The big insight is that at each attempt, the remaining door could have been chosen if it had a goat, but wasn't
It would be extremely lucky for that door to have not been selected 98 times in a row and still have a goat
It would be extremely lucky for that door to have not been selected 98 times in a row and still have a goat
Think of a version with 100 doors, 99 with goats and 1 with a car.
You choose a door, and the host opens 98 doors that have goats. Do you keep your randomly chosen door or switch to the single door that the host didn’t open?