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[H.G.Muller]

I am getting to the point now to fill Spartacus' material table (which so far only held the B-pair bonus). One of the most important tasks of the material table would be to correct the additive piece-value score for drawish end-games, so that the engine no longer prefers (say) KBK (+325) over KPP (+200).

My question was what end-games need such a correction, and how large that correction should be. Obviously KBK, KNK and KBKB (like B) can be corrected to a hard zero, pruning further search. KNNK is trickier (like KBKN etc., but those don't really need a correction), because there can be checkmates and mate-in-1, and you want the engine to recognize those when it enters KNNK is such a position (e.g. after a forced capture in KNNKQ). So I guess I should evaluate those as zero, but not prune the search (or prune based on the 50-move counter being large enough. I could then apply that same routine to KBKB (unlike), KBKN, KNKN, KRKR (to effect the pruning) if I have it anyway.

Other end-games that need special treatment seem to be:
Strong side has no mating potential:
KBKP, KNKP (corrected to slightly negative ~-0.1)
KBKPP, KNKPP (~ -0.4 ?)
KBKPPP, KNKPPP (~ -0.7 ?, but not as the natural much as when the Pawn side had 4 Pawns)
KNNK... Are problematic. They need a huge correction, and KNNKP could actually be a light advantage for the Knights (although I understand that due to the 50-move rule this will almost always be draw). But what about
KNNKPP
KNNKPPP
KNNKPPPP
...?
Is the Pawn side always better off in those? I guess that with 4 Pawns the Knights might start to face a serious challenge. Furthermore, two Knights is so much that the weak side now also can have a minor, or even a Rook!
KNNKB and KNNKN seem totally drawish (treat like KRKR?)
What if the weak side has 1, 2 or 3 Pawns on top of it? Should this be treated exactly the same as after trading a minor? Or is it slightly better or worse for the Pawn side?

With any other combination of two minors you have mating potential, but only barely so, and if the opponent has non-Pawn material it is very questionable if you will be able to annihilate that without jeopardizing your mating potential.
KBBKN is the only 2 vs 1 minor case that is theoretically won (although also here the 50-move rule makes that very doubtful). How about KBBKNP? I suppose this must be better than KBBKBP, because that would even be draw if you manage to get the Pawn without trading the minor. Of course the natural scoring would award the B-pair here, but that does not explain the difference between a defending B or N.

In general for Pawnless end-games the rule of thumb could be used that this halves your advantage (e.g. KRBKR, KRNKR = +1.5, just at the draw limit, and KRKB, KRKN would be +1, or preferably even somewhat lower). The problem is always how to evaluate it with extra Pawns.