I only started to understand how to look at this problem once I realized the host was going to eliminate a bad door _no matter what was chosen_. Of course if y

I only started to understand how to look at this problem once I realized the host was going to eliminate a bad door _no matter what was chosen_. Of course if you have already selected a bad door he won't eliminate it. Another useful exercise is to stretch the number of doors to some large N and suppose the choice was posed repeatedly with a decreasing number of doors. If you can have anywhere from 2 to N guesses and as N decreases the number of bad doors decreases, it seems more obvious that you should always switch.