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Not this again... https://duckduckgo.com/?q=monty+hall+site%3Anews.ycombinator.com https://duckduckgo.com/?q=monty+hall+site%3Anews.ycombinator... I need to wr

Not this again... https://duckduckgo.com/?q=monty+hall+site%3Anews.ycombinator.com https://duckduckgo.com/?q=monty+hall+site%3Anews.ycombinator... I need to write a blog post or something convincing everyone we need to stop talking about the Monty Hall problem and replace it with a new problem with all the ambiguities removed. (Unless ambiguity is the point, then Monty Hall is fine.)

the_af 2y ago
There are no ambiguities in the Monty Hall problem. It's usually people who skim read and make assumptions about the challenge. No new problem is going to stop people from skim reading. For example, going by that ddg search, one result is making a fuss about not knowing whether Monty opens a door at random and happens to show a goat, or purposefully opens a door with a goat behind it. But we do know: it's always on purpose, Monty never opened a door with a car behind it, thus prematurely ending the bet. So there's no ambiguity. The problem is cool because the right answer doesn't seem intuitively right, even though it can be formally shown to be right.
- chikere232 2y ago
  I imagine one reason people have a hard time with the monty hall problem is that they have learnt a rule that seems to fit but really doesn't. A person not trained at all in math might do better as they haven't learnt that rule. There's probably a name for that cognitive bias, but I don't know it.
- default-kramer 2y ago
  > But we do know: it's always on purpose, Monty never opened a door with a car behind it We only know that if the problem tells us. Sometimes it doesn't. > There are no ambiguities in the Monty Hall problem The problem has been written up thousands of times. I'm sure that some writeups are sufficiently unambiguous, but many are not. For example, consider the two "variants" described by this comment https://news.ycombinator.com/item?id=8664550 https://news.ycombinator.com/item?id=8664550 > The host selects one of the doors with a goat from the remaining two doors, and opens it. > The host chooses one of the remaining two doors at random and opens it, showing a goat. This commenter was trying hard for semantic precision, and yet, I think if you encountered the first variant in isolation it would be perfectly reasonable to interpret it as "The host [randomly] selects one of the doors with a goat [although he might have selected the prize]" even though this is clearly not what the commenter was attempting. If you disagree, that only proves my point: this problem is prone to silly and wasteful semantic debate, rather than the interesting probability result it should be focused on.
  - the_af 2y ago
    I don't think it's reasonable to assume Monty picks a door at random, no.
- dllthomas 2y ago
  The original wording was "You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat." I think there's a good argument that the intended interpretation should be the favored one. If he doesn't use the knowledge to always reveal a goat, why did they bother specifying that he has the knowledge? But it still doesn't quite explicitly say that he's not picking randomly.
  - penteract 2y ago
    What if he used the knowledge to decide whether or not to open a door and offer you the choice? I think that scenario is why most people instinctively want to not switch (even if they aren't consciously aware of it), so it's a pity to disregard it.
    - the_af 2y ago
      People instinctively want not to switch because the probabilities involved aren't intuitive. Notice if Monty uses the knowledge of whether to open the door based on what you choose, he'd be giving the whole game away, so that's not it.
  - the_af 2y ago
    It seems to me you're answering your own question. There's only one reasonable interpretation; you have to go out of your way (unreasonably!) to find any ambiguity.
    - dllthomas 2y ago
      Nah, there's a lot of space between "this should be the favored interpretation" and "this is strictly implied" - especially in the context of a math puzzle!
      - the_af 2y ago
        I don't think there is. This is a simple brain teaser. It's fun because the right answer is counterintuitive, that's all. It's not at all about "rules lawyering" the premise of the puzzle.
rbits 2y ago
What new problem without ambiguities do you suggest?
- default-kramer 2y ago
  I'm still working on it, but I think a key idea is that 1) The "host" tells you he is going to eliminate one of the two losing options, and then allow you to choose from the two remaining options. 2) The host allows you, if you wish, to "protect" one of the options from being eliminated. If you choose to protect, you may still choose either of the remaining options after elimination occurs. The correct solution is to protect one of the options and then choose the other option. The real challenge is coming up with appropriate flavor text for this idea, but I think I'll get it eventually.

