Recycled Monty Hall Puzzler... Again

Okay, it is finally time for the new puzzler... But it is not a new puzzler. This is the recycled puzzler. In fact, since we gave everyone an extra week, this is the recycled, recycled puzzler. This one was extended by a week, due to the holiday and the amount of interest we have had in this very popular puzzler.

Here's a recap.

The famous Monty Hall, "Let's Make a Deal" Puzzler.

Monty Hall would present people with 3 doors. You get to pick door #1, door #2, or door #3. One of the doors had a wonderful prize behind it, like a car or a vacation or something. The other two had crummy prizes.

So, when you picked a door, you had a 1 in 3 chance of getting the great prize and a 2 in 3 chance of winning a crummy prize. A life supply of scotch tape, or 600 boxes of Eskimo pies, or something like that.

And here is the puzzle.

Monty Hall says, "Pick a door." And so you pick door #1. And he asks if you'd like to switch now. And you say no because it wouldn't matter. At this point, your chances are still 1 in 3, no matter what.

Then he says, "I'm going to show you one of the two doors that you did not pick." So he shows you what is behind door #2. And it is a crummy prize. All Eskimo pies.

Then Monty says, "You picked door #1, but you don't know what's behind it. I've shown you what's behind door #2, and it is Eskimo pies for days... Would you like to switch to door #3?"

So this is the puzzler that is worth two weeks of responses. Because now that you know what is behind door #2, your chances are better than 1 in 3. So, do you stay where you are, with door #1, or do you take the chance and switch to door #3?

What do you do, and why?