The Three Doors

You've been trapped by Mage Snargle in his Evil Tower of Doom™! But Snargle is giving you one chance to escape. Before you are three doors: One leads to freedom, the other two to certain death.

You pick a door. Snargle then reveals one of the other two doors, always showing you the hideous demise you're certain to get if you pick wrong. Now he offers you a choice: do you want to stick with your current door, or switch to the remaining door? Does it make a difference whether you stay or switch?

Think Mathematically / Have You Heard The One / The Three Doors