Marilyn vos Savant discusses the now famous "Monty Hall" problem in her column in the 9 September issue of "Parade" magazine.

In the Monty Hall problem, an imaginary contestant is given the choice of three doors such as those found in the game show "Let's Make a Deal." Hidden behind one door is a brand new car, and hidden behind the other two doors are goats. After the contestant chooses a door, the host reveals where one of the goats has been hidden and offers the contestant the oppurtunity to switch doors. The question becomes: is the best strategy to switch doors (assuming--of course--the contestant would rather have a car than a goat)? The answer is yes.

The door the contestant initially chose maintains its 1/3 probability of hiding a car. The two doors not chosen have a combined 2/3 probability of hiding the car. When the host reveals the contents of one of those doors, the remaining door not initially chosen now has a 2/3 probabilty of hiding the car. In the long term, the optimal strategy in this game is to switch doors.

The former host of "Let's Make a Deal," Monty Hall, for whom this problem is named was among those to find the actual flaw in this problem. The problem assumes that the host will always act in the behavior stted. However, realistically, if the hosts motives are not known, no optimal strategy can be found. When a person initially picks a door with a goat, the host may decide to simply award the goat without revealing another door or offering a chance to switch.

Sadly, the bulk of the over 10,000 letters vos Savant received in response to her column incorrectly stated that the two doors remaining each had a 1/2 probability of concealing the car after a door with a goat was revealed. A large portion of those letters came from professional mathematicians. Probability is tricky and deceptive, otherwise Las Vegas would be just another town in the desert.

Author: Paul Koenig

References:
Chance Project. Untitled page. 9 October 1998 <http://www.dartmouth.edu/~chance/course/topics/Monty_Hall.html>.

Loy, Jim. 1998. "Monty Hall Trap." 9 October 1998 <http://www.mcn.net/~jimloy/monty.html>.

Sky Coyote. 1995. "Three Door Puzzle: Intro." 9 October 1998 <http://www.intergalact.com/threedoor/threedoor.html>.

Weiner, Herb. 1998. "Marilyn is tricked by a game show host." 9 October 1998 <http://www.wiskit.com/marilyn.gameshow.html>.

Zabrocki, Michael. Untitled page. October 9, 1998 <http://math.ucsd.edu/~crypto/Monty/montybg.html>.