Clicking on an open door - rational students

Lots of my students have been trying the door game available on Dan Ariely’s web site. One student wrote in with this review of how he saw the game - pretty smart for a 16 year old.

“In the first game switching effectively loses you around 50 points (roughly the average) since it doesn’t give you any points to switch. Since the ranges are between 100-0 (or 70 - 30 in my experience) only in the case of a 100 point scoring door would switching help. The fact that doors are dissappearing doesn’t take anything away from the switching. There is a one in three chance that the door picked would be the door with the high point numbers and in this case one shouldn’t switch. In the case that one gets the door with the low numbers one should switch but only once and in the case of a middle value one shouldn’t because there is an equally likely case of one wasting 50 points on the door with the low set of values. However the ranges are so close that to switch and lose a potential 50 points or so would not actually be worth the ‘profit’ made from switching. Therefore in both games, as a general rule, one musn’t switch.”