The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall.
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a Gold; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
The contestant should switch to the other door. Under the standard assumptions, the switching strategy has a 2/3 probability of winning the Gold, while the strategy that remains with the initial choice has only a 1/3 probability.
When the player first makes their choice, there is a 2/3 chance that the Gold is behind one of the doors not chosen. This probability does not change after the host opens one of the unchosen doors. When the host provides information about the 2 unchosen doors (revealing that one of them does not have the Gold behind it), the 2/3 chance of the Gold being behind one of the unchosen doors rests on the unchosen and unrevealed door, as opposed to the 1/3 chance of the Gold being behind the door the contestant chose initially.