1. Choose a door.
2. Play the game.
3. See the result.

Play the game many times to get a good average result for the ratio of the number of times that a switch wins versus number of times hold wins.



Well, if you've played the game enough times, you can see that switch wins twice as often as hold. Most people, however, at first argue that it makes no difference whether you switch or stay with the same door. (This was my first guess too)

Why are you twice as likely to win if you switch? The answer is that by opening one of the two other doors, the host is in effect telling you that if the money is behind either of them, then it is behind the one that he has not opened. By choosing to switch, you are guarenteed to win if it was behind either of them. Your odds of winning are 2 out of 3. If you stay with your original choice, the odds remain 1 out of 3.

Sound hard to believe? Well, the simulation above confirms it!

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