6 ms·

Wow, I knew about the problem and was vaguely aware that it had generated some controversy amongst statisticians but I had no idea about the insanely arrogant a

Wow, I knew about the problem and was vaguely aware that it had generated some controversy amongst statisticians but I had no idea about the insanely arrogant and obnoxious (not to mention wrong) abuse Marilyn had received from the "intellectual elite". I have little sympathy for the "ambiguous question" defence. Not only is Marilyn's interpretation grammatically valid, it just wouldn't make sense in the context of the game show for the presenter (who knows where the goats are) to ever open a door to reveal the car and give you the option to switch. The game would be reduced to "does Monty feel like gifting you a car or a goat today". Furthermore, Marilyn's own explanation of her answer makes it very clear that she interpreted the question as meaning that the presenter will only ever open goat doors. And all the attacks seem to focus on her grasp of the math rather than her interpretation of the problem question. To be clear, I think it's perfectly reasonable for a person to interpret the problem the other way without thinking too much about it, and casually throw out an incorrect answer. But I would expect an academic to devote at least another 30 seconds of thought to the problem before publicly excoriating a woman known for her high intelligence.

tialaramex 3y ago
Also regardless of whether she's a woman or she's known for intelligence, a response in which you say "You're wrong" needs an extra second's thought to consider whether, in fact, they are wrong, or maybe just their understanding is different from yours and you need to reconsider with their context. Some time back in an HN thread about programming languages I read a response in a thread about inference which said that a particular feature doesn't really save on typing. And it seemed ludicrous. Until I realised the author of the comment has seen the word "typing" (which everybody else in the thread is reading as "The thing you do with a keyboard") and they're interpreting it as "The thing the compiler does". And yeah, with that perspective of course inference isn't saving typing, all your variables still have types, we were just happy because we spent less time operating the keyboard to write a program. Their comment was not wrong and we weren't correcting them, we'd just understood things differently! Edited to add, link: https://news.ycombinator.com/item?id=36593110 https://news.ycombinator.com/item?id=36593110
- city41 3y ago
  I almost never say "you're wrong", no matter how confident I am. Because I can be, and often am, wrong myself. If there is a disagreement, a miscommunication, etc, why not instead work with the person to find where you two differ and look for common ground? If the other person really is wrong, it's almost always naturally revealed that way.
  - petesergeant 3y ago
    Also it’s a lot more fun to simply shout “FALSE”
bazoom42 3y ago
> it just wouldn't make sense in the context of the game show for the presenter (who knows where the goats are) to ever open a door to reveal the car and give you the option to switch. None of it makes sense because it is not a real game show, it is a thought experiment.
- apetresc 3y ago
  Apropos the topic of being confidently incorrect, it was indeed a real show: https://en.wikipedia.org/wiki/Let%27s_Make_a_Deal https://en.wikipedia.org/wiki/Let%27s_Make_a_Deal Hosted by a real Monty Hall: https://en.wikipedia.org/wiki/Monty_Hall https://en.wikipedia.org/wiki/Monty_Hall It even had the gag prizes like goats (or, as in the photo from the wiki page, a llama)
  - svat 3y ago
    The Monty Hall problem is a thought experiment (based on a real game show). As evidence, see this letter from Monty Hall himself ("no trading boxes after the selection"): Dear Steve: Thank you for sending me the problem from "The American Statistician." Although I am not a student of a statistics problems, I do know that these figures can always be used to one's advantage, if I wished to manipulate same. The big hole in your argument of problems is that once the first box is seen to be empty, the contestant cannot exchange his box. So the problems still remain the same, don't they. . . one out of three. Oh, and incidentally, after one is seen to be empty, his chances are no longer 50/50 but remain what they were in the first place, one out of three. It just seems to the contestant that one box having been eliminated, he stands a better chance. Not so. It was always two to one against him. And if you ever get on my show, the rules hold fast for you -- no trading boxes after the selection. Next time let's play on my home grounds. I graduated in chemistry and zoology. You want to know your chances of surviving with our polluted air and water? Sincerely, Monty https://web.archive.org/web/20100408200824/http://www.letsmakeadeal.com/problem.htm https://web.archive.org/web/20100408200824/http://www.letsma...
  - dfxm12 3y ago
    I think importantly, the "Monty Hall Problem" as described is different from how any iteration of the Big Deal at the end of Let's Make a Deal is actually run. Hall himself recognized this and mentioned it in a NYT interview in the 90s. It's paywalled, but the excerpt is here: https://en.wikipedia.org/wiki/Monty_Hall_problem https://en.wikipedia.org/wiki/Monty_Hall_problem Hall understood the problem, giving the reporter a demonstration with car keys and explaining how actual game play on Let's Make a Deal differed from the rules of the puzzle. When I first heard about the puzzle, I struggled with the solution precisely because I kept making assumptions about the puzzle based on my knowledge of the show. It wasn't until I thoroughly read the question, setting aside those assumptions, that I realized it is materially different from the show and I was able to really understand the solution.
XCabbage 3y ago
> it just wouldn't make sense in the context of the game show for the presenter (who knows where the goats are) to ever open a door to reveal the car and give you the option to switch No, but it would make perfect sense for him to open a door at random and - if doing so reveals the car - tell you sadly that you've lost as a disappointed klaxon plays. Indeed this is almost the only possible way that the initial door opening could realistically make sense in a game show; if it works in any other way, there's no tension when the first door is opened since there's no risk!
- psd1 3y ago
  > there's no tension There certainly is. It's a high-stakes scenario and the door-opening presents new information. It makes the conclusion feel less certain. Revealing the car would conclude the game, of course. Unless the contestant were holding out for the better goat.
flomo 3y ago
In reality, Monty Hall often did not behave in the way the problem describes, that might be the source of confusion surrounding this. (e.g. sometimes he would reveal a prize and imply there might be a better prize behind one of the doors. sometimes there were only prizes and no goats, etc.)
lucas_membrane 3y ago
