the monty hall problem really isn't that interesting mathematically. if you pick the car and switch you get a goat, if you pick a goat and switch you get the car. 2/3 of the doors are goat, therefor the probibility of getting a car when switching is 2/3. ALL the math needed was counting 2 goat, counting 3 doors and dividing 2 by 3. the counter intuitiveness just comes from how the problem is presented
