I think part of the issue is people are overly attached to the door they picked, and think it is special.
The thing is, if there were 100 doors and you picked any other door, then the door you initially picked is incredibly likely to be among the 98 doors that monty opens.
You only feel it is special because you picked it initially, and it is one of two doors left after monty is done opening.
>>11716896>or if the guy opening the door picks a door at random which then just so happens to contain a goat (in which case switching door does not change likelihood of outcome).it changes the likelihood of the outcome because you observe that it is not a car.
it is highly likely he will open the door with the car if he worked like this, but if he opened the door with the car you would know, and there would be no point swapping.
As long as you are in a universe where he opens a goat door, you are better of swapping
OF COURSE, this 100% contingent on that you the player is ALWAYS given a choice; if monty is able to decide whether or not to give you a choice, then he could refuse to give you a choice whenever swapping would land you a car.
For the case where he always gives you the choice AND he does not know, the likelihood of getting a car by swapping only matters if you discard the universes where the door he opened accidentally had a car (because obviously swapping here is pointless).
>>11717261it does not change the priors, but conditonal on the car not being behind the doors monty opened then the belief you as a rational person should place in the car being behind the remaining door should be higher.
