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 makes 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.
i like to use the 100 door case to highlight how the probability “transfers” to the remaining unopened door. i understand what you mean about it feeling like the rules are changing though. in some ways opening only 1 door would be more natural. that being said, if 98 doors open it stays true to the original game in the sense that after the doors get opened, you’re left with two closed doors. at least to me, this makes it clearer how the probabilities of the 98 doors get “transferred” to the remaining unopened door.
i also think part of the beauty of the 100 door explanation is that it does make it feel like the host wants you to change. in that way, increasing the number of opened doors brings out a “hidden truth” about why you should change doors.
but at the end of the day it’s all just a different way to understand the problem. if the traditional way makes more sense to you, then there’s value in that as well.
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 makes 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.
Because the problem is explicitly about the choice between two doors. You have to eliminate all but two choices.
But even then, you’d still have a better chance by switching.
Your intuition about the change is the whole point - it exposes why the result is what it is.
In both cases the host opens every door but one.
i like to use the 100 door case to highlight how the probability “transfers” to the remaining unopened door. i understand what you mean about it feeling like the rules are changing though. in some ways opening only 1 door would be more natural. that being said, if 98 doors open it stays true to the original game in the sense that after the doors get opened, you’re left with two closed doors. at least to me, this makes it clearer how the probabilities of the 98 doors get “transferred” to the remaining unopened door.
i also think part of the beauty of the 100 door explanation is that it does make it feel like the host wants you to change. in that way, increasing the number of opened doors brings out a “hidden truth” about why you should change doors.
but at the end of the day it’s all just a different way to understand the problem. if the traditional way makes more sense to you, then there’s value in that as well.