You should switch - your odds are better. This debate is a long-standing statistics problem made famous by Marilyn Vos Savant (sp?)in her weekly column in parade magazine. For a story on it - including the retractions some huge mathematical names had to make when they realized she was right - see http://www.dartmouth.edu/~chance/course/topics/Monty_Hall.html

Noe that this is from a site dedicated to finding fault with Ms Vos-Savnt's answers, and even they have to admit she is right.