This is a legacy post from December 10th, 2004

Stick or Switch game

There are a hundred other things I should have done with the time, but I've written a little game to test one of my favourite quirks of mathematics.

The game involves guessing which of three cups the red ball is under... when you've made a first guess, one of the other cups without the ball under it is then removed, leaving you with two: one with the ball under it and one with nothing. You then have the chance to stick with your original guess or switch to the other remaining cup.

Intuition seems to say that your original guess is just as likely to be right as switching to the other cup, but the statistics show that switching significantly improves your odds of picking the right cup.

I know it sounds wrong, but it really works. I've programmed the game to keep track of the percentage of times switching finds the ball in a given session, and to keep track of a percentage for everyone who ever plays the game. It's currently on 377 plays and the results are working out exactly as I've said.

It's actually less a quirk of mathematics as a quirk of human perception. But a fascinating one, I think.

Play the Stick or Switch game to see for yourself.