The Monty Hall Problem

This puzzle is called the Monty Hall Problem.

You should switch because if you do, you have a 2 in 3 chance of winning. If you don't switch, the probability of winning is 1 in 3.

The intuitive answer for many people is that the probability will be 1 in 2 after the host opens one of the doors. But our intuition misleads us here, as it does in many cases.

Think about it this way: If you initially picked the wrong door, and you switch, you will certainly win. There is a 2 in 3 chance you initially picked the wrong door, so there is a 2 in 3 chance you will win if you switch!