I find that Monty Hall is easier to understand with N doors, N > 2.
N doors, one hides a car. You pick a door at random yielding 1/N probability of getting car. Host now opens N-2 doors which are not your door, all containing goats. The probability the other door left has a car is not (N-1)/N.
Set N to 1000 and people generally agree that switching is good. Set N to 3 and they disagree.
I find that Monty Hall is easier to understand with N doors, N > 2.
N doors, one hides a car. You pick a door at random yielding 1/N probability of getting car. Host now opens N-2 doors which are not your door, all containing goats. The probability the other door left has a car is not (N-1)/N.
Set N to 1000 and people generally agree that switching is good. Set N to 3 and they disagree.