Puzzles

The Monty Hall Problem

Prove it

The 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

  1. You choose a door. Say you pick Door 1. It stays closed for now.
  2. 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.
  3. 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.