Curtis Cappellsaid, with great eloquence....
> You watch Monty look in the hat, pull out a white ball and
> put it in his
> pocket.  You know it's still a 2/3 chance the black ball is
> on the other
> side of the fence, because no balls crossed the fence after
> you passed the
> hat to Monty.  But the ball in his pocket is white (0%
> probability it is
> black), so the 2/3 probability *must* be with the ball in the hat.
>

The error in logic creeps in when you say
"You know it's still a 2/3 chance the black ball is on the other side of the
fence".

In fact you now know that there IS NOT 2 in 3 chance of it being one of the
other 2 balls ( the other side of the fence), because you proved it was not
one of them.  That makes it a certainty that the 2 out of three odds lies
with the pair of balls remaining.  Yours and the other one on the other side
of the fence.

Don't forget that it by itself had a 1 in 3 chance in the beginning, the
same as yours.  From it's perspective, the fence between "us and them" is in
a different place with it on one side and your ball and the eliminated ball
on the other side.  Using your logic, it would assume you had the right ball
because "you guys on the other side" had a 2 in 3 chance by his perspective.

When you removed one of the non-winning balls, it changes the game and you
now have a 1 in 2 chance of having the right one.

Tony "geese you guys are great to argue with" Peters