Wait, what happened in the second to last bullet point? You can’t convert a power like that when subtracting (you can when dividing).

It’s like you’d convert “2^4 - 2” into “2^(4-1)”, which gives two different results (14 vs 8).

I never understood why in the 100-door case, the host opens 98 doors, and not just one door. That feels like changing the rules.

I fully understand the original problem with 3 doors; I know the win probability is 2/3 if you change. But whenever I hear the explanation for 100 doors case, it just made everything confusing. By opening 98 doors, it feels like the host wants you to switch to the other door. In 3 doors case it’s more natural.