Redundant knight

[Lyudmil Tsvetkov]

[d]r1r3k1/1p3ppp/p2np3/1n6/8/1P1BP3/PB3PPP/4Q1K1 w - - 0 1
Another position where white should have big advantage in terms of redundancy. White has only one partial redundancy of diagonal pieces, while black 2 full redundancies of the rooks and knights. This would make more than 20cps additional bonus for white. It is impossible to take account of this just by changing piece values, as in all positions piece values will remain the same, but in part of those redundancy will be present, while in other part not.

So you really need a specific term to distinguish where pieces are redundant and where not.

[hgm]

Of course in reality (as opposed to your imagination) that position is likely to be lost for white. The Queen suffers greatly from the presence of so many lower black pieces. So the Q-2R imbalance, which should already slightly favor the Rooks, should be magnified by the presence of the minors. Probably this causes a devaluation of more than the Bishop-pair bonus.

Monte-Carlo playouts of this position would be really interesting.

[Lyudmil Tsvetkov]

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.

The draw margin is well above 150cps, somewhere at at least 3-4 full pawns, with most cases even 4.5 pawns. There are exceptions with lower margins, but very few indeed, and not incidentally many of those involve a pair of knights for the losing side. Please take a look at http://en.wikipedia.org/wiki/Pawnless_chess_endgame.

RB vs NN is a win in all cases, independently of the specific position.
RN vs NN is mostly a draw, but there are also winning cases.

[d]3r2k1/8/2B5/8/5N2/3N4/8/6K1 w - - 0 1
This one is a draw, again involving a pair of knights. A draw in all cases. White has 450cps material advantage, but still insufficient for a win. How do you explain it? I say the knights are very redundant, they control same squares, and do it in an awkward way.

The engine output of the position I posted with added queens would be very useful to give us an indication as to what we should expect. There are no obvious factors in the position favouring either side, so I would really be happy if someone is able to post a 2-3 minute top engine analysis on the 2 positions.

It is better of course to investigate a large database, but when this is difficult or no one is willing to do this, we should be happy with whatever we could do. Your point about the engines possibly having some built-in redundancies is not valid, because the position is very simple.

Again, redundancy is a sophisticated term. It is not for every engine, it is for those that aspire to the top.

[Lyudmil Tsvetkov]

Of course in reality (as opposed to your imagination) that position is likely to be lost for white. The Queen suffers greatly from the presence of so many lower black pieces. So the Q-2R imbalance, which should already slightly favor the Rooks, should be magnified by the presence of the minors. Probably this causes a devaluation of more than the Bishop-pair bonus.

Monte-Carlo playouts of this position would be really interesting.

[d][d]r1r3k1/1p3ppp/p2np3/1n6/8/1P1BP3/PB3PPP/4Q1K1 w - - 0 1

That position is easily won for white and any engine analysis could easily confirm it. Unfortunately, no one posting.

[kbhearn]

I haven't actually looked at it with an engine but i doubt his position would be terribly interesting, he has rather intentionally put black's pieces in position to emphasize their redundancy (many tempos to get them to a better position) while leaving black's king naked and white's pieces well positioned to take advantage of it... (all penetration points covered, simply f3 and Qh4 to start provoking pawn weaknesses) Which is to say, the position doesn't demonstrate the need for a general redundancy penalty at all with the pieces so out of position.

More generally, the concept of a redundant knight in human chess does not merely refer to having two knights, but rather two knights with only one good tour for them, seldom is the ideal position for the knights a position where they're protecting each other (only when it's to get one of them to a key deep square without being traded).

I think it'd be a complicated term to design however (as would knight on a bad tour, something that's irked me before in computer analysis that they don't understand) as it would involve a whole-pawn structure analysis to find 'good' tours and when the structure is fluid it could be very deceiving.

[Lyudmil Tsvetkov]

I haven't actually looked at it with an engine but i doubt his position would be terribly interesting, he has rather intentionally put black's pieces in position to emphasize their redundancy (many tempos to get them to a better position) while leaving black's king naked and white's pieces well positioned to take advantage of it... (all penetration points covered, simply f3 and Qh4 to start provoking pawn weaknesses) Which is to say, the position doesn't demonstrate the need for a general redundancy penalty at all with the pieces so out of position.

More generally, the concept of a redundant knight in human chess does not merely refer to having two knights, but rather two knights with only one good tour for them, seldom is the ideal position for the knights a position where they're protecting each other (only when it's to get one of them to a key deep square without being traded).

I think it'd be a complicated term to design however (as would knight on a bad tour, something that's irked me before in computer analysis that they don't understand) as it would involve a whole-pawn structure analysis to find 'good' tours and when the structure is fluid it could be very deceiving.

Actually, this is the most equilibrated position possible, as equilibrated as one could think of with this material configuration. The bishops guard the penetration squares on first and second rank, but black already has a rook on an open file (is not this an advantage?), the black knights are defended, Nb5 is supported by a pawn (is not this an advantage?), the rooks are connected.

But I would be happy if you present another position with the same imbalance to judge upon it.

Actually, there is nothing easier than implementing redundancy: you just count if there are repeating pieces, and if so, assign a penalty. Then tune it until it starts working.

Interesting what Harm will say about the below draw:

[d]6k1/8/8/8/8/3NN3/8/6K1 w - - 0 1
So why 2 white knights, 6 full pawns material advantage, are unable to win against a lone king? There is no pawn span there, no major pieces to excuse that knights get weaker with less pawns, but rooks stronger, absolutely nothing. Why is white not able to win this?

Well, the answer is very simple, because the knights are redundant, even more so in the absence of any other pieces.

[hgm]

That position is easily won for white and any engine analysis could easily confirm it. Unfortunately, no one posting.

You still don't get it. Engine analysis never confirms anything. Engine analysis has nothing to do with reality. It is just the engine's imagination, which is not better than your own fantasies about the position.

Houdini can evaluate itself better than +8.00 in positions that are totally lost for it.

The only reality is checkmate.

[BBauer]

[D]8/8/3k4/8/3B4/4B3/3K1B2/8 w - - 0 1

What penalty would you give for three redundand bishops?
Hope this shows the nonsense.

Kind regards
Bernhard

[Lyudmil Tsvetkov]

Engine analysis has nothing to do with reality.

I think this sums it up very nicely.

[Lyudmil Tsvetkov]

Engine analysis has nothing to do with reality.

I think this sums it up very nicely.