I already explained it here https://bitcointalk.org/index.php?topic=1306983.msg65161690#msg65161690, but you keep preferring to omit the existence of compound probability. This is something real! According to your logic, each key is the same because each prefix has the same probabilities on its own, as an independent event. I agree with you, each prefix has the same individual probability of occurring. But I don’t rely on a single event for you to use that as a counterargument. My logic is this: if I am going to scan 1,000,000 sequential keys, since the hashes are distributed uniformly, and being aware that they are not related to each other, compound probability tells me that if I find a hash with 10 prefixes, it is highly unlikely to find the same matching prefix in so few attempts. When you generalize by saying that longer prefixes always appear, you are considering all possibilities and not a specific target. In this case, if you have already found a hash with a specific prefix, the probability of finding that same prefix several times in a limited number of attempts is extremely low.