This is 100% correct.

If Montyrandomlyflung open either of his two doors, the two remaining doors would have identical odds. That would be 50/50 if the door revealed a goat, and 0/0 if the door revealed the car.

But there is nothing random about Monty's choice of door. If the car is to the right, he opens the left. If the car is to the left, he opens the right. The only time he can pick a door randomly is if the contestant has picked the car.

The whole concept of the "always switch" argument revolves around this introduction of Monty'snon-randomchoices to the mix.

If everything remained completely random, there would be no advantage in switching.