The Monty Hall Problem, also known as the Car and Goat Problem or the Three-Door Problem, is a mathematical game problem originating from game theory. It is loosely based on the American television game show "Let’s Make a Deal." The problem is named after the show's host, Monty Hall.
The rules of the game are as follows: The contestant is presented with three closed doors. Behind one of the doors is a car, and selecting the door with the car behind it wins the contestant the car. The other two doors each hide a goat. When the contestant selects a door but does not open it yet, the host, who knows what is behind each door, opens one of the two remaining doors to reveal a goat. The host then asks the contestant if they would like to switch to the other unopened door.