The Monty Hall Problem - a state-space explanation

Here is yet another explanation of the answer.

It requires tables and color.

Some other pages
The WWW Tackles The Monty Hall Problem
Monty Hall Problem
Three Door Puzzle
Monty Hall Problem

There are 3 doors
 ?   ?   ? 
one of which has a Prize.
So the universe is in one of 3 possible states
state1
 P   -   - 
state2
 -   P   - 
state3
 -   -   P 
Now, you choose a door.
 ?   ?   ? 
Looking inside, we see P in just one of the 3 possible states.
state1
 P   -   - 
state2
 -   P   - 
state3
 -   -   P 
If the universe is in state1, we get the P.
But if it is in state2 or state3, we don't.
Our chances are 1/3 for "P", and 2/3 for "-".
Now "Monty" takes the other two doors
state1
 P   -   - 
state2
 -   P   - 
state3
 -   -   P 
and opens one without the prize
state1
 P   -   - 
state2
 -   P   - 
state3
 -   -   P 

Now which door do you want, red or green?
state1
 P   - 
state2
 -   P 
state3
 -   P 
In green, we get two P's!
If the universe is in state2 or state3, we get the P.
Only if it is in state1, do we lose.
So our chances are 2/3 for "P", and 1/3 for "-".

As you know, a 2/3 chance of getting the Prize
is better than a 1/3 chance,
so we tell "Monty" we've switched our choice to green.

Comments encouraged. - Mitchell N Charity <mcharity@lcs.mit.edu>

Notes:
  A friend called to ask about the Monty Hall Problem.
    I liked this explanation, but it didn't work over the phone.
    Not seeing it already online, I wrote this.
  This presentation is similar to this Answer to the Monty Hall Problem,
    but sufficiently different that I went ahead with this one anyway.
   
Doables:

History:
  1998.Oct.15  Created.