Post
by H.G.Muller » Thu Jan 21, 2016 10:55 am
I once experimented in this respect with Fairy-Max, having it keep a count for each piece type, and discounting scores for a leading side that had 0 or 1 Pawn by a factor 2, 4 or 8. This 'Pair-o-Max' was surprisingly stronger than the regular Fairy-Max, nearly 100 Elo IIRC. But it was not the only change; I also used the piece counts to award a bonus for the Bishop pair, awarding extra score when the piece count for Bishops went from even to odd. This allowed me to pick better piece values, and solved the problem that Fairy-Max would squander a B-pair advantage (BB vs BN) by trading Bishops (which it could do no matter how you set the B and N value). I suspect a large part of the Elo rise must have been due to that.
It probably depends a lot on which end-games exactly you recognize. Just discounting pawnless end-games probably would not bring a lot, as it just makes the engine avoid the opponent sacrificing a minor for the last Pawn, at the expense of not being able to advance that Pawn, which makes it just as much a draw 50 moves later.
In Pair-o-Max I assumed a end-game without Pawns for the strong side with <= 2 pieces against <= 1 piece (excl. Kings and defender Pawns) would be a draw when not more than 350 cP ahead according to naive material counting. Such 'drawn' end-games themselves would then be discounted by a factor 8. When more than 350 cP ahead under the same conditions they would be considered 'difficult wins', and these would still be discounted by a factor 2. Except when the defender had nothing but King and Pawns, in which case there was no discount at all. If the strong side had exactly one Pawn, it would cancel the opponent's least-valuable piece, and a remaining advantage of less than 350 cP under the same conditions as above would be discounted a factor 4 instead of 8. So in summary
K + <= 2 pieces vs K + 1 piece [+ pawns?]:
drawn: divide by 8
difficult: divide by 2
K + <= 2 pieces vs K [+ pawns?]
drawn: divide by 8
other: no discount
K + <= 2 pieces + 1 pawn vs K + 2 pieces [+ pawns?]
drawn after piece-for-pawn sac: divide by 4
other: no discount
The 350-cP limit for qualifying as 'drawn' was subject to some exceptions:
When the leading side had...
1) a pair of pieces indicated as 'defective pair' it would be considered drawn irrespective of true material value
2) a single piece that was color bound, it would be considered drawn irrespective of true material value
3) a piece indicated as 'mating minor', it would NOT be considered drawn irrespective of true material value
4) a single piece, and the (remaining) piece of the lagging side was indicated as 'tough defender', it would be considered drawn irrespective of true material value
In orthodox Chess only case (1) is needed, for a pair of Knights. These rules would cause KBNPKNN (which could still involve a substantial advantage if the Pawn is on 7th rank) to be discounted by a factor 4, and KNNPKB and KNNPKR by a factor 4 as well (by virtue of exception 1). The 'mating minor', 'color-bound major' and 'tough defender' cases only occur in Chess variants. (E.g. a non-royal King M is both a mating minor and a tough defender; KMK is won and KQKM is draw, but it is worth only as much as a Bishop.)