Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it
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Thanks! With your math skills, you've just exposed the pioneer creators of vanity address software by estimating how often you're likely to encounter an N-character prefix. They should be ashamed of themselves for implementing an inefficient calculation.
It would have been more productive to simply pinpoint where you started to disagree.
But you are correct: the calculation of how often you're likely to encounter an N-character prefix is an estimation indeed! Good catch! So, you agree that a uniform distribution does not mean that you get evenly-spaced same-size predictable amounts of prefixes, so you are on a good path.
I don't need to answer 1,000 lines of a questionnaire where you only talk about the hashes themselves. That's all you've discussed, just the simple theory. It's absurd, it strays from the main topic, which is the probability of a prefix of N characters repeating within an estimated range and why it's less probable for this to occur relatively close to another. You're skipping over compound probability, Poisson distribution, statistical frequency. In short, you're misinforming the forum just to be right, and AI are terrible at reasoning.
Everyone here already has the general answer; it's not necessary to know mathematics to deduce that when you're looking to find a given prefix, the longer it is, the less likely you are to find it nearby than far away.
Why is it less likely to find identical prefixes that are close together?
Due to the random nature and independence of events, the probability that two rare events (like finding a specific long prefix) occur in nearby positions is extremely low. This is because we not only need a rare event to happen but for it to happen twice in a short space, which is even more unlikely. Therefore, in the case of probabilistic software, we use compound probability to calculate the probability of a given prefix appearing and the Poisson distribution to estimate the expected frequency of rare events(long prefix) over a wide range.
And yes, before you search in AI, two independent events, unrelated to each other, each maintains their own identical probabilities. But they change like when you flip 2 or more coins trying to get both heads.
Exercise:
Two subjects head to a casino, subject A called 'Near' bets with subject B that we will call 'Far'.
Far bets Near $1000 that he won't flip 3 coins and have all of them result in heads. Who has a higher probability of winning, Near or Far?