1: http://lesswrong.com/lw/ii/conservation_of_expected_evidence...
1: http://lesswrong.com/lw/ii/conservation_of_expected_evidence...
Imagine that after opening the door everyone goes home and a new participant who has no knowledge of the previous experiment is called to make a decision between the two remaining doors. Obviously in this case the probably is 1:2, as there is no information regarding the previous test. Actually, if we imagine a similar situation happened before the initial problem with a previous show with 4 doors, we may as well see that the initial probability of 1:3 is also wrong if we had access to the knowledge about the previous experiment.
I still agree with the switch suggestion, but the mechanism behind it is still not entirely clear.
A more intuitive example would also be to invert the problem: leave one of the non picked doors (C) out of the random opening and use the door the contestant picked (A) as a possible case in the random opening experiment. If we start by opening A, then we already know enough to see if the user won or lost, if we open B and there is the car behind it, we already know everything. If we open B and there is a goat behind the door, consider whether you would switch your choice from A to C. I guess you probably wouldn't and it would feel easier to justify your position, as this doesn't involve the "psychological pain" of changing a previous choice by reasons that you don't entirely understand (associated with possible loss-aversion feelings).