The problem stated as stated by vos Savant hinges on the words "Monty (the host) knows". It implied that Monty intended to only open a door with a goat, so usin

The problem stated as stated by vos Savant hinges on the words "Monty (the host) knows". It implied that Monty intended to only open a door with a goat, so using his behind-the-scenes knowledge he opened door #2 (goat). However, such knowledge does not imply intention a priori. It could be that Monty doesn't give a f---, and he made the choice completely at random, for example by flipping a coin. Under this interpretation, he could have chosen door #3 (car) with equal likelihood, despite knowing that it would end the game early. In this case, the 50-50 answer would be correct. I think this is what trips many readers up, given that we tend to associate impartiality with game show hosts. A better statement of the problem might be something like "The producers have instructed Monty in advance that after the initial selection, he must open one of the unselected doors to reveal where a goat is (under such instruction he will never open the door with the car.)"