White lines mark the mathematical probability (33.3% vs 66.6%)
Fast-forward:
Why Switch?
It feels like a 50/50 choice, but your brain is playing tricks on you.
The 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. His hands are tied—he cannot pick the car. He effectively consolidates that entire 2/3 chance into the one remaining door.
By always switching, you instantly win the car every single time your first pick was wrong!