In the Monty Hall problem there are three doors, one car, two goats. You pick a door. The host, who knows where the car is, always opens a different door with a goat. If you switch, you win the car two times out of three. Staying wins one time out of three. The host's knowledge is the whole trick. He did not open a door at random.

Worth knowing

Switching doors wins twice as often, because the host deliberately showed a goat.

Monty Hall problem · Encyclopaedia Britannica · Year unknown