https://uploads.disquscdn.c... Forget the whole backstory of that Morgan show. Forget the choices involving doors that have to be made. It is precisely all that irrelevant information that makes it hard to grasp.
Let’s get to the essence of probability theory.
OK... there are 3 rooms, and a car is placed randomly in one of them.
I cannot look inside the rooms, and I am asked about the probability of the car being in any given room. It is perfectly clear that the probability is 1 in 3 for each room. The order of the rooms doesn't matter, either.
Now for the crucial trick. The setup with the 3 rooms and the single car remains exactly the same; however, I remove 2 adjacent doors and replace them with a single door. If I open that door, I am looking into 2 rooms at once.
It stands to reason that the probability of seeing the car—behind that combined door—thereby increases to 2/3. (It’s not a case of 2 doors resulting in a 50% chance.) It is not the doors that determine the probability, but the number of rooms!
Once you grasp this, the Monty Hall Problem ceases to be a problem.
The confusion arises because the conversation constantly revolves around whether doors are opened or not, and about making choices, even though these factors do not affect the probability distribution of the rooms.

The mistake is treating the final two doors as though they arose by random elimination. They didn’t. Monty deliberately opens a door he knows contains a goat. That action carries information about where the car is. If the opened door were chosen at random, then 50/50 would indeed be correct (after conditioning on the fact that a goat happened to be revealed). But that’s not the Monty Hall problem. The host’s knowledge and strategy are part of the probability model.

What are your thoughts on the version where it is scaled up to 100 doors, where you choose one and 98 are then eliminated? Would you stay with the same door as before or swap door?

No, it is not. Hall will always open a goat door and take it out of play. That leaves it a simple choice between two doors. One has a car, one has a goat and nothing in the first round provides any information about where the car is. It is 50/50.

This is exactly right. He will always open a goat door, leaving a game of two choices. Switch doors or keep your door. It makes no difference. One has a car, one has a goat. It is a coin flip.