It doesn't matter. If Monty knows what's behind the doors, we arrive at the scenario immediately where the door that's left has 2/3 chance of hiding the car, b

It doesn't matter. If Monty knows what's behind the doors, we arrive at the scenario immediately where the door that's left has 2/3 chance of hiding the car, because the door you picked has 1/3 chance of hiding the car. If Monty doesn't know what's behind the doors, and goes into a cycle of opening doors and shuffling the prizes if it was the car, or rewinding the universe, or whatever, at the end of that sequence, you will still hold on to the same door you initially picked that has 1/3 chance of hiding the car. And the door that you get the offer to switch to therefore has a 2/3 chance of hiding the car.