I don’t believe there is any such estimate because it is fundamentally derivative of human psychology and numerology and culture. Why is 168 a remarkable number but 167 is not? Because of an accident of Chinese telephones. And so on. There is no formula for those. Look at Littlewood’s examples or Diaconis & Mosteller 1989. These things do happen.
And you can expand the space of possibilities even more. What if the same person gets 4 dice in a row within a turn? Across 4 turns? What if the first player gets 1 dice, then the next player gets the same dice, and so on? Would not all of those be remarkable? And note that it would be incorrect to do ‘p^4’ because you are looking at a sliding window over an indefinitely long series of rolls: anywhere in that could be the start of a run of good luck, every roll offers the potential to start a run.
That is exactly the problem I am trying to address. On one hand, I can’t figure out how to estimate the likelihood of a situation. On the other hand, it’s quite evident that some people would fake a picture as mentioned above since many people find it of some importance. I just can’t figure out how to try and evaluate the likelihood of one versus the other. When should I be confused?
I don’t really know. The likelihood of ‘generating an amusing coincidence you can post on social media’ is clearly quite high: your 1⁄160,000 merely examines one kind of amusement, and so obviously is merely an extremely loose lower bound. The more kinds of coincidences you enumerate, the bigger the total likelihood becomes, especially considering that people may be motivated to manufacture stories. Countless examples (but here’s a fun recent example on confabulating stories for spurious candidate-gene hits). The process is so heterogeneous and differs so much by area (be much more skeptical of hate crime reports than rolling nat 20s), that I don’t think there’s really any general approach other than to define a reference class, collect a sample, factcheck, and see how many turn out to be genuine… A lot of SSC posts go into the trouble we have with things like this, such as the ‘lizardman constant’ or rape accusation statistics.
Personally, considering how many rounds there are in any D&D game, how often one does a check, how many players running games there are constantly, how many people you know within 1 or 2 hops on social media, a lower bound of 1⁄160,000 for a neutral event is already more than frequent enough for me to not be all that skeptical; as Littlewood notes of his own examples, many involving gambling, on a national basis, such things happen frequently.
I don’t believe there is any such estimate because it is fundamentally derivative of human psychology and numerology and culture. Why is 168 a remarkable number but 167 is not? Because of an accident of Chinese telephones. And so on. There is no formula for those. Look at Littlewood’s examples or Diaconis & Mosteller 1989. These things do happen.
And you can expand the space of possibilities even more. What if the same person gets 4 dice in a row within a turn? Across 4 turns? What if the first player gets 1 dice, then the next player gets the same dice, and so on? Would not all of those be remarkable? And note that it would be incorrect to do ‘p^4’ because you are looking at a sliding window over an indefinitely long series of rolls: anywhere in that could be the start of a run of good luck, every roll offers the potential to start a run.
That is exactly the problem I am trying to address. On one hand, I can’t figure out how to estimate the likelihood of a situation. On the other hand, it’s quite evident that some people would fake a picture as mentioned above since many people find it of some importance. I just can’t figure out how to try and evaluate the likelihood of one versus the other. When should I be confused?
I don’t really know. The likelihood of ‘generating an amusing coincidence you can post on social media’ is clearly quite high: your 1⁄160,000 merely examines one kind of amusement, and so obviously is merely an extremely loose lower bound. The more kinds of coincidences you enumerate, the bigger the total likelihood becomes, especially considering that people may be motivated to manufacture stories. Countless examples (but here’s a fun recent example on confabulating stories for spurious candidate-gene hits). The process is so heterogeneous and differs so much by area (be much more skeptical of hate crime reports than rolling nat 20s), that I don’t think there’s really any general approach other than to define a reference class, collect a sample, factcheck, and see how many turn out to be genuine… A lot of SSC posts go into the trouble we have with things like this, such as the ‘lizardman constant’ or rape accusation statistics.
Personally, considering how many rounds there are in any D&D game, how often one does a check, how many players running games there are constantly, how many people you know within 1 or 2 hops on social media, a lower bound of 1⁄160,000 for a neutral event is already more than frequent enough for me to not be all that skeptical; as Littlewood notes of his own examples, many involving gambling, on a national basis, such things happen frequently.