Sunday, December 31, 2006

The Monty Hall Problem

I've had a problem with Monty Hall for quite some time now. I'm not the only one though -- apparently there are a lot of really smart people who do too. In fact so many people have a problem with him that they named a problem after him.

What is "The Monty Hall Problem"? It's basically a math problem and as it turns out has nothing to do with the fact that he's Canadian. Suppose you're on a game show and the host tells you to choose between three doors and one has a car and the other two goats behind them. You choose door 1 and the host then reveals that behind door 3 is a goat and gives you the chance to switch to door 2. Should you switch? It might surprise you to hear what the smart people of the world will tell you (assuming also that you'd prefer a car to a goat).

This question was made famous in a Parade Magazine column in 1990 by writer/playwright/world's smartest person Marilyn vos Savant. As it turns out, Ms. vos Savant didn't frame the question and its assumptions properly and her answer set off a firestorm of controversy/criticism. Read all about it at the links provided above.

As a side note, if you're wondering how I came across this , I'll tell you. I'm watching football and a commercial came on for Cialis or Plavix or some drug (whichever one is for heart disease, not ED) and there was some guy hawking it who claims to have invented the artificial heart. He looked just greasy enough to not be real, but also just unattractive enough to not be an actor, so I decided to ivestigate. It turns out that this guy is the real deal. He did in fact invent the world's first artificial heart and did the first transplant at the University of Utah. Then he married Marilyn vos Savant, but not necessarily in that order.


Marc said...

Nice way to make us scour through links for the meat of your post. Sad to say I read the wiki article on the Monty problem and I still don't understand it.

SmootheP said...

ahhhh... just figured it out. you have to go through the different scenarios to understand it:

basically, you have 3 options with your first choice - 1) car, 2) goat A or 3) goat B. then just carry it on from there and you can't miss it. always better to switch.

if you always switch when given the option (after being shown a goat), the only way you can lose is if you have already picked the car on your first choice (1/3 chance). if you picked a goat on your first choice (2/3 chance), then by default when you switch you will be switching to the car (because they always show a goat).

too bad there's no way to know whether your initial pick was a car or goat before making the switch... ;)

i'm really glad i know people who post on substantial, educational topics. (much unlike my latest post on luffas.) you guys are making me look either a little smarter, or a lot dumber.

David Kennedy said...

The problem with the way it was framed in the Parade column is there were certain assumptions left out. The way it was stated leaves room for other motives by the game show host: for example, is the host only opening the third door and allowing you to switch because you already chose the car and he doesn't want you to get it? This part of the wikipedia page gives a much better explanation of what I'm trying to say.

Marc said...

I gotta' say... I think Pete's explanation is better than Wiki's personally.

The Fella said...

my explanation works because there are no capital letters. there are some underlying societal problems with all these capital letters we use so frequently. think about it.

Uri Kalish said...

I've got my own version:

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