The Monty Hall Problem
Prove itThe Setup
You're the final contestant on a game show. In front of you are three closed doors.
Behind one of them is a brand-new car. Behind each of the other two is a goat.
You have no information about which is which. The host, however, knows exactly what's behind every door.
How a Round Works
- You choose a door. Say you pick Door 1. It stays closed for now.
- The host opens a different door — one he knows has a goat behind it. He never opens your door, and he never reveals the car. Say he opens Door 3, and sure enough, there's a goat.
- He makes you an offer. You can stay with Door 1, or switch to Door 2. Whatever's behind your final choice is yours to keep.
That's the whole game. So — does it matter what you do? Take a moment with it. This one is famous precisely because the obvious answer is so hard to let go of.
Make Your Call
Pick the strategy you think wins more often — and see whether you can say why before you click. The reason is harder to pin down than the answer.