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> The host knowing what's behind the doors doesn't specify the host's behavioural protocol. I agree. I just said that it was not _that_ bad. > If more than a

by kgwgk 3y ago

> The host knowing what's behind the doors doesn't specify the host's behavioural protocol. I agree. I just said that it was not _that_ bad. > If more than a 1000 PhD's wrote back in complaint, then perhaps a more probable explanation is that while reading the problem statement they assumed distinct host protocols, I wonder how many of them pointed out that the problem was ill-posed - instead of assuming distinct protocols or just failing to solve properly the problem. At least one those PhDs went from "Since you seem to enjoy coming straight to the point, I’ll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful." to "I wrote her another letter, telling her that after removing my foot from my mouth I'm now eating humble pie. I vowed as penance to answer all the people who wrote to castigate me. It's been an intense professional embarrassment."

DoctorOetker 3y ago
>> The host knowing what's behind the doors doesn't specify the host's behavioural protocol. > I agree. I just said that it was not _that_ bad. It's great we can agree the problem is ill-posed. But that is a binary thing, either it is ill-posed or it is not. It can't be a little bit ill-posed. I don't believe it's a coincidence that the ill-posed problem gets the high profile attention. It's not easy to design a proper puzzle, so it's tempting to simply hide a non-given "given" in the "solution". The best way to not get caught is to have separate identities ill-pose-without-the-given and "solve"-with-the-given. Flame wars guaranteed... EDIT: now that I think of it, I even fail to verify that the poser "Craig F. Whitaker" didn't collude, or even that he existed. Looking at the archive.org copy of vos Savant's own website: https://web.archive.org/web/20130121183432/http://marilynvossavant.com/game-show-problem/ https://web.archive.org/web/20130121183432/http://marilynvos... I see something very suspicious about the first 2 letters quoted (including the one you requoted): They are ostensibly written by different people, yet use very similar wording, and essentially contain the same information sentence by sentence. First I will repost both integrally: Since you seem to enjoy coming straight to the point, I’ll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful. Robert Sachs, Ph.D. George Mason University You blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I’ll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame! Scott Smith, Ph.D. University of Florida Both use "blew it", where there are many other alternatives like "mess it up" (which I used). Robert: If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. Scott: After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. Both also somehow connect this with public literacy and public shaming. Robert: As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful. Scott: There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame! These people at least seem to exist, but something strange is going on. It's also regrettable I can't find the original Parade articles on the internet archive...
- kgwgk 3y ago
  > I don't believe it's a coincidence that the ill-posed problem gets the high profile attention. In this case even the well-posed problem(s) can be highly controversial as it can be seen from other comments - including someone who claims that probabilities are meaningless here because "it’s not a repeated game." > something strange is going on. The New York Times may be part of it then, I got the second quote from https://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html https://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-do...
  - DoctorOetker 3y ago
    Sadly I can't read the NYT. > In this case even the well-posed problem(s) can be highly controversial as it can be seen from other comments - including someone who claims that probabilities are meaningless here because "it’s not a repeated game." I will take a look at such a comment if you link it, but I'm not going to actively search for such comments as I don't plan to play Monty Hall police. The most intelligent probably just responded on the internet when they first got acquainted with it, and upon realizing the problem is ill-posed just ignore it. So the visible flamewar tends to be between people who don't realize the problem is ill-posed...
    - kgwgk 3y ago
      I was referring to https://news.ycombinator.com/item?id=36736947 https://news.ycombinator.com/item?id=36736947 but I didn’t expect you to read all the exchanges or comment on them. “In Monty Hall, you’re just making a guess and no matter how clever you are about it, it’s still just a guess. There is no strategy because the game doesn’t last long enough for strategy to matter.” The point is that the discussions are not always related to a misunderstanding about the protocol followed by the host to open a door. Someone else doesn’t accept that (after the host’s protocol is fully specified) the problem is conditional on the stated run on events - insisting that it only makes sense to consider “the whole game”: https://news.ycombinator.com/item?id=36737326 https://news.ycombinator.com/item?id=36737326
- kgwgk 3y ago

by kgwgk 3y ago

DoctorOetker 3y ago

>> The host knowing what's behind the doors doesn't specify the host's behavioural protocol. > I agree. I just said that it was not _that_ bad. It's great we can agree the problem is ill-posed. But that is a binary thing, either it is ill-posed or it is not. It can't be a little bit ill-posed. I don't believe it's a coincidence that the ill-posed problem gets the high profile attention. It's not easy to design a proper puzzle, so it's tempting to simply hide a non-given "given" in the "solution". The best way to not get caught is to have separate identities ill-pose-without-the-given and "solve"-with-the-given. Flame wars guaranteed... EDIT: now that I think of it, I even fail to verify that the poser "Craig F. Whitaker" didn't collude, or even that he existed. Looking at the archive.org copy of vos Savant's own website: https://web.archive.org/web/20130121183432/http://marilynvossavant.com/game-show-problem/ https://web.archive.org/web/20130121183432/http://marilynvos... I see something very suspicious about the first 2 letters quoted (including the one you requoted): They are ostensibly written by different people, yet use very similar wording, and essentially contain the same information sentence by sentence. First I will repost both integrally: Since you seem to enjoy coming straight to the point, I’ll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful. Robert Sachs, Ph.D. George Mason University You blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I’ll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame! Scott Smith, Ph.D. University of Florida Both use "blew it", where there are many other alternatives like "mess it up" (which I used). Robert: If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. Scott: After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. Both also somehow connect this with public literacy and public shaming. Robert: As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful. Scott: There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame! These people at least seem to exist, but something strange is going on. It's also regrettable I can't find the original Parade articles on the internet archive...

kgwgk 3y ago
> I don't believe it's a coincidence that the ill-posed problem gets the high profile attention. In this case even the well-posed problem(s) can be highly controversial as it can be seen from other comments - including someone who claims that probabilities are meaningless here because "it’s not a repeated game." > something strange is going on. The New York Times may be part of it then, I got the second quote from https://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html https://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-do...
- DoctorOetker 3y ago
  Sadly I can't read the NYT. > In this case even the well-posed problem(s) can be highly controversial as it can be seen from other comments - including someone who claims that probabilities are meaningless here because "it’s not a repeated game." I will take a look at such a comment if you link it, but I'm not going to actively search for such comments as I don't plan to play Monty Hall police. The most intelligent probably just responded on the internet when they first got acquainted with it, and upon realizing the problem is ill-posed just ignore it. So the visible flamewar tends to be between people who don't realize the problem is ill-posed...
  - kgwgk 3y ago
    I was referring to https://news.ycombinator.com/item?id=36736947 https://news.ycombinator.com/item?id=36736947 but I didn’t expect you to read all the exchanges or comment on them. “In Monty Hall, you’re just making a guess and no matter how clever you are about it, it’s still just a guess. There is no strategy because the game doesn’t last long enough for strategy to matter.” The point is that the discussions are not always related to a misunderstanding about the protocol followed by the host to open a door. Someone else doesn’t accept that (after the host’s protocol is fully specified) the problem is conditional on the stated run on events - insisting that it only makes sense to consider “the whole game”: https://news.ycombinator.com/item?id=36737326 https://news.ycombinator.com/item?id=36737326
kgwgk 3y ago