I think the easiest way to grasp this without getting into the math is to make such a counter intuitive problem intuitive again. Let's change the number of doo

I think the easiest way to grasp this without getting into the math is to make such a counter intuitive problem intuitive again. Let's change the number of doors ! First, I'll rephrase the original problem ================================================ You have 3 doors, 1 hides a car, all others hide goats. You pick one door, then __ALL doors you have NOT selected AND that hide goats are revealed, except one__ Here it's only one door because we have a total of 3. But it's one door that is indeed, ALL except one, for this particular situation. Do the same, but with 100 doors ==================================================== You have 100 doors, 1 has a car, all others have goats. You pick one, then __ALL doors you have NOT selected AND hide goats are revealed, except one__ Now you get: - 1 selected, 99 not selected => the car is most probably among the 99 ones. - Monty reveals 98 goats - 1 selected, 98 goats, 1 not selected => the car is most probably in the later one.