6 ms·

You're quoting Priceonomic's 2021 description of the problem. This is NOT the 1990 Parade Magazine description of the problem that generated all the responses.

mkl 6y ago
The 1990 Parade Magazine description is almost identical (and actually more explicit, since "say #3" is a removable parenthetical): "the host, who knows what’s behind the doors, opens another door, say #3, which has a goat" -- https://web.archive.org/web/20130121183432/http://marilynvossavant.com/game-show-problem/ https://web.archive.org/web/20130121183432/http://marilynvos... The host's knowledge is explicitly mentioned, and the only purpose this could have is that so he can use it to avoid giving the game away.
- FabHK 6y ago
  That is literally not explicit (where by "literally" I mean literally, not figuratively, and by "explicit", I mean explicit, not implicit). It is sort of hinted at, but it is not explicitly said that the host will mechanically reveal a door that has a goat. It is quite conceivable that the host picks a door randomly, or in fact that he picks the door with the car with a certain probability (saving the show quite some money).
  - ncallaway 6y ago
    > It is literally explicit in the 1990 rendition. > You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat Remove the parenthetical example "say #3", and the parenthetical "who knows what's behind the doors" and that sentence reads: "...and the host opens another door which has a goat". The "has a goat" is not a hypothetical example. It's a (both literal and explicit) declaration of the rules statement. The rules seem very clear that the host will open a door with a goat.
    - slavik81 6y ago
      It matters whether they choose the door because it has a goat vs. they randomly choose a door that happens to have a goat. It's not explicitly saying the former even when stating the result, because everything is written as a certainty in retrospect. You can say, "the roulette wheel stopped on 00," but it was still a random event when it happened.
    - dekhn 6y ago
      nope, it's ambiguous as stated, if you're a literalist.
- listenallyall 6y ago
  It's a tv show - a valid purpose is that he needs to stretch by 30 seconds before going to commercial. Another purpose is that the audience thinks seeing a goat is funny. Another purpose is to prove the show uses two different goats and doesn't do a switcheroo behind the scenes. What the Parade article does NOT say is that the first door opened is ALWAYS not the contestant's choice and ALWAYS reveals a goat.
  - wahern 6y ago
    That he always opens a door that is not the contestant's choice is a necessary implication of saying that he opens "another" door. That he opens a door containing a goat is similarly implicated. It's not even an implication, really; it's just definitional in vernacular English. And in any event, any of the academics writing in would have been perfectly familiar with the semantic structure of such logic puzzles. Also, most of the population of the country would have been familiar with the game show. Let's Make a Deal was one of the most popular programs on television. Even if they didn't particularly like it, people didn't have much of a TV program selection back then. And even if someone didn't regularly watch TV, it's likely they would have seen it and been familiar w/ the rules regardless simply because it was so widely watched around them. The vehemence of the respondents may even have been an effect of their familiarity, unable to recognize and accept that they'd missed a crucial analytical element after having watched the show so many times before. What makes the puzzle counterintuitive, IMO, is that you're actually answering two different questions: the first before the host makes his selection, and the second (the only one that matters) after he makes his selection. Developing the habit of rigorously "updating your priors"--that is, recognizing when the available evidence has changed, requiring a reassessment--is an applied skill that even experts aren't particularly good at. (Nor was I the first time I read the problem.) The real-life narrative structure actually makes for a great logic puzzle as people are primed to miss the final constraint (his selection) for what it is. They're used to analyzing static situations, or a series of linked static situations--solve X correctly to solve Y. That makes the Monty Hall Problem peculiarly distinct from the typical type of logic puzzle that simply includes a misleading, irrelevant constraint or requires resolving a complex set of constraints.
    - 6y ago
- galaxyLogic 6y ago
  Yes. The probability that car is behind the door NOT selected by the host is 1/2 - because the host had only two choices which are equally good for him. Probability that car is behind the door initially selected by the user is 1/3 because that is what happens when you randomly choose one out of three. We have to think in terms of two different probabilities: a) That user selects the correct door initially and b) That door not selected by the host has the car. But yes it is counter-intuitive. I can't quite point out which step in the flawed reasoning of no benefit from switching occurs. How do people come up with the incorrect result, and what are the flawed assumptions they make that cause them to arrive at the wrong answer? Where exactly does the logical error happen?
  - listenallyall 6y ago
    People come up with the incorrect result because with 2 doors remaining, it would initially appear that they both have equal chance of containing the car. Because it is unclear HOW we arrived at the final two doors. If we arrived there randomly, the probability is in fact 50-50. If there was some manipulation - i.e. if the host knows where the car is AND deliberately opens doors that do NOT contain the car - then the probability is not 50-50, and switching away from the initially-chosen door is advantageous.
    - defterGoose 6y ago
      I find it a little more intuitive in a visual way with the 100 doors. If the 98 doors that the host subsequently eliminates leaves one in the middle of the pack (e.g. #52), most rational people would look at that door and say "hmm its probably in there rather than in the one i picked, #1"
      - thaumasiotes 6y ago
        Eh, the formulation I like goes: You pick a door. The host runs up and knocks on one of the other doors, without opening it or saying anything. He just indicates a door. Now you have the option to stick with your one original door, or to take both of the other two doors. Which is better? And then: how is that scenario different from the one where he opens the special door and reveals a goat?
- dekhn 6y ago
  I read this and thought that sometimes, the host would open the door with the car.

mkl 6y ago

The 1990 Parade Magazine description is almost identical (and actually more explicit, since "say #3" is a removable parenthetical): "the host, who knows what’s behind the doors, opens another door, say #3, which has a goat" -- https://web.archive.org/web/20130121183432/http://marilynvossavant.com/game-show-problem/ https://web.archive.org/web/20130121183432/http://marilynvos... The host's knowledge is explicitly mentioned, and the only purpose this could have is that so he can use it to avoid giving the game away.

