The easiest way to think about this problem is this:

Pretend that instead of three doors, there are a million doors. You pick one to start and Monty opens up 999,998 other doors, all goats. Now, would you switch? You would go from 1 in a million to 999,999 in a million.

You know how those dance dance revolution games are really popular? I saw a *DOG WALKING* arcade game in Japan. It's like a treadmill, pretty much, with a cute dog on the screen and you hold this leash thing and you take this dog on a walk. Sometimes you have to run and chase cats and stuff. What's up with that?!