The Monty Hall puzzle is a brain teaser based on the game show, Let’s Make a Deal. The contestant is presented with three doors and must choose one. Choose the correct door and win a car. Choose either of the wrong doors and win a goat. (Note to rural readers: The puzzle is a first-world conundrum and assumes you’d prefer the car.)
Once the contestant chooses, the host opens one of the doors with a goat and asks the contestant whether he wants to stay with his original choice or choose the other unopened door. As explained here, the contestant should always switch doors, since switching provides a 2/3 chance to win. The math here is not intuitive, but read about it and you’ll understand.
The gimmick relies on the fact that the host knows what’s behind each door and will only reveal a door that hides a goat. The host never reveals a car.