>> The game would be reduced to "does Monty feel like gifting you a car or a goat today". But, in fact, that is the way the real show worked. He was more likely to give you a car when he hadn't given away any cars for a while. And Marilyn's description of the problem included no information about whether or not Monty offered to swap doors rarely, frequently, or always, or about the previously observed outcomes depending on whether or not the contestant took the bait. And she surely did not say that Monty was a robot and had no interest in what happened on his show. The way the game actually worked is like how poker and life work until proven otherwise. Every high-stakes game has a sucker, and if you do not know who is the sucker, it is you. Read the story in which a NY Times reporter interviewed Monty about the controversy and you will learn how it really worked.
- harshreality 3y ago
  If you're playing the game as stated, and if the host opens a door revealing a goat, you must switch for the best odds. The offer to switch doors is part of the problem statement. You can't justify your decision based on the possibility in the real game that you might not get the offer to switch (which would mean that when you do it might be an intentional red herring). Even if there's a 50% chance there are all goats, or a 75% chance, you still switch. That reduces the overall probability of a win, but it doesn't affect the relative probability from switching. The only reason you might not want to switch is if the first choice had been forced, such that there was an above-random chance that your first pick was the car.
  - grogers 3y ago
    The person you are responding to is pointing out that if the host doesn't offer you to switch all the time, then it isn't the best strategy to always switch when you are given the option. For example, knowing that everyone switches when given the option, the host might only offer to switch when you've picked the correct door. In that case, not switching would be better. Hence the poker aspect.
    - lucas_membrane 3y ago
digitalscribe 3y ago
> Not only is Marilyn's interpretation grammatically valid I would consider both interpretations equally valid. If anything, in law we have the "rule of the last antecedent" (phrase/clause modifies nearest antecedent noun) so that the hater's interpretation could be more correct if based only on this rule. This language is ambiguous: "host ... opens another door, say #3, which has a goat." The two options are Marilyn's interpretation of the door always containing a goat (invariant version), or that one door he opens (say #3) just happens to contain a goat (hater's version) but it could have contained a car. As suggested by someone below, a much clearer formation could have said "host opens a door with a goat, say door #3" to avoid this particular ambiguity. There's also the issue of usage of "which" signifying a non-restrictive non-essential clause.
- hulium 3y ago
  If the the door contains a car, then it doesn't matter whether you switch or not. If it is a goat you get the problem as intended. You still have the intended problem as a subproblem, so this is just a distraction and not a serious objection.
  - tga_d 3y ago
    If a goat was revealed randomly instead of intentionally, there is no advantage to switching. See the "Monty Fall Problem" in this paper already linked elsewhere in the discussion: https://web.archive.org/web/20230706235720/https://probability.ca/jeff/writing/montyfall.pdf https://web.archive.org/web/20230706235720/https://probabili... To use the 100 door extension some people find helpful: If Monty always reveals the 98 doors that don't contain goats, then 99% of the time (every time you picked a non-car door), the other door will have the car. If Monty is opening a random set of 98 doors, then 98% of the time Monty will reveal the car, 1% of the time you'll have picked the car on the first guess, and 1% of the time the car is in the other door. When you're in those 2% of cases where no car is revealed, you have a 50/50 shot of being in either of the 1% states where that happens.
wslh 3y ago
On this topic, please watch what I think is one of the greatest scenes in movies: Kaspar Hauser directed by Warner Herzog [1]. [1] https://youtu.be/C9uqPeIYMik?si=ZjJIH1RhQFTN_ARR https://youtu.be/C9uqPeIYMik?si=ZjJIH1RhQFTN_ARR
- deleted 3y ago
  [deleted]
- swayvil 3y ago
  Hey that riddle was in Labyrinth (with David Bowie as the goblin king!)
  - esafak 3y ago
    https://www.youtube.com/watch?v=grOpvXBmTx8 https://www.youtube.com/watch?v=grOpvXBmTx8
HarHarVeryFunny 3y ago
I think the problem statement is clear, and is independent of how the TV show actually operated. The problem posed is that you have three closed doors, behind one of which is a car, and behind the other two are goats. You get to pick one of the closed doors, and will win whatever is behind it (you want the car). One of the doors you did not pick is now opened, revealing a goat. You therefore now know the car is either behind the door you picked or behind the other closed door. In this setup, the question is: if offered the chance to switch your selection from the door you initially picked to the other closed door, should you switch? Does it make a difference? Mariyln Vos Savant said switch. The peanut gallery (some statisticians who should have known better) said it makes no difference - with two doors left you've got a 50/50 chance of winning the car whether you switch or not. First off, you can run multiple simulations of the game (with random positions of the goats and car), and prove for yourself that always switching is a better strategy, so it's sad that anyone would insist that it's not, even if that seems logical. The simplest way to explain why switching is the correct strategy is this: When you make your initial selection, you have: a) A 1/3 chance of selecting the car, and b) A 2/3 chance of selecting one of the two goats So, 1/3 of the time you selected the car and will therefore lose if you switch, and 2/3 of the time you selected a goat and will therefore win if you switch. Switching will therefore be a winning strategy 2/3 of the time.
- petesergeant 3y ago
  > The simplest way to explain why switching is the correct strategy In my experience the most _intuitive_ explanation is to simply ramp it up to 100 doors, with Monty opening 98 of them, to make it clear that switching offers you the benefit of all unopened doors.
  - HarHarVeryFunny 3y ago
    Maybe different explanations resonate with different people. Another explanation: After initial selection there is 1/3 chance car is behind your door, and 2/3 chance it is behind one of the other two doors. When one of the other doors is opened revealing a goat, we NOW know (new information to be taken advantage of!) the 2/3 chance represented by those two other doors lies with the unopened one. So, your choice is stick with original choice which has 1/3 chance of being correct, or switching to the other door which you now know has a 2/3 chance of being correct! Obviously you switch. The big lie to "with two doors left it's 50/50" is that opening doors makes no difference. You're original choice had 1/3 chance of being correct, and you can't go back in time and change that.
deleted 3y ago
[deleted]

