How to do the Kruskal count

In the Kruskal count, a spectator secretly picks a number from 1 to 10, deals through a shuffled deck counting by card values, and stops on a final “key” card. You follow the same rules from a card of your own choosing, and most of the time you land on the same card. No sleight of hand, no setup: it works on probability.

What is the Kruskal count?

It is a self-working card trick in which the magician “guesses” a card the spectator reached by a counting procedure. It is named after the mathematician Martin Kruskal. A 2001 paper by Jeffrey Lagarias, Eric Rains and Robert Vanderbei, “The Kruskal Count,” says that “With high probability the magician can correctly ‘guess’ the card.”

What are the counting rules?

These rules follow Futility Closet’s write-up:

• Think of a secret number from 1 to 10.
• Deal the shuffled deck face up, one card at a time, counting silently.
• When you reach the secret number, that card’s value becomes the new secret number.
• Aces count as 1 and face cards count as 5.
• Start counting again from 1 each time, and remember the last secret card you reach before the deck runs out.

How do you perform it?

1. Hand over the deck. Let the spectator shuffle as much as they like.
2. Explain the rules. Ask them to think of a number from 1 to 10 and keep it to themselves. Teach the counting rules above.
3. They deal, you follow. As Futility Closet describes it, the spectator deals the cards face up while you note the value of an early card and silently follow the same steps.
4. Keep your own chain going. Count along from your card to the next, and the next, all the way through the deck.
5. Reveal. When the deck runs out, your last secret card is your guess. Name it, write it down, or pull it from the dealt cards for a big finish.

Why does it work?

Each chain of counts jumps through the deck, landing on some cards and skipping others. If your chain and the spectator’s chain ever land on the same card, they follow exactly the same counts from then on, so they finish on the same card. Futility Closet puts the odds at “Five times out of six.” The Lagarias, Rains and Vanderbei paper analyzes simplified versions of the trick and estimates its probability of success.

What if it goes wrong?

• It can miss. Our suggestion: present it as an experiment in reading the spectator, so a miss feels like part of the challenge rather than a failure.
• Counting mistakes. A single miscount breaks the chain. Our suggestion: ask the spectator to deal slowly, and say the rules out loud before they start.
• Losing your place. Our suggestion: start your own chain on one of the first few cards, so your chain has the whole deck to meet theirs.

What else can you try?

• How to do the key card trick, another self-working classic.
• How to do the 21-card trick, with an explanation of why it works.
• Magic tricks for math lovers: a buyer’s guide, for more number-based magic.

What helps you take it further?

• Mathematical Recreations and Essays by W. W. Rouse Ball. A free 394-page PDF of the 1922 tenth edition, with arithmetical card tricks, magic squares and famous puzzles. Its description calls it “a favourite source for magicians who build self-working and number-based effects.”
• Royal Road to Card Magic (eBook) by Jean Hugard and Frederick Braue. A 307-page PDF whose contents include the key card, the glimpse and the overhand shuffle.

Find more free classics in our free eBooks collection, or a new deck in playing cards.

Frequently asked questions