It's called the Monty Hall Paradox and it's a pretty damn interesting teaser to puzzle your mind over. I came across it in the book The Curious Night of the Dog Incident and thought some of you dear readers (Is it one or two now? I can't ever remember, there's getting to be some many of you!) would appreciate it as well. It goes something like this; Marilyn Vos Savant, the women with the highest IQ in the world, as according to the Guinness Book of World Records, has a column in Parade Magazine in which she attempts to answer difficult questions, often of the mathematical and logical variety, sent in by her readers. In 1990 Craig F. Whitaker of Columbia, Maryland famously sent in the following question.

You are on a game show on television. On this game show the idea is to win a car as a prize. The game show host shows you three doors. He says that there is a car behind one of the doors and there are goats behind the other two doors. He asks you to pick a door. You pick a door but the door is not opened. Then the game show host opens one of the doors you didn't pick to show a goat (because he knows what is behind the doors). Then he says that you have one final chance to change your mind before the doors are opened and you get a car or a goat. So he asks you if you want to change your mind and pick the other unopened door instead. What should you do?

In her response, Marilyn Vos Savant said that you should always change your mind and pick the final door because by doing so would give you a 2/3 chance of getting a car. Now at first blush this seems wrong; intuitively you see it as a clear 50/50 type of proposition. Two doors left and you have to select one, just like flipping a coin, right? What could be more clear or simple or American than that? Well not so fast so says Marilyn with that high powered overgrown cranium of hers.

The answer she gave set off a minor firestorm of sorts among the readers of her Parade Magazine column. Approximately 92% of the letters she received in response claimed she got it wrong...dead wrong. Many of the letters that were sent in were from mathematicians and scientist from around the country. Here are some samples of what was said:

I'm very concerned with the general public's lack of mathematical skills. Please help by confessing your error.

Robert Sachs, PhD, George Mason University

There is enough mathematical illiteracy in this county, and we don't need the world's highest IQ propagating more. Shame!

Scott Smith, PhD George Mason University


I am in shock that after being corrected by at least three mathematicians, you still do not see your mistake.

Kent Ford, Dickinson State University

You are utterly incorrect. How many irate mathematicians are needed to get you to change your mind?

E. Ray Bobo, Ph.D., Georgetown University

Well sorry geniuses, but ole Marilyn is right, and don't you feel like giant dumbasses?

So anyway, the graph at the top of the post I think best illustrates how Marilyn is right. There is a mathematical equation that proves it as well, but you have to be some kind of real wiz to see it in those terms and so I will save us all the brain damage and present it visually.

So going back to the graph we can see the consequences of each possible selection . If you choose curtain 1 and stay with your choice when given the option to change, you will get a goat, but if you CHANGE then you get a car. So moving to the next possible choice, curtain number 2. If you choose curtain 2, you can see that by sticking with you choice you would again get a goat, but if you CHANGE you once again get the car. You follow me? So of the two possible choices so far, curtain 1 or curtain 2 when given the option to change and change indeed you do... you get the car.

Ok so let's move on to the third possible choice. Curtain number 3 where in this case if you stay you get the car and you if you change you get the goat.

So to recap, that 1 times of out 3 if you change you get the goat in other words 2/3 times you change you get the car... just like Marilyn said. Capiche bitches!