How you play this game determines your chances of winning, but you may be surprised to learn what the best strategy is.

This month’s math puzzle is named after the host of an American television game show called  Let’s Make a Deal  that was on the air some years ago. In one of the games, Monty presents contestants with three doors.

Behind one of them is a car. Behind each of the other two doors is an empty room. Monty knows what’s behind each door, but you don’t.

The game is played in three steps:

1. You get to pick a door.
2. Monty opens one of the two doors you did not pick to reveal an empty room. (He never opens the door with the car behind it.)
3. You now have a choice to either remain with the door you picked in step 1 or to switch to the other door that is still shut.

Let’s say you pick door A. Monty opens one of the other two doors, let’s say B.
Now you have a choice to switch to C or stay with your original choice, A. If you stay, you may be lucky
or not.

On the other hand, if you switch to C, you may be lucky…or not.

What do you do? Do you stay with your original choice or switch after Monty opens a door. Why?

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