# 11/18/2004

On a Linux newsgroup, of all places, there’s been a two-day discussion about the famous Monty Hall Paradox. From the UC-San Diego math department comes this explanation of the problem:

The particular game that we are concerned with here is where Monty Hall offers you the opportunity to win what is behind one of three doors. Typically there was a really nice prize (i.e., a car) behind one of the doors and a not-so-nice prize (i.e., a goat) behind the other two. After selecting a door, Monty would then proceed to open one of the doors you didn’t select. It is important to note here that Monty would not open the door that concealed the car. At this point, he would then ask you if you wanted to switch to the other door before revealing what you had won.

Apparently in September 1991, a clever reader wrote to Marilyn vos Savant (reputedly one of the smartest humans alive) and presented this problem. She answered that you should switch your choice to the other door and thus double your chance of winning. Apparently thousands of people wrote to her and said she was flat wrong, and that in fact your chance of winning remained 50-50 because there were now two doors from which to select.

It makes your brain hurt to think about, but the math shows irrefutably that if you pick the other door your odds of winning are 66%, compared with 33% if you’re stubborn and remain with your original choice.

Now if I could just find someone with three doors, two goats, and a nice car…