Wednesday, 9 April 2008

Monkeys And Monty Hall

How can anyone resist an article with the title "Cognitive Dissonance in Monkeys"?

Well, actually that's the page's title. The article is titled "And Behind Door No. 1, a Fatal Flaw", which really isn't as fun.

Anyway, the Monty Hall problem is well described by the writer here:
Here’s how Monty’s deal works, in the math problem, anyway. (On the real show it was a bit messier.) He shows you three closed doors, with a car behind one and a goat behind each of the others. If you open the one with the car, you win it. You start by picking a door, but before it’s opened Monty will always open another door to reveal a goat. Then he’ll let you open either remaining door.

Suppose you start by picking Door 1, and Monty opens Door 3 to reveal a goat. Now what should you do? Stick with Door 1 or switch to Door 2?

The odd thing is that the answer feels entirely counter-intuitive. It seems that it goes against all that "coins don't remember results" guff, because the answer is:

[W]hen you stick with Door 1, you’ll win only if your original choice was correct, which happens only 1 in 3 times on average. If you switch, you’ll win whenever your original choice was wrong, which happens 2 out of 3 times.

That is, if you switch you are twice as likely to win.

To see how this relates to monkeys and M&Ms read the rest of the article.

1 comment:

Vince said...

I thought the whole monkeys and M&Ms business clouded the issue myself. But after spending waaaay too much time playing the Monty Hall game at the Times site, I now get it.