http://en.wikipedia.org/wiki/Monty_Hall_problem

I know we don't all love and trust Wikipedia, but therein is presented several ways to the solution, from a basic grid to a formal mathematical problem, and they all agree that one should always switch on the second round. This strategy results in winning the car (mathematically) twice as often as standing pat.

BTW, you can trust Darrin on the Sunset Coast (if not Wiki) who is a logician/linguist by training. He explained it, sans math, such that even I understood it.