I may be deluded (please tell me if see any counterexample!) but I found the following nifty rule for deciding which pawnless chess endgames are generally wins, versus which are generally drawn: WARREN'S PAWNLESS ENDGAME RULE: In a pawnless endgame with 6 men or fewer (this includes kings): Compute the total material points for both sides using the (very nontraditional!) N=4, B=3, R=7, Q=24, bonus if own two bishops of opposite colors=5, penalty if own two knights=3, bonus if own both a rook and a non-rook=2, bonus if own two rooks=6, penalty if own "loner queen" facing 2 or more enemy officers=6, Let M>=0 be the difference between these two material points totals. If M>6.5 then WIN. If 0<=M<6.5, then DRAW. Allegedly the only exceptions are: the KQknn endgame, which is generally a draw although 24-5=19>>6.5; the KNNBkn and KNNBkb endgames, generally wins; and KBBNkb with the BBs having same square-color (not of great importance!) which is a draw. I am not sure what the KQQkqr ending usually is (win or draw?) but by redefining the word "non-rook" in the final bonus if necessary, it should be able to handle this also. It might also be able to handle quite a few of the most common 7-man cases, but I have not checked and an additional term might then be needed.