alt Hacker NewsYes, I didn't mean it as it being a paradox just the problem I hate the most. I should've worded that better.
The reason I hate it is that it's a example of how to lie and mislead using statistics and that the only reason it exist is that a content creator in the print media wanted to give an edgy true answer to farm engagement, and now as a consequence many introductory statistics course make students suffer for the same reasons. The assumptions made to reach that answer are not made explicit and it changes the response. And teachers mess it up a lot of the time which lead to a lead of head-scratching (or sometime just leave under-specified on purpose).
It was the right answer to a question that wasn't asked. the host opens the door before giving the choice and the door he's choosing isn't random.
Wikipedia explains this better than I would be here's the part I'm talking about:
> In Morgan _et al four university professors published an article in _The American Statistician_ claiming that Savant gave the correct advice but the wrong argument. They believed the question asked for the chance of the car behind door 2 _given_ the player's initial choice of door 1 and the game host opening door 3, and they showed this chance was anything between 1/2 and 1 depending on the host's decision process given the choice. Only when the decision is completely randomized is the chance 2/3 .
[Monty Hall problem - Wikipedia](https://en.wikipedia.org/wiki/Monty_Hall_problem)
The game theoretic explanation (in the same page) as to why you should switch is more convincing and less click-baity though without needing to give a specific probability value or assume the host strategy.
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...