With more than 3 doors, it is essentially a different problem. Imagine an evil host who only opens a door and offers to switch when the guest chose the door wit

With more than 3 doors, it is essentially a different problem. Imagine an evil host who only opens a door and offers to switch when the guest chose the door with the car, and not offer to switch during other episodes. Or, more evil, infrequently open a bad door and offer to switch, just to confuse the candidate. With 1,000,000 doors such an evil host will never open and offer the switch.