# Welcome to the game of doors

1. Sep 25, 2009

### tanujkush

Welcome to the game of doors!!

Anchor: Alright then, you have three doors in front of you, A, B, C. Two of these three contain nothing, one contains the proof of the unified theory yet unknown to man . You can choose any one door, which one do you choose?

You: Uhmmm.. I think I'll go with door A

Anchor: Are you sure?

You: Yeah!

Anchor: (opening door C) Well well, there is nothing behind door C! Arent you glad you didnt choose that door?

You: (wiping the sweat off) Yeah! Now show me whats behind door A.

Anchor: Wait a minute, what if I made you an offer. Would you like to change your door? Would you like to choose door B instead?

You: (Damn, I should have paid attention to those undergrad probability lessons!!) Uhmmm.. I dont know... I think I will go with what probability tells me. Lets ask the folks over at Physics Forums what they think? Should I change doors or stick?

2. Sep 25, 2009

### CompuChip

Re: Welcome to the game of doors!!

Change.

(CompuChip wonders why this puzzle has been around since like 1000 AD and nobody got to see the proof yet).

3. Sep 29, 2009

### tanujkush

Re: Welcome to the game of doors!!

there is a proper closed form proof for this really.

4. Sep 29, 2009

### lanedance

Re: Welcome to the game of doors!!

Ch-ch-changes
Just gonna have to be a different man
Time may change me
But I can't trace time

Last edited: Sep 29, 2009
5. Sep 30, 2009

### CompuChip

Re: Welcome to the game of doors!!

Then you should publish it and get famous.

(I was talking about the Riemann hypothesis of course, the proof of why changing the doors increases your odds of winning to 2/3 can be written out on a single line).

6. Sep 30, 2009

### tanujkush

Re: Welcome to the game of doors!!

I of course, was talking about the second part of your quote.

7. Sep 30, 2009

### Rogerio

Re: Welcome to the game of doors!!

It depends.
Does the Anchor know the doors a priori?
If he doesn't know what is behind each door, then changing from door A to door B makes no difference.

8. Sep 30, 2009

### HallsofIvy

Staff Emeritus
Re: Welcome to the game of doors!!

I remember, about 20 years ago, seeing this problem as an exercise in chapter 1 of an introductory probability text.

9. Sep 30, 2009

### EnumaElish

Re: Welcome to the game of doors!!

This problem still stumps me somewhat, philosophically speaking. Suppose the anchor did not know a priori, but I didn't know that she didn't know. Shouldn't I still change?

Put differently: suppose I don't know with certainty whether she knew. If she knew, then I better change. If she didn't, then (by the logic presented somewhere along the thread) it's all random and I'll be no worse off if I changed. On the net, I should change.

Since I can never know with certainty that she didn't know, I should change every single time I am in this position.

Last edited: Sep 30, 2009