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

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