H. G. Muller wrote on Sun, May 5, 2019 12:50 PM UTC:
A pair of WA is a general win. The rule of tumb is that one of the minors must be able to move from c1 to a1 (or their symmetry equivalents) in three moves (more precisely, for divergent or asymmetric pieces an uncapture, a move and a capture). A WA can do that (c1-c2-c3-a1), and can thus inflict a corner mate (moving c2-c3) with its King on b3 after the other minor has driven the bare King with check from b1 to a1. Furthermore, edge mates can be forced when one minor can 'fork' a1 and c1 at the the same time, and the other minor can move from c1 to b1 in three moves. But that doesn't work if the forking piece has to be on b3 (as a Knight would have to be), where it would collide with the King.
As to the level of ambition: perhaps I should start indeed a bit more simple. The general scheme is to discount a pawnless advantage by a factor 2 even if it still is a win (except for known easy wins such as KQK and KRK), to properly reflect the relative difficulty of the win. But known general draws should be discounted much more, e.g. by a factor 8 if there still is some hope, or even 16 or infinite if it is a truly dead draw. (A factor 16 would even shrink the KNNK advantage to much less than a Pawn, and when that would still make it the best option the alternatives will almost certainly offer no hope for a win either.)
That leaves room for discounting end-games with a single Pawn by 4 times smaller factor, when the opponent can afford to sac a piece for that Pawn to leave the pawnless general draw. Such a sac typically increases the advantage from +1 to +3, but the relative factor 4 makes the latter +0.75, so the leading side would be biased against allowing the sac. The remaining discount factor (2 or 4) would still discourage converting to such end-games, e.g. by trading Pawns in KBNPPKBNP.
This scheme would need a table that specifies which non-Pawn material should be considered a dead or a general draw. The simplest version of this would just list single minors vs nothing: KBK and KNK in FIDE. But having some 4-men endings in there (like non-mating pairs of minors, such as KNNK, or 'exchange'-type advantages like KRKN) would not be too demanding either. These entries would already extend their influence to KNNPKB and KRPKNN, through the sac-rule. The really tedious part would be to add 5-men end-games such as the 'minor ahead' situations KBNKN, KRBKR, KQBKQ,... But I already generated a lot of those tables; I will summarize those results in another comment.
It could also be good to discount cases like unlike Bishops with a difference of up to 2 Pawns by a factor 2, but at the moment I have no idea how to generalize that. (E.g. it seems that end-games with unlike Ferzes are not particularly drawish.)
A pair of WA is a general win. The rule of tumb is that one of the minors must be able to move from c1 to a1 (or their symmetry equivalents) in three moves (more precisely, for divergent or asymmetric pieces an uncapture, a move and a capture). A WA can do that (c1-c2-c3-a1), and can thus inflict a corner mate (moving c2-c3) with its King on b3 after the other minor has driven the bare King with check from b1 to a1. Furthermore, edge mates can be forced when one minor can 'fork' a1 and c1 at the the same time, and the other minor can move from c1 to b1 in three moves. But that doesn't work if the forking piece has to be on b3 (as a Knight would have to be), where it would collide with the King.
As to the level of ambition: perhaps I should start indeed a bit more simple. The general scheme is to discount a pawnless advantage by a factor 2 even if it still is a win (except for known easy wins such as KQK and KRK), to properly reflect the relative difficulty of the win. But known general draws should be discounted much more, e.g. by a factor 8 if there still is some hope, or even 16 or infinite if it is a truly dead draw. (A factor 16 would even shrink the KNNK advantage to much less than a Pawn, and when that would still make it the best option the alternatives will almost certainly offer no hope for a win either.)
That leaves room for discounting end-games with a single Pawn by 4 times smaller factor, when the opponent can afford to sac a piece for that Pawn to leave the pawnless general draw. Such a sac typically increases the advantage from +1 to +3, but the relative factor 4 makes the latter +0.75, so the leading side would be biased against allowing the sac. The remaining discount factor (2 or 4) would still discourage converting to such end-games, e.g. by trading Pawns in KBNPPKBNP.
This scheme would need a table that specifies which non-Pawn material should be considered a dead or a general draw. The simplest version of this would just list single minors vs nothing: KBK and KNK in FIDE. But having some 4-men endings in there (like non-mating pairs of minors, such as KNNK, or 'exchange'-type advantages like KRKN) would not be too demanding either. These entries would already extend their influence to KNNPKB and KRPKNN, through the sac-rule. The really tedious part would be to add 5-men end-games such as the 'minor ahead' situations KBNKN, KRBKR, KQBKQ,... But I already generated a lot of those tables; I will summarize those results in another comment.
It could also be good to discount cases like unlike Bishops with a difference of up to 2 Pawns by a factor 2, but at the moment I have no idea how to generalize that. (E.g. it seems that end-games with unlike Ferzes are not particularly drawish.)