alt Hacker Newsmonty hall is not a true paradox. it could be classed as "veridical" (truthful) paradox, or i've seen it called a pseudo-paradox.
but you realize that it's unambiguously mathematically true without gimicky word-play or puns or other logic puzzle trickery.
it's just simply an un-intuitive result. most statistics really is.
curious: why the hate for the monty-hall problem?
Replies
naniwaduni • 12/09/2024
The claimed Monty Hall result becomes untrue with very subtle changes to the premises. For example, if the host blindly chooses randomly between remaining doors, the resulting distribution is 1/3 contestant door choice correct (switch loses), 1/3 contestant and host both incorrect (switch wins), 1/3 contestant incorrect host correct (no switch can be offered).
Yes, 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.