The Monty Hall Problem

[Shrunk]

OK, anyone who's already heard this one, you're not allowed to answer!

I've just come across this mathematical puzzle that completely stumped me.

Suppose you're a contestant on the old TV game show "Let's Make a Deal."  You're shown three doors and told that behind one of the doors is a new car, behind the other two, goats.  You have to choose one door.  After you have chosen, the host, who knows what is behind each door, will open one of the doors you did not choose, and the door he opens must have a goat behind it.  (If both unchosen doors conceal goats, he can choose either at random.)  After he has  opened one of the doors with a goat, he will give you the options of either sticking with your original choice, or switching to the other remaining door.  So, for instance, if you choose Door #1, the host may open Door #3 and show you that there is a goat behind it.  He will then ask you if you want to stay with #1, or switch to #2.

Is it to your advantage to stay with your original choice, change, or does it make no difference which you do?

(Oh, and the puzzle also assumes you would rather win a car than a goat.  This was a bit of a stumbling point when I tried the question out on my kids.)

[The new erato]

This porblem has been thorougly covered a zillion times on the web. If you don't want the solution, don't click on the.