# The Monty Hall Problem

## Math Puzzles of the Month The Monty Hall Problem

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

This math puzzle is named after Monty Hall, the host of an American television game show called Let’s Make a Deal, which was on during the 1960s and 1970s. In one of the games, Monty presents contestants with three doors.

Behind one of the doors 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?

After you've tried this for yourself, check our solution.