The Monty Hall Problem

[denny]

Some friends bent my brain yesterday with a thing called 'the Monty Hall problem' - I thought I'd share the sheer confusion with others...

Description of problem, and ensuing discussion (including lots of explanations which may either help or hurt your head, or possibly both):
http://www.livejournal.com/users/duranorak/790534.html?thread=4120070#t4120070

An off-site explanation, also linked in the above discussion but posted separately here out of sheer helpfulness (I still didn't get it after reading this personally):
http://www.io.com/~kmellis/monty.html

Comments

[stuartl.livejournal.com]

Right. This afternoon I set about writing a C program to prove you wrong.

The program plays the part of the player and the host and does 20,000 iterations of the game using 512 doors in about a tenth of a second. Yes, it's quite nippy, and highly unoptimised because I wanted to be 100% sure the logic was right.

However, halfway through the program I realised why you're all correct. I continued writing the program anyway to prove the point (and yes, it does prove it perfectly) but I saw the bit I'd missed before.

This is how I explained it to myself:

After you randomly choose your door there is a (n-1):1 chance that the prize is in the remaining doors. i.e. It's almost definate.

By the host opening the remainder of the doors he's narrowed down the prize location to the one remaining closed door. As someone else said, the chances of it being in that door are still (n-1):1.

QED, I guess. Apologies for being an arse :)

[dennyd.livejournal.com]

Wish I'd thought of doing that... I argued with people about it for ages before I suddenly clicked :)