Monty Hall problem
That 2/3 (two out of three) chance comes from the fact in the initial door choice, the player has a 1/3 (one out of three) chance of picking the door with the car. There is a 2/3 (two out of three) chance if the car is behind one of the other two doors. If the player could switch from their one door to the other two doors this would improve their chances. The fact that the host reveals that one of the other doors contains a goat does not change this probability. The player is still effectively swapping their one door for the other two (even though one of them has been opened).