The Monty Hall Game

Door 1 Door 2 Door 3
Distribution graph


In the Monty Hall game, there are three doors; a car is behind one and goats are behind the other two. Click on the Play button to start a new game. Then select a door by clicking on the numbered buttons. The host will open one of the other two doors. Finally select a door again (you may stick with your original selection or switch). This door is opened and you either win or lose.

Either of two host strategies can be selected with the list box. In the standard strategy, the host always opens a door with a goat); in the blind strategy, the host randomly opens one of the two doors available to him. Variable \(u\) is the number of the door with the car; \(x\) is the number of the first door selected by the player; \(v\) is the number of the door opened by the host; and \(y\) is the number of the second door selected by the player. Variable \(w\) indicates a win: \(y = u\). The variables are recorded in the record table on each update. The relative frequency distribution of \(w\) is shown in the data graph and is recorded in the data table.