At 5:39 PM -0800 3/2/00, Gavin Scott wrote:
>Three contestants, three doors.  Each contestant picks a door.
>
>Monty opens one (guaranteed to be non-winning) door, and eliminates the
>player who chose that door.
>
>Now there are two contestants left who each have an unopened door.
>
>Each appears to be in the same position as the contestant in the original
>problem.  Each has chosen a door and seen one of the remaining doors opened.
>
>If both are attentive HP3000-L readers, shouldn't they *both* think that
>they should switch to the *other's* door in order to increase their chances
>of wining from 1/3 to 2/3?
>
>Should they trade doors or not?


That's a good one. I had to think about this a bit...

The trick to understanding Gavin's conundrum is to observe the subtle shift
in focus that has occurred.

In the original problem, it's You vs Monty. You get 1/3 of the doors, and
he gets 2/3. When he opens one of his doors, the other one still has 2/3
chance of being the winner.

In the new problem, we're competing against two other contestants, each of
which has a 1/3 chance of winning. (In other words, the 3 doors are being
divided into 3 groups now instead of 2). When Monty eliminates a player in
this scenario, he hasn't just opened a door, he as removed one of the three
groups. Now there are just two groups and your odds become 50-50!

--blake