Stay or Switch is an entertaining new site devoted to the “Monty Hall” problem.
Here’s the game:
- There are 3 doors. Each door conceals a prize: an expensive car or one of two goats. The prizes have been placed randomly. You want the car.
- You pick a door. It remains closed for now.
- The host, who knows what is behind each door, always opens a door other than the one you picked, and always shows you a goat.
- The host gives the choice of staying with your original choice, or switching to the other closed door.
- You decide whether to stay or switch, and get either a car or a goat.
Althought it seems that each of the two closed doors carries a 50-50 chance of success, you actual have a 2/3 change of winning if you switch. This counterintuitive problem stirred up a fierce controversy several years ago.
Stay or Switch allows you to play the game as many times as you want. It keeps running statistics on how you do, and it includes your stats in the totals for all players. It also offers a history of the problem and four different video explanations.
This is an excellent interactive tool for teaching a difficult concept. I found it through Wild About Math.