July 4, 2006

The article mentioned that Marilyn vos Savant "encouraged her readers to simulate the game and draw their own conclusions"... Well, here's a simulation! You can modify the speed to run lots of simulations, "Wargames"-finale style. You can select always switch, never switch, or some probability of switching.

2020 UPDATE: Jim Holt's "When Einstein Walked with Gödel" provides one of the best summaries of why you should switch, and I feel I "get" it now in a way I don't remember if I did when I wrote this simulation:

Counterintuitively enough, the answer is that you should switch, because a switch increases your chance of winning from one-third to two-thirds. Why? When you initially chose door A, there was a one-third chance that you would win the car. Monty’s crafty revelation that there’s a goat behind door B furnishes no new information about what’s behind the door you already chose—you already know one of the other two doors has to conceal a goat—so the likelihood that the car is behind door A remains one-third. Which means that with door B eliminated, there is a two-thirds chance that the car is behind door C.So, "obviously" you had a 1/3 chance of the car at first, but a 2/3 chance you got it wrong. Switching after the reveal lets you safely jump from the side of the 1/3 chance to the 2/3 - or in other words IF that initial 2/3 chance was the right one from the outset THEN you will now definitely win! After a goat is revealed and you switch you can ONLY lose if you were going to win at first (back when your chances were 1 in 3) and vice versa.