Monty Hall
A car is behind one of three doors and goats are behind the other two. You pick a door. Monty, who knows where the car is, opens another door to show a goat and offers you the chance to switch. Should you?
From the slides: Why should anyone care about chance? and Probability and what happens when you learn something.
Play it yourself
Simulate thousands of games
Games that count
0
Win rate if you stay
—
Win rate if you switch
—
What to notice
- Staying wins exactly when your first pick was right: 1 time in 3. Switching wins in the other 2.
- Slide to 100 doors. Monty opens 98 goat doors and leaves one closed. Your door still has its original 1/100; the door he pointedly left shut has 99/100.
- Now tick Monty doesn't know. He opens doors at random, and the games where he accidentally reveals the car are thrown away. Among the games that survive, staying and switching are equally good. Monty's knowledge is what makes switching better — the information you get depends on how it was produced.