The Monty Hall problem[1] is a counter-intuitive statistics puzzle: You are on a game show with 3 closed doors. Behind one is a car. Behind the other two are goats.
- You pick a door.
- The host, who knows where the car is, opens a different door to show a goat.
- He then asks:
Do you want to keep your first door, or switch to the other closed door?
- We think:
Okay, there are 2 doors left. One has a car, one has a goat. It must be a 50/50 chance!
The Answer
You should ALWAYS switch! It doubles your chances of winning.
Why?
| Init pick | Host must open (Goat) | you STICK | you SWITCH |
|---|---|---|---|
| D1 (CAR) | D2 or D3 | CAR | Goat |
| D2 (Goat) | D3 | Goat | CAR |
| D3 (Goat) | D2 | Goat | CAR |
| 1/3 | 2/3 |
Lets pretend there are instead 100 doors. Host opens every single door that you didn't choose, and that doesn't have the prize (all 98 of them). There are 2 doors left. Is it still 50/50?
The key here is: The host is not random. He knows result, he must protect it.