Why Switch?
It feels like a 50/50 choice, but it isn't.
- Start: You have a 1/3 chance of picking the car. The other doors have a 2/3 chance.
- The Reveal: Monty opens a door. He cannot pick the car. He effectively consolidates that entire 2/3 chance into the one remaining door.
By switching, you are betting against your original (unlikely) guess.