You're on a game show. Behind one door is a car, behind the others are goats. You pick a door. The host, who knows where the car is, opens other doors to show goats until only one other door is left closed. Then he asks: do you want to switch?
Keep score
Every game you play is counted by the strategy you chose. Too slow? Let the computer play thousands of games for you.
The thin line marks where each bar settles after many games.
Why switching wins
Forget the host for a moment. Your first pick is right only 1 in 3 times. That never changes, because the host never opens your door and never reveals the car.
Whenever your first pick was a goat, the host's doors point straight at the car. Switching turns your 2 in 3 chance of being wrong into a 2 in 3 chance of winning.
Still not convinced? Try 50 doors. You pick one, the host opens 48 goats and leaves one door shut. Would you really stick with your first guess?