I think this might have been the answer that helped me the most. Most of all, it's that the Monty Hall problem isn't about you, it's almost entirely about the host's action of revealing doors.

There's a 98/99 chance he left that door because it's the car, or 1/99 because it's the goat (assuming the one left out of calculation is your door which he can't choose). Your original choice, whether or not you picked the car, is largely irrelevant. His actions can't affect your door because he can't choose it

You're not betting on a new set of 1/2, you're not even betting on the door itself having a new probability. You're betting on the act of the host revealing doors.