This was the clearest explanation in my opinion. I'm still a bit confused regarding how much information have we actually got and what mechanism is behind "pass

This was the clearest explanation in my opinion. I'm still a bit confused regarding how much information have we actually got and what mechanism is behind "passing a test" to influence the amount of information when the test result is not definitive (as in this case). We were just given a complete information about one of the options the user didn't choose, but not any direct new information specific of the door the user didn't choose and that remains closed. 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).