tialaramex 3y ago

Also regardless of whether she's a woman or she's known for intelligence, a response in which you say "You're wrong" needs an extra second's thought to consider whether, in fact, they are wrong, or maybe just their understanding is different from yours and you need to reconsider with their context. Some time back in an HN thread about programming languages I read a response in a thread about inference which said that a particular feature doesn't really save on typing. And it seemed ludicrous. Until I realised the author of the comment has seen the word "typing" (which everybody else in the thread is reading as "The thing you do with a keyboard") and they're interpreting it as "The thing the compiler does". And yeah, with that perspective of course inference isn't saving typing, all your variables still have types, we were just happy because we spent less time operating the keyboard to write a program. Their comment was not wrong and we weren't correcting them, we'd just understood things differently! Edited to add, link: https://news.ycombinator.com/item?id=36593110 https://news.ycombinator.com/item?id=36593110

city41 3y ago
I almost never say "you're wrong", no matter how confident I am. Because I can be, and often am, wrong myself. If there is a disagreement, a miscommunication, etc, why not instead work with the person to find where you two differ and look for common ground? If the other person really is wrong, it's almost always naturally revealed that way.
- petesergeant 3y ago
  Also it’s a lot more fun to simply shout “FALSE”

bazoom42 3y ago

> it just wouldn't make sense in the context of the game show for the presenter (who knows where the goats are) to ever open a door to reveal the car and give you the option to switch. None of it makes sense because it is not a real game show, it is a thought experiment.

