3 Doors

There's 3 doors. 1 door has a million dollars behind it, the other 2 nothing. All three doors are equally likely to have the million behind it. You pick one of the three doors. Someone who knows which door has the million, opens a door that doesn't have the million and is not the door you've chosen. Now, you have the option to change doors. Should you stay with the door you originally chosen or change your selection to the other door?

 

Ah, the classic Monty Hall problem This is how I view the problem:

1) When you first make your choice, you have a totally random 1/3 chance of being right.

2) The person already knows which door has the money and and which doesn't contain anything at all, and gives you the option to choose from the 2 remaining doors.

3) This means there are now 2 options left, one door with the $1,000,000 and the other nothing, thus you have a 1/2 chance either way.

4) The question is, whether to switch or not. Your original descision was based on a 1 in 3 chance, whereas if you do switch, that is based on a 1 in 2 (50:50) chance.

tl;dr - It doesn't matter what door you choose, you have an equal chance of picking the door with the $1,000,000.

 

But those who ended up making the switch had a bigger chance of being correct!

I forget the math behind this.

 

I'd love to see the math behind why switching doors were to increase your chances.

I'm seeing it is as 33.3% chance to 50% chance regardless of the door you chose.

 

Doesn't mater? Same chance 1/2 INHO

 

I know that there is proven math behind it that backs up that you should always switch because it's a higher chance, but my mind can't fathom it.

Spoiler: The solution

 

This is basic game theory: If it's KNOWN that the money isn't beside the first door selected then you should switch doors. If it's not known it really doesn't matter. The math is shown below in the source but for thoses of you too lazy it has been statistically proven.


Source: http://www.math.ucsd.edu/~crypto/Monty/montybg.html

 

I'm not sure why this is a mathematically hard concept to anyone, seems pretty simple/obvious to me. Kind of like a question that they might have given me in my fourth grade enrichment class and asked to explain why..

 

Explained well here:

http://www.youtube.com/watch?v=mhlc7peGlGg

 

Wasn't this explained in the movie "21" as well? One of my favorite movies.
It was asked by the proffesor in the beginning of the movie.

 

Is that the gambling one? Maybe I'm thinking of something else >.<

 

This is proven so not really a discussion

Also ya, 21 is the gambling movie