### From Wikipedia, the free encyclopedia

The **Monty Hall problem** is a probability puzzle based on the American television game show *Let’s Make a Deal*. The name comes from the show host, Monty Hall. The problem is also called the **Monty Hall paradox**, as it is a veridical paradox in that the result appears absurd but is demonstrated to be true. ^{[1]}

A well-known statement of the problem was published in *Parade* magazine:

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; 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? (Whitaker 1990)

Because there is no way for the player to know which of the two remaining unopened doors is the winning door, most people assume that each of these doors has an equal probability and conclude that switching does not matter. In fact, the player should switchâ€”doing so doubles the probability of winning the car from 1/3 to 2/3.