My brain is boggled

[drcpunk]

rob_donoghue has a post explaining why, if you pick one of three doors behind which there is a prize, and one of the other doors is opened showing that it does not have the prize, you should switch your pick to the remaining door.

I thought at first that the key is that the reveal is not random in a game show. But, I think now that it doesn't actually matter whether the reveal is random or not. The math is the same.

Comments

[batyatoon]

OH GOD IT'S THE MONTY HALL QUESTION RUN AWAAAAAAY


Personally I think the fact that the reveal is not random actually destroys the math. Because the math is based on odds and probability, and probability is based on information, and someone with more information than you have is manipulating how much information you get.

[avram]

It has to matter whether that the reveal isn't random, because if the reveal is random, there's a significant chance the the reveal will open the door with the prize behind it.

Or let me put it another way: There are three doors, A, B, and C. One has a prize, two have junk. Monty asks you to pick a door, you pick A. Now Monty opens a door, but he doesn't open the door you picked, so he's going to open either B or C.

If the prize is behind A, he can pick between B and C at random. But if the prize isn't behind A, then it's behind either B or C, and he can't pick at random, he has to pick whichever one doesn't have the prize.

[jl8e]

It matters if it's random -- if it's random, he can randomly open the door with the prize.

The reason it works the way it does is because his choice isn't random 2/3 of the time -- if the prize is behind B, he must open C and vice versa.

I've got a variety of ways to explain it. It's isomorphic to a problem that often comes up in the play of a bridge hand, so bridge discussion groups get the thread all the time.

[kent-allard-jr.livejournal.com]

Heh! I teach this in class sometimes :)

[scbutler.livejournal.com]

I believe it's actually called the Monty Hall Theorem.

[ckd]

Also, if the prize is an airplane on a treadmill....