Lyudmil Tsvetkov wrote:Larry Kaufman already showed based on investigations of his large database that Q+N have and advantage over Q+B, although small. Of course, those were just master games. I would be happy if someone conducts an investigation of a large computer games database to reassess the same factor on a higher level. I am certain the conclusion will be confirmed.
Analyzing games from a database (whether it be human GM games or engines) is a dubious method, because the imbalanced positions were often consciously selected by the players for compensating factors. E.g. you would conclude from GM games that a Pawn in the presence of all material has no or negative value, because no GM is stupid enough to blunder away a Pawn that early in the game, and all positions where one side is 'leading' by a Pawn were the consequence of intentional gambits, where the player sacrificing the Pawn knew there was at least a Pawn in positional compensation, so that the results do not suffer from being a Pawn behind. But of course randomly sacrificing a Pawn for no compensation at all, will tell us quite a different story.
So it is in general better to start from synthetic positions, designed to have no compensation from positional factors (e.g. quasi-symmetric positions).
Concerning 2 knights endgames, first you talked of pawn span, and now you claim that it is minimal number of pawns, actually non-existent, that gives white the decisive advantage in RB vs NN. Sliding pieces really become increasingly stronger as pawns come off, but that is far from insufficient to explain how it is possible to win such an endgame with only 150cps material edge. You need to consider also other factors.
Where do you get this 150cP from? Last time I checked a Rook alone is worth 175cP more than a Knight. Besides, 150cP is about the draw margin for Chess. So quite naturally some 150cP advantages would be wins, other would be draws. How did you select this position? Is it an exception, or is KRBKNN a generally-won end-game? There are plenty of KRKN positions that are won.
And again, whether a single imbalanced position is won or not doesn't say anything about redundancy. It only tells us something about piece values.
[d]4q3/5n2/3nk3/8/8/2R1B3/4K3/4Q3 w - - 0 1
You might also want to take a look at the below position
I would appreciate very much if someone posts engine analysis, even if brief, on the above 2 positions. I guess that the score of black will be better in the second position with added queens.
What would that prove? Engines report the scores that were programmed in there evaluations. Garbage in, garbage out...
So yes, comparison between those two positions (with or without the Queens) is relevant for the 'Queen redundancy' compared to the other pieces. But analyzing it with an engine will tell you exactly zero about the issue. No engine will be able to decide if the position is won or not (i.e. calculate all the way to the mate). And if it would, it would still not tell you anything, because it could just accidentally be a won position of a generally drawn end-game, or vice versa. You would have to try many different positions with that material composition, and look at the percentage of wins.
What would help is to empirically play out the position between equally strong opponents, which randomize their early moves well enough to first generate a large number of independent positions from it before something really gets traded or otherwise decided. Or randomly generate such a set of starting positions with this material, to allow the use of non-randomizing engines for this.
Analyzing the position will only tell you what redundancy penalty the engine has built in. Which is completely useles infos, as whatever it has built in, you wouldn't know if it is any good.