== Lead change == 

 The two sentences added to the lead (see this diff) assume the host opening a door has no effect on the probability of initially selecting the car (which is true only because of the constraints on the host), and essentially explain the fairly trivial point that 1 - 1/3 = 2/3.  How about if we state the major reason that the initially picked door remains a 1/3 chance?  For example:  

 :Because there is no way for the player to know which of the two unopened doors is the winning door, most people assume that each door has an equal probability and conclude that switching does not matter. In the usual interpretation of the problem the door the host opens is not randomly selected and opening this door does not affect the player's initial 1/3 chance of having picked the car. The car is behind one of the two unopened doors; if there is a 1/3 chance it is behind one there must a 2/3 chance it is behind the other.  The player should switch—doing so doubles the probability of winning the car from 1/3 to 2/3. 

 The critical point is that the host opening the door does not affect the player's initial 1/3 chance of picking the car - mostly because the host does not open a random door.  I think assuming this to be true, without no explanation whatsoever, does not accurately summarize the solution.