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Monty Hall!

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This is not a traditional game, since it has no win or lose; it is an opportunity to explore an interesting probability question.

If you are not familiar with the Monty Hall Three Door puzzle, the premise is this: There is a prize behind one of three doors. The game show host (Monty Hall) invites you to pick a door. Once you've picked a door, instead of opening it, Monty points at one of the other doors, and says "That one is empty." Now he gives you a choice. Do you keep your guess? Or do you switch to the other possible door?

There are three different answers people give to this question:

  1. It doesn't matter which I choose
  2. I'll keep my guess - my odds are better that way
  3. I'll change my guess - my odds are better that way

Which way would you play? When you play this game, you can find out which method works the best. Try always changing your guess. Try always keeping it the same. Try being random. 

Does it work the way you expected? Or were you surprised?

You can click the "Automation" button to let the computer play for you. When the computer plays the game, it always changes its guess after Monty tells which door is empty. If you let the computer play several hundred games, you'll start to get a pretty good idea of the probability involved.

You can also explore related questions by changing the number of doors, or changing the number of empty doors Monty opens for you.

By the way, the information you learned here may be helpful in another game on this site...

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