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[H.G.Muller]

Well, I think that a perfect system would need both offsets and multipliers. Originally my material table just implemented offsets. But the problem is the large variabilty of the Pawn value. In KBK or KNK you could simply cance the base value of the piece (although that calls for pretty large offsets), and the minor positional bonus is small enough to not cause any problems. (E.g. if you go for an illusory +0.15, in stead of a real +0.1 in a still very simple precursor end-game, your prospects for winning must have been pretty close to 0 anyway...)

But in KBKP the Pawn value can range from ~1 to 2.5. If you subtract 2 to make sure the Bishop is not even ahead against a very poor Pawn, the Pawn side would be ahead by +1.5 with a 7th-rank passer. While for the Pawn side this also is pretty much a dead draw, the only Pawn being threatened by a Bishop sac. Definitely not as good as, say KBPKNPP with only a 5th-rank Pawn, which could be close to +1 (for black). So it is OK if KBKP scores in favor of the Pawn, but when the Pawn value increases from 1 to 2.5, the score should more realistically go from 0 to 0.4 (i.e. multiplier 1/4, after an offset +2).

The case KBKPP would need an offset slightly above 1 (to make KBKPP better for black than KBKP, even when the Pawns are pretty poor), but the value of the Pawns could in principle rise to +5, i.e. +3 against the ofsetted Bishop value, which is again rather high for something that can be a hopeless draw. (One unprotected 7th-rank passer being stopped by the Bishop, the other, King-protected 7th-rank passer blocked by the King). So an offset +1.2 combined with multiplier 1/2 seems more realistic here.


For now I solve the problem by never using a multiplier 0, except in the cases of a trivial draw (e.g. KNNKB), where blundering away material of the side that is behind indeed has no consequences whatsoever. That means I can use a pretty simple system, where the material table just has to flag which side(s) have to be discounted (when ahead), and the actual multiplier is then purely determined by the number of Pawns that side has: Pawnless -> x 1/8, 1 Pawn -> x 1/4, more Pawns -> x 1/2. That allowsme to flag both sides for a discount in, say, KBPPPPKBPP, with unlike Bishops. Of couse for most material combinations with 2 or more Pawns a discount is undesirable, but then I simply do not flag those.

The trivial draws are flagged by another code in the material table, because apart from the discounting they can break off the search after the 50-move counter (and ply level!) reaches a value that makes it safe to do so. The number of ply for pruning the node can depend on the material combination (immediate in KK, KNK, 1 in KBKN, 5 in KRKR), and if not pruned, the score is a hard 0.

This does away with the subtlety with which Fruit treats the KNNK* combination (1/16 when the opponnent has Pawns, 0 otherwise), by grouping them all in the Pawnless 1/8 category. (KNNK, KNNKB and KNNKN of course fall in the trivial-draw category, and other opponent combinations where you still can be ahead all have Pawns, so NN couldin theory still win.) In compensation I can do something that Fruit doesn't do, namely discount KBPP or KNPP against KNN or KNNP, (with 1/2, because of 2 Pawns) because black can afford to sac both N.