Probabilities can change based off what is known...


With three doors:


1. When beginning, the chance that the prize is behind any given door is equal. It doesn't matter which door you choose.


2. Once a door without the prize is opened, the probability of ? doors changes ?


With four doors:

1. When beginning, no matter how many doors, the chance that the prize is behind each door is equal.


2. When opening one door without the prize, the probabilities of the others ? change so that among the three remaining doors the probability that the prize is somewhere is 100%. If you switch everytime you increase your chances of winning compared with staying, but your chances are not as good as in the three door version.


3. With new information, the probabilities continue to change. With four doors, and 2 opened, switching is an even better strategy than switching in the three door version.


And so on...