The Monty Hall Game

The Game

In the Monty Hall Game, there are three doors. One door is a winner and the other two are losers. The game begins with the player choosing one of the three doors. Of the other two doors, the host reveals one to be a loser. The host then offers the player the choice of keeping the original door, or switching to the remaining door.

There are a few underlying assumptions:

1. The player does not know what is behind any door.
2. Each door has the same likelyhood of being selected.
3. The host must reveal a losing door.
4. The host must offer the player the option of switching their selection.

With the links above, you may play individual games or run automated trials with a specified strategy and see the game statistics.

The Problem

Two strategies present themselves: The player may always keep their original choice or always switch to the remaining door. When the problem was first published, a proof was given indicating that the player should always switch door to maximize the chance of winning with probability 2/3. Two other proofs has been published since the original. Despite the proofs, many people find the result to be paradoxical and refused to believe it.

The purpose of this site is to allow people to play the game to generate empirical evidence that support the theoretical results. This site will record the results and report the stastics.