Umm, the correct answer is to switch doors. It has been discussed ad naseum as you mention. The simplest way to see that the switch doors gives you a 2/3's ch

Umm, the correct answer is to switch doors. It has been discussed ad naseum as you mention. The simplest way to see that the switch doors gives you a 2/3's chance of winning is as follows. Without loss of generality, assume that you always pick door 1. If the car is placed randomly, you have a 1/3 chance of getting the car. To see this, note that when not switching, you only win if your initial guess has the car behind it, which happens 1/3 times. When you switch doors you only win if not switching loses. Since not switching wins 1/3 times, switching wins 2/3 times. You can write a simple program to simulate the game and see that switching wins 2/3 times.