Maybe your interpretation of full random can be different. Example. public pools are full 100% random. They randomly select a subrange and run it 100%. They do not go start at beginning subrange and then move sequentially to the next.
My real point was, he wasn't using a vanity search, but more than likely, the h160s hard coded into the kernel call, for his PoW and the actual address searching for. That's like 4 lines of code.
And I guarantee you, he did not find a match and stop the search and jump around to another spot in the overall range. He ran full 2^58 subranges. The order in which they were selected were 100% random. But I am guessing, he ran each subrange from key 1 to end of subrange, checking every key in that subrange. Maybe Bram can confirm/clear it all up lol.
My real point was, he wasn't using a vanity search, but more than likely, the h160s hard coded into the kernel call, for his PoW and the actual address searching for. That's like 4 lines of code.
Anyway, I understand your deduction, but given Bram's statements about "full random," it doesn't make clear what his script does.
There could be many tricks where a random search covers the entire range. You put one on the table, which is the least efficient if you don't have a GPU farm, and I presented another equally valid one, more efficient for us mortals. If he did it as you say, that's fine; we don't know for certain, we're just speculating. I could join a pool and randomly scan the 1024 checks and justify that I went through all the keys (when I didn't), and no one in the pool would know.
I can tell you have never participated in a pool or ran your own in-depth, search.
Public pools do not use this format, because the pool needs to know you actually ran the range assigned. That is why they give out x amount of random PoW keys, spread out over the entire, assigned range. Also, the client software is closed source, so you can't enter into a "random" mode. So no, with a public pool, you could not fake your range.
If you are doing your own private pool, you can run as Bram did. Because who are you going to fool, yourself?!?! That would not make sense at all lol.
Let us say you could run a random search in a public pool, to fool them...some ranges would not have the full 1,024 probabilistic leading 48 bits of a h160, so your random mode search would actually do more searching, for infinity, trying to find the magical number 1,024 matches lol. You see?
You do understand the 1,024 is probable, not guaranteed. I think Bram said the lowest range contained only 938 found and the highest contained 1108.
Do you see why your "random" method would not work to fool a pool, or why a public pool cannot run the same way as Bram did his private search/pool??