Ah, I remember this problem from a high school class.
It may seem counterintuitive at first, but switching doors *is* better.
I can explain it in a slightly different way.
Say you run through the scenario a large number of times. Every single time, you pick a door, see the goat in one of the other doors, and you STICK with your choice.
If the odds of winning are truly 50/50, then you should win the car 50% of the time.
But think about it. If you pick a door, and always stick with it, you'll win 33.3% of the time.
After the revelation of the goat, there are only two doors left, and there is a 100% chance that the car is behind one of them. If picking and STICKING yields a 33.3% chance of winning, then SWITCHING to the other door would necessarily yield a 100% - 33.3% = 66.7% chance of winning.
Thus, it's better to switch.
I love these brain twisters.
~mimi