Sure, this has been done before. I just thought i'd write up my answer for this problem. I will assume you have read what the problem is already.
There are only two possibilities behind the door you pick: either a car or a goat. The probabilities for each are 1/3 for a car and 2/3 for a goat (before you do any switching etc).
Let us consider the first case, with the car behind the door you pick. Now the GSH reveals a goat. In this case, since the other, unrevealed door is also a goat, it would be best to not switch. Therefore, in the 1/3 case that you do have the car, you should not switch.
The other case would be if you had a goat. The GSH will unveil another goat. The unrevealed door now contains a car. In this case, you should switch, in order to obtain a car. However, the chance that this case is the one you have is 2/3.
This means that, overall, switching will be beneficial, since 2/3 times switching will will allow you to win.
I found this way of thinking through a little easier than the methods on Wikipedia. I'm not sure why. I hope my explanation is not wrong.
exercise #10: sci-fi
3 weeks ago