Oddbean

it's a funny thing... it can be 5 seconds and it can be a week i was vanity mining for my current npub and i'd probably run it for 2 or 3 days and then one day after i'd given up for a week i run it 5 minutes and bam! it's hard to explain how it works but "a few days" "average" are quite vague compared to how it really works - "average" is the peak of the bell curve and that thin edge can mean literally weeks or seconds

there is zero guarantees about where your solution will fall, it just is probably going to fall around the middle of the bell curve for your target partial hash collision my research and experiments with this kind of process show there is ways to make the curve taller and the edges lower (decreasing variance) but i don't think this can apply very easily to an irregular timing system like you have with nostr note ID hashes, the methods i discovered had to do with target variation over time, one that worked was a doubling series with averaging across multiple targets and another was the use of integrals, and i have read more about PID controllers and possibly derivatives can improve the timing of distribution if the integral has a noise filter added to it prior to my foray into this area i knew about the principle of "mass action" in chemistry and it is also a similar thing that is the basis of statistical probability and the gaussian distribution (bell curve) but the only thing that improves timing other than varying your target in response to historical timing is increasing the number of attempts at finding a solution so, i'm just telling you this because reality is not going to be what you expect, the numbers are too small to get such smooth predictable results

This seems completely wrong to me. How could it be anything other than Geometric? I don't see how an experiment would even be necessary, it is self-evident. If hash functions are good than doing one hash will not help with the next, which will mean each is an independent trial from an identically disteibuted bernouli distribution with p = 1/2^target_difficulty where am I wrong?