another way to think of it is: monty has the car 2/3 of the time. when he has the car, he must tell you where it is (by showing you where it isn't). that last

another way to think of it is: monty has the car 2/3 of the time. when he has the car, he must tell you where it is (by showing you where it isn't). that last part is key. he is not making a random selection. so if you go with his remaining door, it will have the car the same 2/3 of the time.