You are now given the option to stay with your original guess or switch to the remaining unopened door. Mathematician: In my opinion, the easiest way to understand the Monty Hall problem is this: Suppose there are three doors, A, B and C and you originally chose door A. If the prize was originally behind door B on the other hand (which also has a chance of 1 in 3), then when you pick door A, door C will be removed. Hence, if you switch you will be switching to door B, and therefore you will win. Hence, if you stay with your original door, you win if and only if the prize was originally behind door A.