::::::::To distinguish "did the host open door 2 or door 3" refers to some suspected underlying asymmetry. But as long as such asymmetry and its direction is not known for sure at the outset but can only be considered as suspected to exist for this one game given, it makes no sense to use it, especially as it can't change the decision to switch. It remains what it is, a less important side aspect that could be mentioned also, later on. What the sources say: In short, as long as you don't know for sure about existing asymmetry, to distinguish between door 2 and door 3 is not worth the trouble. But I would like to see a conditional formulation, clear and in odds form, already in the beginning also, just as an aid to understand that the odds are not 1/2 in general, but that in general the odds are 2/3.