This morning, my friend Chris (who is– and I say this with affection– truly the biggest geek I know) sent me a link to yesterday’s Wikipedia featured page, “The Monty Hall Problem.” This is essentially a math puzzle. Allow me to quote at length from the wikipedia site:
The Monty Hall problem is a puzzle in game theory that is loosely based on the American game show Let’s Make a Deal. The name comes from the show’s host, Monty Hall. In this puzzle a player is shown three closed doors; behind one is a car, and behind each of the other two is a goat. The player is allowed to open one door, and will win whatever is behind the door. However, after the player selects a door but before opening it, the game host opens another door revealing a goat. The host then offers the player an option to switch to the other closed door. Does switching improve the player’s chance of winning the car? With the assumptions explicitly stated below, the answer is yes â€” switching results in a 2/3 chance of winning the car.
The problem is also called the Monty Hall paradox, in the sense that the solution is counterintuitive, although the problem is not a logical self-contradiction. It has generated heated debate.
“Generated heated debate…” ya got that right. Now me, being an enormous idiot when it comes to math, I didn’t exactly weigh in with my reasoning and opinions. But when I first heard about this puzzle 15 or 18 or so years ago, I do recall there being “heated debate” among my geeky friends. I remember one friend of mine arguing bitterly that this could not possibly be true. The problem is that this particular friend didn’t know a whole lot about math either.
I did have one friend of mine who immediately said that he knew this seemingly illogical solution was correct. This guy is someone I have long lost touch with, but just to give you an idea of his geek credentials: he finished his Ph.D. in genetics at Harvard University, where he was being funded by a Howard Hughes Foundation fellowship. Anyway, his response when I brought this all up with him way back when was something like “it’s math you wouldn’t understand, Steve.”
Anyway, I recall actually testing the Monty Hall problem one drunken night, I think with a friend of mine named Lisette (who is now a professor someplace– lost touch with her, too). I played the role of Monty, controlling the doors and the location (metaphorically, of course) of the goats and new cars, and she played the role of contestant. One hundred times in a row, she picked one door first and then switched. And damned if she didn’t “win” 66 times.