Behind two of the doors is nothing, and behind one of the doors is a cash prize:

Each time you play the game, the door that the prize is behind will be chosen randomly by the gameshow host.

Your task is to pick the door which has the prize behind it.

To add some interest to the game, it will proceed as follows:
1. The gameshow host will place the prize (randomly) behind one of the doors (ie. the host knows which door the prize is behind)
2. The gameshow host will ask you to pick a door.
3. The gameshow host will then open one of the other doors so that you are only left with two unopened doors. The host will make sure he never opens a door which has the prize behind it.
4. The gameshow host will then give you the chance to either keep your original selection, or allow you to change to the other door which is left unopened.

The question is, what do you do?
Is it
(a) Better to keep your original choice?
(b) Better to change to the other door?
(c) Doesn't matter what you do, since it's still a random pick and the prize could be behind either of the two doors?

In other words, the question is:

• What is the probability that you will get the prize if you keep the door you have originally chosen, and
• What is the probability that you will get the prize if you change your selection to the other unopened door?

Think about the problem for a while before you look at the answer, as it may surprise you!

Try it for yourself

(NOTE: The game requires a forms-capable browser. If, during the game, you get a message from your browser saying "No data in document", just reload the page (and repost the fields, if asked) until you get a full page.)

Go to:

• Game simulation
• Answer to problem
• N-door generalization