Is That Your Card: The Math Behind It

If you’ve seen at least one card trick in your life, you’ve probably seen this one. You pick out a card, put it back magicians rummages through the deck, pulls out a card, exclaims, “Is this your card?” That one.

When I was younger, I studied math at the University of Toronto and so I loved this explanation by UK math teacher, author and comedian, Matt Parker about the math behind about guessing what card someone chose. Because as it turns out that with just about everything to do with probability and statistics, that our intuitions are almost always wrong. And not just a little bit wrong, but wrong by a lot.

Now of course no sensible magician would do this trick by guessing. There has to be something else going on. But they might pretend they were guessing for dramatic effect. You never can trust those magicians.

One of the world's most popular card tricks

If someone has shown you a card trick at some point in your life, odds are it was this one. It's not popular because it's necessarily the most miraculously astonishing thing you've ever seen. You probably wouldn't see it on a David Blaine or David Copperfield special, but it has the advantage of being one of those tricks that is knowledge-based rather than skill-based. 

Often after a show someone will ask me how much I have to practice certain things. Some of the pieces in my show are extremely difficult. If I don't practice for more than a day, I start to feel rusty. But in other tricks, the secret does absolutely all of the heavy lifting for me. Once I know the secret, I could put the trick down for years and pick it up again the next time. (Although I'd probably forget what I was supposed to say, the trick would still work!)

This trick (if you're interested in learning) is especially rewarding for kids to learn because you can learn the steps and remember them and when you try it, you get immediate feedback. (You either have the right card or you don't.) So if you're curious to add a bit of magical mind-reading to your next social gathering, you can try and pick up:

The Fabulous Twenty-One Card Trick

(Hope you like math nerds with British accents.)

You'll notice she mentions modular arithmetic, but for whatever reason, they skip that part of the explanation. Which is ok, because six years ago, they already explained it five years ago with a slightly more advanced version that requires a bit more mental arithmetic, but still manageable: