You are shown three boxes, and told that one of them contains a prize. You are then asked to pick one box, and if that box is the one with the prize, you will win it. After picking a box, you are shown that one of the other two boxes is empty, and offered a chance to change your selection.

Should you do this? Would changing your choice to the other remaining box affect your odds of winning? Why or why not?

First let me say I stood by 50% doggedly until I was challenged to produce an experiment. Sitting with a C compiler, I proved myself wrong. Here's why:

I show you three boxes. When you choose a box, you're right 1/3 of the time. Here we all agree.

However, think of what's next like this: I am holding 2 boxes. I am going to offer you one. 1/3 of the time, I'm going to offer you an empty box (both of mine are empty, you picked correctly). 2/3 of the time, I AM GOING TO OFFER YOU THE PRIZE. The 50% is broken by the facts that 1) the prize does not move, and 2) I have knowledge of the prize -- I am not showing you a random box.

Posted by Paul on 2002-08-14 11:14:20