Risk Management/attitudes to Risk

The Monty Hall Dilemma

The emotional element in decision-making is highlighted by a famous mathematical problem known as the Monty Hall dilemma. Monty Hall was the host of an American game show where the winning contestant had to select their prize from behind one of three closed doors. Behind one of the doors was a car and behind the other two were goats. The contestant would pick a door and Monty Hall (who knew what was behind each door) would open a different door to reveal a goat. At this point the contestant would be offered the chance to stick with the door s/he had chosen or to switch. What should they do?

The answer to the Monty Hall Dilemma is that, based on purely logical, mathematical reasoning, it is better for the contestant to switch doors (assuming of course that they want to win the car). The contestant initially had a one in three chance of picking a car. If they stick with the same door those odds don't change. However, now that one goat has been revealed, if they switch doors there is a two in three chance that their second choice will win them a car. Human nature however encourages us to stick with the first choice. This is for the simple reason that we don't want to look foolish. If you have changed your mind and then selected the wrong option the embarrassment factor is far greater than if you simply chose wrongly in the first place. There are many web sites that offer complex mathematical proofs of the Monty Hall dilemma some of which are listed below.

The following website has a simulation of the Dilemma as well as an explanation of how it works -
http://math.ucsd.edu/~crypto/Monty/monty.html

An entertaining animated simulation (with sound effects) of the Monty Hall Dilemma can be found at -
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/MontyHall/MontyHallSim.html

Website urls were correct at 11 August 2004.

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