I finally "got it," that is, I can now explain why you should switch every time.

I think of the three doors as "two groups of doors."

One "group" is the ONE door I choose, the other "group of doors"--the other two doors.

IT IS OBVIOUS THAT: IF the prize is placed randomly, the prize will only be in my "group" one time out of three, or 33.3% of the time.

TWO-THIRDS OF THE TIME, THE PRIZE WILL BE LOCATED IN "THE OTHER GROUP."

When I finally saw the problem this way, "I got it."

I should always jump to the group which has the prize 2/3 of the time.