"Where we differed: I assumed that the new person was getting to choose from what was left by the original contestant, and that his choice was influenced by that action. You and Howard, it turns out, assumed that the contestant had lost the game, leaving the car in play--but you did not clearly make that a part of the proposition."

I obviously expressed myself badly - what I had intended to convey is someone facing the same choice of two doors, one concealing the car and the other a goat, but without the first contestant's advantage of having participated in the first round. Without prior knowledge of how those two doors came to be selected, this person can only make a random choice and has a 1 in 2 chance of winning. The first contestant, however, knowing what the first choice was and that it is probably wrong, faces a different set of odds.

I had originally fallen into the trap of believing that the second round of the game is an entirely new choice between two equally likely doors, and hadn't understood what information could be derived from the first round. Light eventually dawned, but it took me a while!