> if Monty Hall had opened those 48 doors at random The fact that Monty Hall opens the doors deterministically (not randomly) is KEY. In the original problem

> if Monty Hall had opened those 48 doors at random The fact that Monty Hall opens the doors deterministically (not randomly) is KEY. In the original problem, Monty ALWAYS opens a door with a goat. In using 50 doors, Monty would ALWAYS open doors containing goats, and not the car. It's not random. Knowing it's not random, it should be very intuitive.