The Monty Hall Problem

The Monty Hall Problem, as originally written, goes like this:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

So, you're more likely to win if you switch?

It seems odd - surely the odds don't change? Yet, if you stick you'll only win a third of the games you play on average. Change your mind, and you'll win twice as many games.

It's important to realize that at the start, you've a 1-in-3 chance of picking the car. Or to put it another way, you've a 2-in-3 chance of picking a goat.

Now if you do start out picking a goat, then there's only one remaining goat I can reveal to you - this means that 2-out-3 times, I've got no choice in which box to reveal to you. This means, 2-out-of-3 times, you are better off switching because the only box I can leave unopened for you contains the car.

Still don't believe it?

This site records all the games played. So far, we've logged 1063 games:

• Out of 334 games where the player didn't switch, they won 106 games (32%)
• Out of 729 games where the player switched, they won 474 games (65%)