> Monty...did not let them replay the game multiple times so the laws of probability do not affect the outcome it was down to luck.

Actually even I can understand that no matter how many times you play (i.e., start choosing one door of three) the odds (whatever they are) remain the same each time.

Like flipping a coin. It's always 1 in 2 for heads the next time no matter how many times heads has come up in the past.

And some of those mathematicians skeptcal of the new 2/3 odds are/were pretty accomplished. According to Wackipedia, which may be reliable in this case,

"Decision scientist Andrew Vazsonyi described how Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until Vazsonyi showed him a computer simulation confirming the predicted result."

I'm wondering if those who say the odds increase by switching understand that Monty would allow you to switch your choice of doors *whether or not your first choice found the car.* So revealing one goat did not imply anything about the wheareabouts of the car behind the remaining two doors. He didn't care if you won the car or not, at least for the purposes of this discussion.

And where is the flaw in the following reasoning? Regardless of what's just happened, you're left with two doors. The car could be behind either one. Somebody coming fresh to the scene would have a 1 in 2 chance of picking the car, whether he switched or not. (Because there would be no spare goat door to open.) Right?

No matter how many times he switched back and forth, his odds of picking the car would be 1 in 2. Right?

So how is it that *your* odds can be increased to 2 in 3 by switching, while his can't, in precisely the same situation at the same moment???? Didn't your odds increase from 1 in 3 to 1 in 2 the minute the spare goat was revealed? Why would that change?

True, you now know that the car wasn't behind the third door. But so what?! That's in the past, like all those coin flips that came up heads! Two doors, one car, one goat, 50/50!