The observer is estimating the range to target; there’s some unavoidable error when you do that. If observers were gods of range estimation, they could just give you a 14-figure grid in the original fire mission, you’d dunk the target and that would be it.
The successive-halving system gets you on target at least as fast as any other method, on average, assuming that the corrections you get are equally distributed, too high 50% of the time and too low 50% of the time, which seems like a good general-purpose assumption.
There might be minor ways to optimize the system, but always remember that whatever you come up with, some slightly scared, tired, getting-shot-at corporal is going to have to do it in the middle of the night in the rain while doing two other things. It has to be clean and simple and also work reasonably well.
*[Note: For all the above I was thinking of an old-school observer, who has worked out their own position on a paper map and is using the Mk I eyeball for range estimation. If you locate yourself with GPS and lase the target to get a range, your initial call will of course be way better. But there’s still tomfoolery like wind and coriolis force that can make arty not hit exactly where it was supposed to, and so even with all the tech toys you still end up having to walk the fire onto target, and do it quick before the bad guys drive away or crawl into their holes.]*
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