Your guess
You pick door 1. The host opens door 3: a goat. Do you switch to door 2?
Why it's two thirds
Your first pick finds the car with a chance of only 1 in 3. With 2 in 3 it is behind one of the other two doors. The host knows where it is and always opens one of those two with a goat. If you first picked a goat – in 2 out of 3 games – switching is sure to land you the car.
A million doors
Marilyn vos Savant offered a picture: imagine a million doors. You pick one, and the host opens all the others except door 777,777 – goats everywhere. Wouldn't you switch at once? Pigeons, by the way, quickly learn to always switch when they face the problem again and again – unlike humans.
10,000 letters
The puzzle had been posed back in 1975 by the statistician Steve Selvin. It became famous in 1990, when Marilyn vos Savant advised in her column in Parade magazine: switch. About 10,000 readers wrote in, nearly 1,000 of them with PhDs – most said she was wrong. Even the mathematician Paul Erdős at first called the solution impossible.
