That's why I said it can be a good improvement to find vanity addresses faster, but since there are skipped ranges, other matching prefixes might get lost, there is no violation. But this is not something that a vanity search would ever care about. Only something that should worry someone who wants to solve a puzzle in an efficient matter (e.g. an exact match).
I still dont see how skipping is more efficient than scanning everything.
A certain density of X bits prefixes (what you call being lucky) in an arbitrary range has zero impact on the probability of finding something on the next key, or on 100m keys later.
You can think of it this way : since distribution is random, any key can be replaced by any other key. As a result changing the traversal order does not improve odds of success.
I clarify my methodology: it's not that I skip keys and guess the result. My approach only prioritizes the statistically most probable ranges but maintains the logic of scanning the entire range, like yours. This is a substantial statistical improvement. You, with your pool, also use statistics because you divide and create sub-ranges, and choose the ranges at random. I could tell you that you might end up leaving the range at the end "in the worst-case scenario" and scan 95% to find it. But although it is true that there is a probability, it is a fallacy to tell you since thanks to the birthday paradox, you would normally have to scan half or a little more. That is what some do to counteract ideas based on the logic "in the worst-case scenario".