator to point to any three piles.
2. Gather the rest. Pick up every other pile and the leftover cards, and hold them face down in one packet. This is your counting packet.
3. Deal ten. Count ten cards off the counting packet into a discard pile.
4. Turn over two piles. Ask the spectator to turn over the top card of any two of the three piles. Deal that many cards again: first the value of one card, then the value of the other.
5. Count what’s left. Deal the rest of the counting packet into the discard pile, counting quietly. The number you reach is the value of the top card of the third pile. If you reach 1, it’s an ace; 11, 12 or 13 is a jack, queen or king.
6. Reveal it. Name the value, then ask the spectator to turn the card over.

Why does it work?

A pile that starts with a card of value v holds that card plus the cards counted from v + 1 up to 13, which is 14 − v cards. A king pile is one card. An ace pile is thirteen.

Call the three chosen top cards a, b and c. Those three piles hold (14 − a) + (14 − b) + (14 − c) cards, which is 42 − a − b − c. Everything else, 52 minus that, is in your counting packet: 10 + a + b + c cards. Deal away 10, then a, then b, and exactly c cards are left. That’s how the NRICH maths site explains it in its solution to the same puzzle.

The leftover cards from an unfinished pile don’t spoil anything, because they go into the counting packet with the rest. The total of 52 is all that matters, so make sure the deck is complete and the jokers are out.

How do you make it stronger?

• Let them do the work. The more of the dealing the spectator does, the less it looks like you control anything.
• Don’t count out loud at the end. In step 5, count silently, so the final number isn’t obviously the answer.
• Write it down first. As a suggestion, jot the value on a slip of paper before the reveal, so it plays as a prediction rather than a calculation.
• Check the deck. A missing card throws the count out by one. Count the deck to 52 before you start.
• Slow down the piles. Mistakes usually happen while the spectator is counting up to thirteen, so remind them to start from the next number, not the card’s own value.

What helps you take it further?

• Card Tricks and How to Do Them by A. Roterberg (1902), free from our public-domain library. The 164-page handbook covers basic sleights and tricks with ordinary cards, including a section on mind-reading and prediction.

For more self-working ideas, browse our card tricks or try the 1089 number trick and the key card trick.

The Futility Closet blog quotes a related puzzle from Henry Dudeney’s Modern Puzzles, in which the piles are counted up to twelve and you work out the total of all the bottom cards from the number of piles and leftovers.

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