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?

In the past 15 years, more pixels have been shed over this puzzle than any other. I have seen intelligent people defend both answers to the death.

IMHO, the best way to really understand this problem is to find a partner and play the game. One of you be the game host, and the other be the contestant. Play repeatedly until one of you "gets" it, then switch. (The host will usually get it first.)

In my experience, this is far more useful than writing programs to simulate the system -- people writing programs often unconsciously build assumptions into the programs that invalidate the results.

Posted by Jim Lyon on 2002-10-16 13:08:30