The Monty Hall Paradox concerns a dilemma which arose in a certain game show many years ago. The contestant was told to choose one of three doors. Behind one door was a fabulous prize, such as a car, while each of the other two doors hid a goat. After the contestant chose a door, the game show host would open one of the other two doors to reveal a goat. This meant that there were two closed doors—a goat behind one and a car behind the other. The contestant was then given the option of choosing the other closed door or sticking with the original choice. Is there an advantage or a disadvantage to switching doors, or does it matter?

The answer may seem obvious: it cannot make a difference, because after one of the goats has been revealed, the contestant begins afresh with a new decision between two doors, one which hides a goat and one which hides a car. Thus, there is a fifty percent chance of getting the car, and the first decision was a meaningless charade.

This is where probability seems to get a little hairy. When this question was first asked, mathematicians were decidedly and vehemently split. Some stood by the above logic, while others claimed that it was advantageous to switch doors. My own reaction was that switching or staying has no effect on the probability of winning the car.

The answer is that the contestant would benefit from switching. Very much so, in fact.

When you switch, you are either switching from a goat to a car or from a car to a goat. This means that the only time switching will make you lose is if your original guess was the door with the car, which everyone agrees will happen one-third of the time. If you lose one-third of the time, you must win two-thirds of the time, so switching doubles your chances of winning.

The confusing aspect of this problem, as with many problems in the field of probability, is that two events are peceived as equally probable, but in fact are not. Everyone would agree that with three choices, a contestant will choose the door with the car behind it 1/3 of the time. Yet when the game is reduced to two doors, we are inclined to think that our original choice will yield a car 1/2 the time.