Imagine that you’re on a game show like Let’s Make a Deal. The host, Monty Hall, presents you with three doors. Behind one is a new car; behind the other two are goats. You choose door # 1. Monty then opens door # 3, behind which is a goat. Monty then offers you the chance to switch your choice to door # 2. Should you switch, or should you stick with door # 1?
Most people answer that it doesn’t make a difference, thinking that the odds are 50:50 that the new car is behind either remaining door. That’s the wrong answer. There is a 1/3 chance that the new car is behind the door you originally chose and a 2/3 chance that it’s behind the remaining door you didn’t originally choose. If you switch, you double your chances of winning the new car.
If you don’t believe this, you can read one of the logical or mathematical explanations of what’s called the Monty Hall paradox (for example, this one or this one). But even then, you probably won’t be convinced until you run your own experiment—which brings us to the point of this post. Click here or here, and play the game several times sticking with your original choice, then several times switching. Keep score. You should find that by switching, you win twice as often.
p.s. 8/26/07: Hat tip to John Bursch.