Moreover, to understand why with a random revelation of the goat the chances of each option are 50%, you first need to understand the real reason why they are n

Moreover, to understand why with a random revelation of the goat the chances of each option are 50%, you first need to understand the real reason why they are not 50% in standard Monty Hall problem. It is because when the player has picked a goat door, the host is restricted to reveal specifically which has the only other goat, but when the player has picked the car door, the host is free to reveal any of the other two, we don't know which in advance, they are equally likely for us, because both would have goats in that case. For example, if you select door 1 and he reveals door 2, it was 100% sure that he would have taken #2 if the correct were #3, as he wouldn't have had another option. Instead, we couldn't ensure that he would have opened door 2 in case the correct were yours, as he could have preferred to reveal door 3 in that case (each of them would have had 50% chance of being removed). So, from the times that you start selecting door 1, it tends to happen with twice the frequency that he opens door 2 once the correct is #3 than once the correct is #1. Instead, if the host does not know the locations and his revelation is random, he cannot make that distinction of revealing one door more than the other depending on the prize location, precisely because he does not know where it is. If you pick door 1, you cannot say that he will open specifically door 2 with more frequency when door 3 is the correct than when door 1 is the correct. If he decides to open door 2, that choice is independent of where the car is.