File:Monty no switch.png

Summary
For a different perspective on the Monty Hall Problem, consider not switching doors. In each of the three possible cases, there is at least one unchosen goat for the host to show, but only in the first of the three cases (1/3 of the time) does not switching win the car.

This means that 1/3 of the time, the car is the contestant's first choice, therefore 2/3 of the time the car is not the contestant's first choice, and switching to the other available choice will win the car.