FabHK 6y ago
That is literally not explicit (where by "literally" I mean literally, not figuratively, and by "explicit", I mean explicit, not implicit). It is sort of hinted at, but it is not explicitly said that the host will mechanically reveal a door that has a goat. It is quite conceivable that the host picks a door randomly, or in fact that he picks the door with the car with a certain probability (saving the show quite some money).
- ncallaway 6y ago
  > It is literally explicit in the 1990 rendition. > You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat Remove the parenthetical example "say #3", and the parenthetical "who knows what's behind the doors" and that sentence reads: "...and the host opens another door which has a goat". The "has a goat" is not a hypothetical example. It's a (both literal and explicit) declaration of the rules statement. The rules seem very clear that the host will open a door with a goat.
  - slavik81 6y ago
    It matters whether they choose the door because it has a goat vs. they randomly choose a door that happens to have a goat. It's not explicitly saying the former even when stating the result, because everything is written as a certainty in retrospect. You can say, "the roulette wheel stopped on 00," but it was still a random event when it happened.
  - dekhn 6y ago
    nope, it's ambiguous as stated, if you're a literalist.
listenallyall 6y ago
It's a tv show - a valid purpose is that he needs to stretch by 30 seconds before going to commercial. Another purpose is that the audience thinks seeing a goat is funny. Another purpose is to prove the show uses two different goats and doesn't do a switcheroo behind the scenes. What the Parade article does NOT say is that the first door opened is ALWAYS not the contestant's choice and ALWAYS reveals a goat.
- wahern 6y ago
  That he always opens a door that is not the contestant's choice is a necessary implication of saying that he opens "another" door. That he opens a door containing a goat is similarly implicated. It's not even an implication, really; it's just definitional in vernacular English. And in any event, any of the academics writing in would have been perfectly familiar with the semantic structure of such logic puzzles. Also, most of the population of the country would have been familiar with the game show. Let's Make a Deal was one of the most popular programs on television. Even if they didn't particularly like it, people didn't have much of a TV program selection back then. And even if someone didn't regularly watch TV, it's likely they would have seen it and been familiar w/ the rules regardless simply because it was so widely watched around them. The vehemence of the respondents may even have been an effect of their familiarity, unable to recognize and accept that they'd missed a crucial analytical element after having watched the show so many times before. What makes the puzzle counterintuitive, IMO, is that you're actually answering two different questions: the first before the host makes his selection, and the second (the only one that matters) after he makes his selection. Developing the habit of rigorously "updating your priors"--that is, recognizing when the available evidence has changed, requiring a reassessment--is an applied skill that even experts aren't particularly good at. (Nor was I the first time I read the problem.) The real-life narrative structure actually makes for a great logic puzzle as people are primed to miss the final constraint (his selection) for what it is. They're used to analyzing static situations, or a series of linked static situations--solve X correctly to solve Y. That makes the Monty Hall Problem peculiarly distinct from the typical type of logic puzzle that simply includes a misleading, irrelevant constraint or requires resolving a complex set of constraints.
  - 6y ago
galaxyLogic 6y ago
Yes. The probability that car is behind the door NOT selected by the host is 1/2 - because the host had only two choices which are equally good for him. Probability that car is behind the door initially selected by the user is 1/3 because that is what happens when you randomly choose one out of three. We have to think in terms of two different probabilities: a) That user selects the correct door initially and b) That door not selected by the host has the car. But yes it is counter-intuitive. I can't quite point out which step in the flawed reasoning of no benefit from switching occurs. How do people come up with the incorrect result, and what are the flawed assumptions they make that cause them to arrive at the wrong answer? Where exactly does the logical error happen?
- listenallyall 6y ago
  People come up with the incorrect result because with 2 doors remaining, it would initially appear that they both have equal chance of containing the car. Because it is unclear HOW we arrived at the final two doors. If we arrived there randomly, the probability is in fact 50-50. If there was some manipulation - i.e. if the host knows where the car is AND deliberately opens doors that do NOT contain the car - then the probability is not 50-50, and switching away from the initially-chosen door is advantageous.
  - defterGoose 6y ago
    I find it a little more intuitive in a visual way with the 100 doors. If the 98 doors that the host subsequently eliminates leaves one in the middle of the pack (e.g. #52), most rational people would look at that door and say "hmm its probably in there rather than in the one i picked, #1"
    - thaumasiotes 6y ago
      Eh, the formulation I like goes: You pick a door. The host runs up and knocks on one of the other doors, without opening it or saying anything. He just indicates a door. Now you have the option to stick with your one original door, or to take both of the other two doors. Which is better? And then: how is that scenario different from the one where he opens the special door and reveals a goat?
dekhn 6y ago
I read this and thought that sometimes, the host would open the door with the car.