Puzzles index

The Monty Hall problem


This puzzle is named after Monty Hall, who is the host of an American television game show. There are three doors, two with goats behind and one with a car. You hope to choose the door hiding the car. When you have chosen, the door isn't opened, but the host opens one of the other doors, showing a goat. (It is essential for the problem that the host knows which door hides the car, that he doesn't reveal the car, and that he doesn't open the door that you've chosen.) Now you have the chance to change your mind. There are two doors left. Should you stay with your original choice, or should you chose the the last door instead?

It's tempting to think that it doesn't matter which you should do. Surely the odds haven't changed. In fact, most people decide to stay with their original choice (probably for psychological reasons rather than mathematical ones!) So let's try an experiment to see if it does make a difference. It's set up to assume that you keep the same door. Click on a door to play the game. There will be an animation to play the game. Carry on doing this a number of times (say about 20 times), and see how often you win or lose. Make a note of what seems to be happening. Now choose "Change your mind". The totals will go back to zero. Carry on clicking on a door to get the new totals, and compare them. Do they seem to be behaving the same way?


Click here for an explanation but think about it yourself first! The explanation is more fun, and makes more sense, after your own attempts.