The Monty Hall Problem

Perhaps the most counter-intuitive probability puzzle ever — it fooled thousands of mathematicians when it was first published.

You're on a game show. There are three doors. Behind one is a car; behind the other two, goats. You want the car.

1. You pick a door — say Door 1.
2. The host, who knows what's behind every door, opens a different door — say Door 3 — always revealing a goat.
3. He now offers you a choice: stick with Door 1, or switch to Door 2.

Should you stay, switch, or does it not matter?