Let's Talk Logic - The Monty Hall Problem

I've been spending the past two days involved in a healthy yet heated debate with some friends of mine. Its been mostly me against them...............................me against the world!!!!!!!!!!!

I've never been on any debate team or anything like that, but I do know my logic. I nearly majored in Philosophy in college and aced all my classes, so I'm aware of what makes a solid argument and how to use math and reasoning to make logical conclusions.

This problem, however, really did kick my butt and still continues to do so.

I was so absolutely, positively sure I was right.
.........and even now after reading through wikipedia and seeing that I'm proven wrong, I'm STILL not readily accepting that I am. Its just so damn counter intuitive that I can't accept it!!
...because I'm so intuitive!!

ARG!!

So the puzzle is called The Monty Hall problem.

It goes like this:

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?

Take a minute to ponder this and then continue reading.............
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Done?
Good.

So what's your answer?

Uh huh...........ok......................

Well here's mine, which I think is pretty straightforward:
Its a given that when you make your initial choice, your odds of picking the car are one out of 3 (1:3). Then, once the third door with the goat is opened, door #3 is no longer a viable option, and since you then have another opportunity to choose between staying or picking door #2, you have a choice of 2 options, which translates to odds of 1:2. Therefore, odds of 1:2 (or 50/50) mean that the likeliness of either door having the car are equal, so there's no benefit to picking door #2. Essentially, once the third door is eliminated, it becomes a new problem with new odds. You're now picking between 1 of 2 which is 1:2 odds.

I was uber-confident this was correct and still am trying to convince myself otherwise, but yes, apparently its wrong.

The supposed correct answer is that by switching to door #2, you give yourself 2:3 odds of getting the car, whereas sticking to door#1 keep your odds at 1:3.

I will not even attempt to explain it to you since I'm still torn and trying to disprove it myself, but if you're still curious, read the wikipedia link above and have fun trying to wrap your brain around this one.

Or, take a break and enjoy crunk Yogi: