I was recently introduced to the following puzzle by another developer (from Vertigo, in fact).  This is actually a fairly well-known problem and you'll find write-ups about it on Wikipedia and elsewhere, but I'll omit links to those sources from this post to prevent some temptation to just click and see the answer (I'll post everything in a follow-up).

The Scenario

Imagine you are on a game show in which a great prize is hidden behind one of three doors.  Behind one door lies a brand new car.  Behind each of the other two, a goat.  The host of the show has explained this to you, and asks you to select a door.  You choose one and inform the host of your decision.  He smiles and says "Let's see what you didn't win" and opens up one of the other doors, revealing a goat!  Then he looks at you and says, "The car is still behind one of these two doors.  If you'd like, I'll let you change your mind and switch which door you've selected.  What do you say?"

Should you switch doors?

Is it in your best interest to switch doors, or does it matter?  When commenting, if you already know this problem, please avoid posting any spoilers or links to write-ups.  I'll publish a follow-up with all of that tomorrow.