The Monty Hall Problem

The Monty Hall problem is great fun. Here's how I rationalise it. There are three doors. I have to choose one. The chance that the door I pick is the correct one is one in three. The chance that one of the other doors is correct is two in three. Stop right there. Now ask yourself the question - is Monty Hall running around behind the doors possibly changing the location of the prize? Nope. The prize doesn't move. It's exactly behind the same door as it was when the puzzle started. So no matter what happens, my chances of winning with the door I first chose was and remains one in three. And remember that means there is a two in three chance that the prize is behind one or other of the doors I didn't choose. Which means that before he opens one of the two doors I didn't choose it's 50/50 which door has the two in three chance of being correct. After Monty opens one of the doors that 50/50 uncertainty disappears. Which means the two in three chance of being correct now applies to the one remaining closed door I didn't originally choose. Since a two in three chance of being right is better than a one in three chance of being right, I should change my initial decision.