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Mathematical card tricks, as a PDF

Ten self-working card tricks, grouped by the mathematics that makes each one work. Every trick gives you the effect, the method, and the part most explanations leave out — why it works, so you know what to do when a spectator does something you did not expect.

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What is in it

Arranged by principle rather than by difficulty, because once you have seen an idea used twice you start recognizing it in tricks you were never taught.

1. Parity — a quantity that cannot change
2. The Piano Trick Cards tucked between a spectator's fingers, and one odd card that lands where you said it would before you started.
3. The Four Robbers Four jacks break into a house on four floors and meet on the roof. The story does the concealing.
4. Base three — counting with three digits
5. The 21 Card Trick Three deals, three answers, and the card arrives at the exact middle. The named column goes in the middle every time.
6. The 27 Card Trick The same machinery with the destination made adjustable — they name any position from 1 to 27 and their card goes there.
7. Base two — counting with two digits
8. The Binary Card Trick Five cards of numbers. The cards they hand back are their number written in binary, and adding the corners reads it off.
9. Arithmetic that wraps — working modulo 13
10. The 13 Card Trick They build the piles while you look away, and one equation gives you the number of cards left in their hand.
11. The Si Stebbins Stack A deck that can be cut all day and still name any card taken from it, because cutting a loop leaves a loop.
12. Order that survives a shuffle
13. The Gilbreath Principle A genuine riffle shuffle by the spectator, and the pairs still come off one red and one black.
14. The Faro Shuffle Eight perfect shuffles return a deck to its exact starting order, and the reason is one line of arithmetic.
15. A free choice that cannot go wrong
16. Out of This World Paul Curry, 1942. Someone sorts forty-eight face-down cards into reds and blacks by guessing, and gets every one right.

It closes with three numbers worth knowing: 52 factorial, how many shuffles actually randomize a deck — and the condition on that famous seven that usually gets dropped — and why a deck has 52 cards, where the arithmetic everyone repeats is real and the history attached to it is not.

Why it is not behind an email form

Two reasons, and the second is the one that decided it.

A file behind a form is a file a search engine cannot read. A gated download does not get crawled, so it does not get found, so the people who see it are the ones who already knew where to look. A download you have to earn your way to is one that very few people arrive at.

The other reason is simpler. This is compiled from pages on this site that are already free to read. Charging an address for the same material in a different file would be a strange way to treat somebody who came here to learn a card trick.

If you want to hear when the next one goes up, the form below does that, and it is entirely separate from the download above.

Questions people ask

More

Every trick in the PDF has a page here you can play through in the browser, from either chair — start at mathematical card tricks, which sorts them by the same principles. The Gilbreath principle and the binary card trick are the two that are most worth seeing run rather than read.