Monty Hall Problem Explained

The solution presented by vos Savant (1990b) in Parade shows the three possible arrangements of one car and two goats behind three doors and the result of staying or switching after initially picking door 1 in each case:

Behind door 1Behind door 2Behind door 3Result if staying at door #1Result if switching to the door offered
CarGoatGoatWins carWins goat
GoatCarGoatWins goatWins car
GoatGoatCarWins goatWins car

A player who stays with the initial choice wins in only one out of three of these equally likely possibilities, while a player who switches wins in two out of three