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Three doors, one car, two goats. You pick a door, the host (who knows where the car is) opens another with a goat behind it and offers you the switch. Do you switch? Yes, always: switching doubles your chances of winning.
It's the Monty Hall problem, and its story is as good as its maths. In 1990, the columnist Marilyn vos Savant published the correct answer in an American magazine: staying wins 1 time in 3; switching, 2 times in 3. She received around ten thousand indignant letters, close to a thousand of them signed by university PhDs, insisting she was wrong. She wasn't wrong.
The key: your first choice had a one-in-three chance, and that doesn't change. By opening an empty door, the host concentrates the remaining two-thirds on the other door. Our probabilistic intuition is, quite simply, terrible. Which is why it's wise to distrust it beyond the game shows too.
Source: The New York Times