very interesting. i love the reply; don't mistake my responses as arguments or disagreement - just ideas:

i think Savant was 100% correct and the original stating of the problem was clear enough. it's not really about torturing students or trying to be tricky or edgy - it's meant to be an important lesson about independence in statistics. it's more of an example of the kind of real problems that are torture. statistics is the torture, not the exposition of it...

> content creator in the print media wanted to give an edgy true answer to farm engagement

this was 1975 and the fight didn't break out until 1990. using terms like "content creator", "farm engagement", etc. gives a vibe that i guarantee was not the case at the time. yes, it was meant to be an engaging puzzle, but back then it didn't have those highly negative connotations.

from wiki: "Several critics of the paper by Morgan et al.,[38] whose contributions were published along with the original paper, criticized the authors for altering Savant's wording and misinterpreting her intention"

if anything people with an axe to grind like the Morgan et. al. analysis were the one twisting words around.

as far as instructors (and many other people) having a bad time explaining it, well... that's not a problem with the puzzle is it? bad teachers are a real thing.

for me the very best most direct way to understand the puzzle and the solution is to look at the decision tree diagram next to "Conditional probability by direct calculation" on the wikipedia page [1]. with only 3 doors and 3 possible first choices and a single 2nd chose (switch or not), you can easily fully directly compute every possible scenario. draw that picture 3 times (one for each initial door chosen) and count up the wins and losses for strategy switch vs no-switch.

[1] https://upload.wikimedia.org/wikipedia/commons/thumb/d/de/Mo...