TalkChess.com

[H.G.Muller]

I digested the Fruit end-game evaluation, and it seems to be based on the following general principles:

You discount the score of the side that is ahead according to naive additive evaluation through a multiplier < 1, to squash unjustified optimism. This is needed in basically two general cases:

A) No Pawns, or 1 Pawn with an enlarged danger of losing it
B) Color-bound pieces of opposite color

Case (A) reflects that Chess basically is a game of Pawns, decided by how efficiently you can guide them to promotion, forcing the opponent to sacrifice a piece for it. In case (B) each side can be so much ahead on its own color that there is no hope to overcome its defence there.

The system of multipliers is is a more logical one than giving material-based additive bonuses , because of the high variability of the Pawn value, which can range from 50 to 250 cP. This makes it difficult to decide who is ahead for a given material composition, so that an additive discount might award the side that is ahead, and shifts the point of natural equality to a non-zero value, leading to inaccuracies in the decision to seek/avoid draws (through repetitiones etc.).

Cases that need dicounts, ranked according to severity:

1) Without Pawns and no (forced) mating potential in your piece combination, you get of course multiplier 0.
2) In Pawnless end-games the advantage of a single minor or the exchange is often not enough (e.g. KBNKB, KRKB, KRKN, KRBKR, KRNKR are all general draws). Fruit multiplies these by 1/8 (even if your opponent does have Pawns, provided you are still ahead).
3) When you are only 1 Pawn away from (1), and the opponent has a piece he can sacrifice for that last Pawn, you get multiplier 1/4.
4a) When the opponent can convert to (2) by sacrificing a piece for your last Pawn, Fruit discounts by 1/2.
4b) It also does this whith unlike Bishops (the only color-bound piece inorthodox Chess), and you are not more than 2 Pawns ahead (presumably because the Bishop on its own color has the advantage over upto 2 Pawns when it does not have to deal with the other Bishop as well.

In Fruit the picture is complicated by a few refinements particular to orthodox Chess: KNN is not only an exceptionally valuable combination without forced mating potential, but suffers from the complication that KNNKP can be a forced win. So you cannot discount to 0 for NN when the opponent still has Pawns. Because you can be very much ahead in power, even against 4 Pawns or minor + Pawn, and it is not inconceivable that the Knights could force their way into KNNKP. So Fruit uses 1/16 in this case.

Another refinement is that minor + {Pawn that can be sacrificed away}, which is already bleak, has virtually no prospects at all if the opponent King is blocking the path of the Pawn on a square that a color-bound minor of the attacker cannot cover. Fruit tests for this, and increases the discount from 1/4 to 1/16 in this case. I guess in general this should also be related to how difficult it is to catch the remaining piece of the defender, which he must preserve to avoid the zugzwang that would otherwise force the King to leave his invulnarable defensive position. B and N are way too strong to be cornered by K+B. But is is not inconceivable that other variants have stronger color-bound pieces, capable of hunting down a piece of the defender weaker than N or B. So if in KXPKY the endgame KXKY would be such that you can force baring of the weak side, even though KXK still would be a draw, the favored defensive position in KXPKY might not be worth much.

Finally there are some exceptions for known end-games: KBBKN is an exception to the rule that a single minor ahead is not enough to win without Pawns. (But Fruit still gives it 1/2, probably because the 50-move rule often makes this a draw anyway.) Also the well-known KBPK and KNPK draws with edge Pawns, and KQKP with 7th-rank Pawns have special recognizers that could force a draw score.

An exception that Fruit does not make, but would be logical, is to discount KBPPKNN (where the B side could be ahead with advanced Pawns), because it has only two Pawns, which could be sacrificed away by the two Knights comparatively easily. So this seems to belong in (4a). To me it is also doubtful whether KNNPKB would deserve a discount as bad as KNPKB; it still is true that a B for P sac would reduce the leading side to the useless KNN, but with two Knights it should not be that difficult to screen the Pawn from attack, something that could be hard with only a single minor. The high discount invites premature conversion of KNNPPKBN to KNNPKB by a Knight sac (N+P ahead discounted by 1/4 is +1, thus lower than an undiscounted PP of +2 even without advanced passers). A discount of 1/2 on KNNPPKBN because both Pawns can be sacrificed away with impunity by the BN would alsohelpsuppress this tendency somewhat (but probably not enough all by itself).