the_af 2y ago

There are no ambiguities in the Monty Hall problem. It's usually people who skim read and make assumptions about the challenge. No new problem is going to stop people from skim reading. For example, going by that ddg search, one result is making a fuss about not knowing whether Monty opens a door at random and happens to show a goat, or purposefully opens a door with a goat behind it. But we do know: it's always on purpose, Monty never opened a door with a car behind it, thus prematurely ending the bet. So there's no ambiguity. The problem is cool because the right answer doesn't seem intuitively right, even though it can be formally shown to be right.

chikere232 2y ago
I imagine one reason people have a hard time with the monty hall problem is that they have learnt a rule that seems to fit but really doesn't. A person not trained at all in math might do better as they haven't learnt that rule. There's probably a name for that cognitive bias, but I don't know it.
default-kramer 2y ago
> But we do know: it's always on purpose, Monty never opened a door with a car behind it We only know that if the problem tells us. Sometimes it doesn't. > There are no ambiguities in the Monty Hall problem The problem has been written up thousands of times. I'm sure that some writeups are sufficiently unambiguous, but many are not. For example, consider the two "variants" described by this comment https://news.ycombinator.com/item?id=8664550 https://news.ycombinator.com/item?id=8664550 > The host selects one of the doors with a goat from the remaining two doors, and opens it. > The host chooses one of the remaining two doors at random and opens it, showing a goat. This commenter was trying hard for semantic precision, and yet, I think if you encountered the first variant in isolation it would be perfectly reasonable to interpret it as "The host [randomly] selects one of the doors with a goat [although he might have selected the prize]" even though this is clearly not what the commenter was attempting. If you disagree, that only proves my point: this problem is prone to silly and wasteful semantic debate, rather than the interesting probability result it should be focused on.
- the_af 2y ago
  I don't think it's reasonable to assume Monty picks a door at random, no.
dllthomas 2y ago
The original wording was "You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat." I think there's a good argument that the intended interpretation should be the favored one. If he doesn't use the knowledge to always reveal a goat, why did they bother specifying that he has the knowledge? But it still doesn't quite explicitly say that he's not picking randomly.
- penteract 2y ago
  What if he used the knowledge to decide whether or not to open a door and offer you the choice? I think that scenario is why most people instinctively want to not switch (even if they aren't consciously aware of it), so it's a pity to disregard it.
  - the_af 2y ago
    People instinctively want not to switch because the probabilities involved aren't intuitive. Notice if Monty uses the knowledge of whether to open the door based on what you choose, he'd be giving the whole game away, so that's not it.
- the_af 2y ago
  It seems to me you're answering your own question. There's only one reasonable interpretation; you have to go out of your way (unreasonably!) to find any ambiguity.
  - dllthomas 2y ago
    Nah, there's a lot of space between "this should be the favored interpretation" and "this is strictly implied" - especially in the context of a math puzzle!
    - the_af 2y ago
      I don't think there is. This is a simple brain teaser. It's fun because the right answer is counterintuitive, that's all. It's not at all about "rules lawyering" the premise of the puzzle.

rbits 2y ago

What new problem without ambiguities do you suggest?

default-kramer 2y ago
I'm still working on it, but I think a key idea is that 1) The "host" tells you he is going to eliminate one of the two losing options, and then allow you to choose from the two remaining options. 2) The host allows you, if you wish, to "protect" one of the options from being eliminated. If you choose to protect, you may still choose either of the remaining options after elimination occurs. The correct solution is to protect one of the options and then choose the other option. The real challenge is coming up with appropriate flavor text for this idea, but I think I'll get it eventually.