Game Show: Let's Make a Deal & Applicability to Poker

[napawino]

I wanted to post a non-trivial game-theory situation, then ask about it's applicability to poker. I'll follow up in another post with the solution, and I'm interested in how to use this theory in my poker games.

For those people outside the US (or under 30), here is the situation:

Let's Make a Deal - US TV Gameshow in the 1970's
The game is very simple. There are three doors: door #1, door #2, and door #3. Behind one door is a new car. Behind the other two doors are two goats. All you have to do is pick which door you want to open, and you get whatever is behind it. But you only get to open one door. By simple math, then, you obviously have a 1 in 3 chance of picking the correct door and getting a new car.

You pick a door. As soon as you tell Monty (the gameshow host) what door you want to open, he stops and says,
Okay, you've made your choice. Now, I'm going to do what we always do here on this game. I'm going to open one of the other two doors for you that didn't choose.
Sure enough, he opens one of the other doors & the stands a goat. Then he asks, Okay, now, would you like to stay with your original guess, or would you like to switch to the other door that's still closed? You only get one shot, so do you want to stay with your original choice, or switch?

Your choice?