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More Off-Topic Fun with Logic Problems

In the wake of the arguments and logical fallacies in the playoff roster comments, I wanted to dig up this old bit and throw it out there for people to think about.  It is from the Straight Dope, way back in the day:

Suppose you're on a game show and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

The answer is after the jump.

The correct answer is that, yes, you should switch.  There's a 2 in 3 chance that the other door has a car behind it, and a 1 in 3 chance that the door you picked has a car behind it.

History tells me that there will now be many, many comments from people telling me I (and Cecil Adams) are wrong.  We aren't...but even Cecil got it wrong, the first time he ran this question in his column.