(These table mean nothing without first reading the original problem, which can be seen by going to Grand Illusions.)

This exercise made things more clear for me, and I hope it does the same for you. I've shown all combinations of car postions, and all combinations of "You pick" / "Monty shows". As you'll see, any one of the examples proves things, but the tremendously counter-intuitive nature of the whole things seems to require TOTAL investigation.

 

 In this first example, the car is always behind door # 1.
In two of the three, switching would win!

 Door # 1

Door # 2

Door # 3

You choose car.

 He shows goat.

 If you switch, you get the goat.

 If you switch, you get the car!

 You choose goat.

 He shows goat.

 If you switch, you get the car!

 He shows goat.

 You choose goat.

 

 In this second example, the car is always behind door # 2.
In two of the three, switching would win!

 Door # 1

Door # 2

Door # 3

 You choose goat.

 If you switch, you get the car!

 He shows goat.

 He shows goat.

You choose car.

 If you switch, you get the goat.

 He shows goat.

 If you switch, you get the car!

 You choose goat.

 

 In this third example, the car is always behind door # 3.
In two of the three, switching would win!

 Door # 1

Door # 2

Door # 3

 You choose goat.

 He shows goat.

 If you switch, you get the car!

 He shows goat.

 You choose goat.

 If you switch, you get the car!

 He shows goat.

 If you switch, you get the goat.

You choose car.