Originally Posted by
nil
After meditating a good deal on this, it is finally starting to make some sense. Although I still think the probability part is little more than mathematical manipulation, let me try to explain my current understanding:
If you have 10000 doors, chances are very high that your guess is incorrect. If the host than opens 9998 doors... as far as I'm concerned, there still shouldn't be any reason the other door should have a higher 'probability' of not containing a goat, but it does, because the host let that door stay. He wouldn't throw out the door with the car behind it, and since your door very likely has a goat, it is therefore 'better' to switch. It seems to be a game of intentions rather than a game of math.