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.
Yes, you can replace any key by other key. However, let's say that we get to the density you mention BEFORE we finish scanning the arbitrary range (or set, more precisely). So let's say we reach some 90% probability we won't find another element in the current range/set.
A logical speedup is to ignore the rest of the elements in the range/set, and choose a new range/set, to maximize chances to find another new element.
But it's easier to skip a range rather than creating some weird permutation, which might work just the same. Do you not agree? This does not affect at all the laws of the uniform distribution, it's just a tradeoff between missing the key with finding smth with a certain prefix.