Exit Monty Hall, but through which door?

Monty Hall will live on as the eponym of the Monty Hall problem.

Since it's now well-understood it might be worth recovering some of its spookiness. So I offer this recollection:

Among those who got it wrong at the time (early nineties) were the logician and philosopher Burton Dreben and the famous and eccentric mathematician Paul Erdös (I almost have an Erdös number of 2. If I can just convinced my friend to publish some sort piece with me!) And "Cecil Adams" of the Straight Dope, which is where I read about it. Marilyn Vos Savant got it right. I remember realizing that, after I read the Straight Dope take down of her, and feeling proud.

One night I explained it to Dreben with quarters over Sangria. We had three quarters, two even years and one odd. I would put them heads down (it was there coin Monty!), and ask him to pick the odd year. He'd pick, I'd flip one of the evens, he'd always stick, and lose 2/3 of the time.

Doing it that way was really eerie because there was a probabilistic ontology to the two remaining quarters, one being twice as likely to be odd as the other. They were physically unchanged and physically unremarkable, and yet this ghostly probability haunted and hung over them.