re: Marilyn vos Savant and the history of the Montel Hall question

The odds improve to switch doors only because Monty always opened a door that didn't have the winning prize behind it first, in order to build up the drama.

If Monty had always just randomly selected a door to open first then sometimes the first door opened by Monty would contain the prize and the excitement would then be over before the contestant had his choice opened. They never did it that way, thus Marilyn knew that the door that the contestant didn't pick and the door that Monty didn't pick had a 2/3 chance of having the grand prize behind it.

The only way the contestant could lose by switching is if he choose the correct door to begin with when he had a 1/3 chance of being right. So switching choices after Monty had eliminated one of the other doors to have the goat gives the contestant 2/3 chance to win instead of sticking with his original 1/3 chance to win.

I'm floored that math professors couldn't figure that out. (of course most were from Florida, so that makes it more understandable)