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.

A Lucky Discovery

Sometimes in my show I reveal the truth about my past, before I was a professional magician, I was at the University of Toronto studying math. Not the fast track to popularity you think it might be, but it teaches you some powerful techniques for problem solving.

I made this lucky discovery when I found out that the most recent (2019) Christmas Lectures at the Royal Institution were presented by Hannah Fry. Hannah is a math — or since this is the UK, I will be respectful and switch to saying maths — communicator and an associate professor at University College London. The Christmas Lectures is cultural institution in the UK started by Michael Faraday (the person who essentially discovered electricity) back in 1825. The program is designed to bring science to a family audience.

I was checking out one of the lectures, which is all about probability, and luck. Everything is presented in the most interactive and visual way possible, and they did a fantastic job. It’s a talk about maths with no blackboard and no formulas. She discusses real problems like “What does it mean when it says there is a 20% chance of rain tomorrow?” and also the problem of false positives in medical screenings. I particularly enjoyed her treatment of the paradoxical “prisoner’s dilemma” from game theory.

But the best part is, she opens with a magic trick!

Not just any magic trick, but it’s a Canadian magic trick, and an old one at that. Her opening piece (which involves a small amount danger — trigger warning) is a giant version of something created by Canadian magician Stewart James. It appeared in a magic magazine in 1926 under the title “A Match for Gravity”. She does an oversize version then repeats with a smaller version with a teacup. The original used a paper match and a pocket watch… but even at the Royal Institution, I doubt there were any children there she could have borrowed a pocket watch from.

Stewart is widely regarded as one of the most creative magicians who ever lived. He was particularly fascinated by mathematical principles, but also created a number of curious pieces that were far more physical in nature, like this one. He was a magician as a hobbyist, working for most of his life as a postal worker in his native town of Courtright, Ontario. His work was collected in the three giant volumes shown below:

Author Allan Slaight holding three very heavy books containing the collected secrets of Stewart James

As if the world were not yet full enough of strange coincidences, this photo currently appears on the wall of the Art Gallery of Ontario as the “Allan Slaight Collection of Magic Posters” is currently on display in an exhibition called Illusions: The Art of Magic.

Also prominently featured in the lecture is another maths communicator Matt Parker, who created what is possibly the best-titled event ever: “The Festival of the Spoken Nerd.” ‘Nough said.

Alternative Math

Before diving head first into the world of magic, I studied Math at the University of Toronto. (And also business, but practical life skills are overrated.) So things like this speak to me:

It's a little long for casual internet time-wasting the payoff at the end was entirely worth it.

Mystery Solved

On my second day at the University of Toronto in a course called Introduction to Proof (which really was a life-changing course that I heard they stopped offering) the Professor gave this question (actually a variation with 100 people and no aliens) and (owing to the fact that all math teachers are inherently creatures of pure evil) neglected to provide the answer.

In the dozen or so years it's been this is the first time I've seen that problem and so here's the answer. Now you don't have to wait quite as long as I did.