Monty Hall Problem
Trying to find the best strategy to win in this game is a famous brain teaser, not least because so many people (including mathematicians) get it wrong.
The game is very simple: you are shown three closed doors. Behind one of them is a car, behind the two others, a cow. You first pick one door, but it does not open right away. The game host, Monty Hall, who knows behind which door the car is waiting, then teases you by opening one of the two doors that you had not picked to show you the cow sitting there. Then he may offer you a choice: staying with your original pick, or switching to the third remaining door. Should you switch or shouldn't you?
Well, it really all depends!
On the next page, you'll play this game in three different versions, with three different hosts.
Play the game a number of times with each host, and try to decide which strategy (switching or not) is the best. Pick the host before each turn; if you don't choose one, you will have the same host as in the previous turn. Next to each host, you'll see a tally totalling:
1) the number of times played
These tallies will help you to do your problem set. WARNING: However, you need to keep track of one additional number mentally---keep track of the number of times that no switch was offered and you won.