OK.
So, if I understand you correctly, and returning to my original question... given the statement "my next roll of this hundred-sided die will not be 12" (P1), and a bunch of background knowledge (K1) about how hundred-sided dice typically work, and a bunch of background knowledge (K2) relevant to how likely it is that my next roll of this hundred-dided die will be typical (for example, how likely this die is to be loaded), I could in principle be confident in P1.
However, since K2 is not complete, I cannot in practice be confident in P1.
The best I can do is make an informed estimate of the likelihood of P1, but this will be a low confidence estimate.
Have I correctly generalized your reasoning and applied it to the case I asked about?
Have I correctly generalized your reasoning and applied it to the case I asked about?
Yeah, kind of.
However, your P1 statement already implies the most important parts of K1 and K2; as just by inserting the adjective "hundred-sided" into P1 loads it with this knowledge. Beyond that the K1 and K2 stuff is cumbersome background detail that most human brains will have (but of course also necessary for understanding 'dice').
By including "hundred-sided' in the analogy, you are importing a ton of implicit confidence in the true probability dis...
It's just occurred to me that, giving all the cheerful risk stuff I work with, one of the most optimistic things people could say to me would be:
"You've wasted your life. Nothing of what you've done is relevant or useful."
That would make me very happy. Of course, that only works if it's credible.