apetresc 3y ago
Apropos the topic of being confidently incorrect, it was indeed a real show: https://en.wikipedia.org/wiki/Let%27s_Make_a_Deal https://en.wikipedia.org/wiki/Let%27s_Make_a_Deal Hosted by a real Monty Hall: https://en.wikipedia.org/wiki/Monty_Hall https://en.wikipedia.org/wiki/Monty_Hall It even had the gag prizes like goats (or, as in the photo from the wiki page, a llama)
- svat 3y ago
  The Monty Hall problem is a thought experiment (based on a real game show). As evidence, see this letter from Monty Hall himself ("no trading boxes after the selection"): Dear Steve: Thank you for sending me the problem from "The American Statistician." Although I am not a student of a statistics problems, I do know that these figures can always be used to one's advantage, if I wished to manipulate same. The big hole in your argument of problems is that once the first box is seen to be empty, the contestant cannot exchange his box. So the problems still remain the same, don't they. . . one out of three. Oh, and incidentally, after one is seen to be empty, his chances are no longer 50/50 but remain what they were in the first place, one out of three. It just seems to the contestant that one box having been eliminated, he stands a better chance. Not so. It was always two to one against him. And if you ever get on my show, the rules hold fast for you -- no trading boxes after the selection. Next time let's play on my home grounds. I graduated in chemistry and zoology. You want to know your chances of surviving with our polluted air and water? Sincerely, Monty https://web.archive.org/web/20100408200824/http://www.letsmakeadeal.com/problem.htm https://web.archive.org/web/20100408200824/http://www.letsma...
- dfxm12 3y ago
  I think importantly, the "Monty Hall Problem" as described is different from how any iteration of the Big Deal at the end of Let's Make a Deal is actually run. Hall himself recognized this and mentioned it in a NYT interview in the 90s. It's paywalled, but the excerpt is here: https://en.wikipedia.org/wiki/Monty_Hall_problem https://en.wikipedia.org/wiki/Monty_Hall_problem Hall understood the problem, giving the reporter a demonstration with car keys and explaining how actual game play on Let's Make a Deal differed from the rules of the puzzle. When I first heard about the puzzle, I struggled with the solution precisely because I kept making assumptions about the puzzle based on my knowledge of the show. It wasn't until I thoroughly read the question, setting aside those assumptions, that I realized it is materially different from the show and I was able to really understand the solution.

XCabbage 3y ago

> it just wouldn't make sense in the context of the game show for the presenter (who knows where the goats are) to ever open a door to reveal the car and give you the option to switch No, but it would make perfect sense for him to open a door at random and - if doing so reveals the car - tell you sadly that you've lost as a disappointed klaxon plays. Indeed this is almost the only possible way that the initial door opening could realistically make sense in a game show; if it works in any other way, there's no tension when the first door is opened since there's no risk!

psd1 3y ago
> there's no tension There certainly is. It's a high-stakes scenario and the door-opening presents new information. It makes the conclusion feel less certain. Revealing the car would conclude the game, of course. Unless the contestant were holding out for the better goat.

flomo 3y ago

In reality, Monty Hall often did not behave in the way the problem describes, that might be the source of confusion surrounding this. (e.g. sometimes he would reveal a prize and imply there might be a better prize behind one of the doors. sometimes there were only prizes and no goats, etc.)

lucas_membrane 3y ago

>> The game would be reduced to "does Monty feel like gifting you a car or a goat today". But, in fact, that is the way the real show worked. He was more likely to give you a car when he hadn't given away any cars for a while. And Marilyn's description of the problem included no information about whether or not Monty offered to swap doors rarely, frequently, or always, or about the previously observed outcomes depending on whether or not the contestant took the bait. And she surely did not say that Monty was a robot and had no interest in what happened on his show. The way the game actually worked is like how poker and life work until proven otherwise. Every high-stakes game has a sucker, and if you do not know who is the sucker, it is you. Read the story in which a NY Times reporter interviewed Monty about the controversy and you will learn how it really worked.

harshreality 3y ago
If you're playing the game as stated, and if the host opens a door revealing a goat, you must switch for the best odds. The offer to switch doors is part of the problem statement. You can't justify your decision based on the possibility in the real game that you might not get the offer to switch (which would mean that when you do it might be an intentional red herring). Even if there's a 50% chance there are all goats, or a 75% chance, you still switch. That reduces the overall probability of a win, but it doesn't affect the relative probability from switching. The only reason you might not want to switch is if the first choice had been forced, such that there was an above-random chance that your first pick was the car.
- grogers 3y ago
  The person you are responding to is pointing out that if the host doesn't offer you to switch all the time, then it isn't the best strategy to always switch when you are given the option. For example, knowing that everyone switches when given the option, the host might only offer to switch when you've picked the correct door. In that case, not switching would be better. Hence the poker aspect.
  - lucas_membrane 3y ago

