2 ms·

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

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.
- listenallyall 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 It really isn't. It's possible Monte Hall always opens the doors in reverse numerical order, so if you picked Door #3, that would get opened first. Or that if Door #3 contained the car, that would be revealed before any goats. The way the scenario was initially described by Ms. Vos Savant is not clear about that. And no, not everybody knew Let's Make a Deal in great detail. It's always been a daytime tv show, meaning, it airs while most people are at work.
  - CRConrad 5y 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 > It really isn't. It's possible Monte Hall always opens the doors in... It really is. The "other" in "another" means, quite literally, "not the one already mentioned". And since the only door mentioned before that was the one the contestant had chosen, "he then opens another" not only implies but quite literally and explicitly says that this "another" door the host opens absolutely isn't, cannot be, the one the contestant chose. That's quite simply what "another" literally means.
nzealand 6y ago
The problem the reader originally submitted clearly implied both those things, at least clearly enough for Marylin > and the host, who knows what’s behind the doors, opens another door ... which has a goat The explanation Marylin originally wrote makes the second assumption explicitly clear to avoid any possibility of confusion > Suppose there are a million doors, and you pick door #1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You’d switch to that door pretty fast, wouldn’t you? People still wrote in claiming she was wrong. > 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. She then explained the solution a second time with a table clearly illustrating the assumptions and the odds. People continued to write in claiming she was wrong. > I’m receiving thousands of letters, nearly all insisting that I’m wrong > 92% are against my answer, and and of the letters from universities, 65% are against my answer. Lack of clarity did not generate all the letters. I run a small website with logic puzzles. I get thousands of emails. Some tell me the problem is misleading. Some tell me the answer is wrong. The one thing I have learned is that once someone's mind is made up, it will never change. The other thing I have learned, is that a good problem is succinct. The smartest people in the room will ask clarifying questions to test out their assumptions before they even attempt an answer.

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.

listenallyall 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 It really isn't. It's possible Monte Hall always opens the doors in reverse numerical order, so if you picked Door #3, that would get opened first. Or that if Door #3 contained the car, that would be revealed before any goats. The way the scenario was initially described by Ms. Vos Savant is not clear about that. And no, not everybody knew Let's Make a Deal in great detail. It's always been a daytime tv show, meaning, it airs while most people are at work.
- CRConrad 5y 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 > It really isn't. It's possible Monte Hall always opens the doors in... It really is. The "other" in "another" means, quite literally, "not the one already mentioned". And since the only door mentioned before that was the one the contestant had chosen, "he then opens another" not only implies but quite literally and explicitly says that this "another" door the host opens absolutely isn't, cannot be, the one the contestant chose. That's quite simply what "another" literally means.

nzealand 6y ago

The problem the reader originally submitted clearly implied both those things, at least clearly enough for Marylin > and the host, who knows what’s behind the doors, opens another door ... which has a goat The explanation Marylin originally wrote makes the second assumption explicitly clear to avoid any possibility of confusion > Suppose there are a million doors, and you pick door #1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You’d switch to that door pretty fast, wouldn’t you? People still wrote in claiming she was wrong. > 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. She then explained the solution a second time with a table clearly illustrating the assumptions and the odds. People continued to write in claiming she was wrong. > I’m receiving thousands of letters, nearly all insisting that I’m wrong > 92% are against my answer, and and of the letters from universities, 65% are against my answer. Lack of clarity did not generate all the letters. I run a small website with logic puzzles. I get thousands of emails. Some tell me the problem is misleading. Some tell me the answer is wrong. The one thing I have learned is that once someone's mind is made up, it will never change. The other thing I have learned, is that a good problem is succinct. The smartest people in the room will ask clarifying questions to test out their assumptions before they even attempt an answer.