The problem I have with this is that the original Monty Hall problem has him opening one door out of 2. With the 100 doors analogy, wouldn’t Monty be opening just one of the remaining doors? Or half? Why all 98?
I think your confusion is because if there are 100 doors then the rule is self-evident. But when there are only 3 doors, the rule of "open all doors except the door that was guessed plus one other" is indistinguishable from "open just one door".
The key is knowing that the rule is the "open all..." rule.
with 3 doors, there are only so many the host can chose to open. with a 100, there is up to 98. sure, it can be 1 or 2... or 98.
The better way of thinking about it is that he is leaving one door closed
Regardless of the number of doors, the space collapses to two options when the host reveals the rest. That new option is the set of all doors the player never picked.
The player’s initial option, 1/3 (33%) for 3 doors or 1% for 100 doors… versus the other option that is the rest of the set. 2 doors or 66% for 3 doors up to 99% of the doors for the 100 case.
That other option being the rest of the set must have better probability for any door count greater than two.