On Wed, Oct 28, 2009 at 10:34 PM, Dan Asimov <dasimov@earthlink.net> wrote:
I maintain that as long as
----- the player has no knowledge of Monty Hall's algorithm to pick a door to open and show a goat -----
(e.g., even if Monty doesn't know where the car is, and just lucks out in picking a goat door to open),
then from the player's point of view, which is what matters here, the probability that the original pick hides a car remains 1/3.
Well, yes: 1/3 of the time the original pick hides a car and Monty shows a goat, 1/3 of the time Monty shows a car, and 1/3 of the time Monty shows a goat and the car can be obtained by switching. So in this case there is no advantage to switching. On the other hand, if Monty knows where the car is and avoids showing it, then we have a 1/3 vs 2/3 situation, and there is a huge advantage to switching. So I agree that the 1/3 probability doesn't change, but the question is not "what is the probability that the originally selected door contains the car?" but rather "is it advantageous to switch?" --Joshua