Yes this makes sense to me. The way I thought about it is if you win if he picks the door with the car, then you’re in essence getting two choices. So the total probability of winning is 1/3 (probability of Monty picking car) + 2/3 * 1/2 (prob of monty picking goat and you picking car). The reason I commented is I can compute the total probability of winning in your scenario by saying Monty has 2/3 chance of picking a goat and I have 1/2 chance of picking a car after that. The result then is 2/3 * 1/2 = 1/3