digitalscribe 3y ago

> Not only is Marilyn's interpretation grammatically valid I would consider both interpretations equally valid. If anything, in law we have the "rule of the last antecedent" (phrase/clause modifies nearest antecedent noun) so that the hater's interpretation could be more correct if based only on this rule. This language is ambiguous: "host ... opens another door, say #3, which has a goat." The two options are Marilyn's interpretation of the door always containing a goat (invariant version), or that one door he opens (say #3) just happens to contain a goat (hater's version) but it could have contained a car. As suggested by someone below, a much clearer formation could have said "host opens a door with a goat, say door #3" to avoid this particular ambiguity. There's also the issue of usage of "which" signifying a non-restrictive non-essential clause.

hulium 3y ago
If the the door contains a car, then it doesn't matter whether you switch or not. If it is a goat you get the problem as intended. You still have the intended problem as a subproblem, so this is just a distraction and not a serious objection.
- tga_d 3y ago
  If a goat was revealed randomly instead of intentionally, there is no advantage to switching. See the "Monty Fall Problem" in this paper already linked elsewhere in the discussion: https://web.archive.org/web/20230706235720/https://probability.ca/jeff/writing/montyfall.pdf https://web.archive.org/web/20230706235720/https://probabili... To use the 100 door extension some people find helpful: If Monty always reveals the 98 doors that don't contain goats, then 99% of the time (every time you picked a non-car door), the other door will have the car. If Monty is opening a random set of 98 doors, then 98% of the time Monty will reveal the car, 1% of the time you'll have picked the car on the first guess, and 1% of the time the car is in the other door. When you're in those 2% of cases where no car is revealed, you have a 50/50 shot of being in either of the 1% states where that happens.

wslh 3y ago

On this topic, please watch what I think is one of the greatest scenes in movies: Kaspar Hauser directed by Warner Herzog [1]. [1] https://youtu.be/C9uqPeIYMik?si=ZjJIH1RhQFTN_ARR https://youtu.be/C9uqPeIYMik?si=ZjJIH1RhQFTN_ARR

deleted 3y ago
[deleted]
swayvil 3y ago
Hey that riddle was in Labyrinth (with David Bowie as the goblin king!)
- esafak 3y ago
  https://www.youtube.com/watch?v=grOpvXBmTx8 https://www.youtube.com/watch?v=grOpvXBmTx8

HarHarVeryFunny 3y ago

I think the problem statement is clear, and is independent of how the TV show actually operated. The problem posed is that you have three closed doors, behind one of which is a car, and behind the other two are goats. You get to pick one of the closed doors, and will win whatever is behind it (you want the car). One of the doors you did not pick is now opened, revealing a goat. You therefore now know the car is either behind the door you picked or behind the other closed door. In this setup, the question is: if offered the chance to switch your selection from the door you initially picked to the other closed door, should you switch? Does it make a difference? Mariyln Vos Savant said switch. The peanut gallery (some statisticians who should have known better) said it makes no difference - with two doors left you've got a 50/50 chance of winning the car whether you switch or not. First off, you can run multiple simulations of the game (with random positions of the goats and car), and prove for yourself that always switching is a better strategy, so it's sad that anyone would insist that it's not, even if that seems logical. The simplest way to explain why switching is the correct strategy is this: When you make your initial selection, you have: a) A 1/3 chance of selecting the car, and b) A 2/3 chance of selecting one of the two goats So, 1/3 of the time you selected the car and will therefore lose if you switch, and 2/3 of the time you selected a goat and will therefore win if you switch. Switching will therefore be a winning strategy 2/3 of the time.

petesergeant 3y ago
> The simplest way to explain why switching is the correct strategy In my experience the most _intuitive_ explanation is to simply ramp it up to 100 doors, with Monty opening 98 of them, to make it clear that switching offers you the benefit of all unopened doors.
- HarHarVeryFunny 3y ago
  Maybe different explanations resonate with different people. Another explanation: After initial selection there is 1/3 chance car is behind your door, and 2/3 chance it is behind one of the other two doors. When one of the other doors is opened revealing a goat, we NOW know (new information to be taken advantage of!) the 2/3 chance represented by those two other doors lies with the unopened one. So, your choice is stick with original choice which has 1/3 chance of being correct, or switching to the other door which you now know has a 2/3 chance of being correct! Obviously you switch. The big lie to "with two doors left it's 50/50" is that opening doors makes no difference. You're original choice had 1/3 chance of being correct, and you can't go back in time and change that.

deleted 3y ago

[deleted]