Why It Is Not 50-50

Scale the game up to 100 doors. You pick one. The host then opens 98 doors, every one a goat, leaving just your door and one other.

Now switching feels obvious. Your door was a 1-in-100 shot from the start, and nothing changed that. The host quietly funneled all the leftover odds onto that single survivor. The exact same thing happens with three doors — it is just harder to feel.

The whole effect rests on one detail: the host knows where the car is and always opens a goat door on purpose. This is not random luck.

Because his choice is informed, it carries information. He is, in effect, telling you something about the door he leaves shut — which is why that door ends up twice as likely to hide the car as your first pick.