I’ve found pointing this out is an “aha” moment for people with even little understanding of statistics. Regardless of the number of doors, the space collapses

I’ve found pointing this out is an “aha” moment for people with even little understanding of statistics. 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.