Redundant knight

[BBauer]

[D]6k1/1n6/3n2p1/7p/1P5P/6P1/8/R5K1 w - - 0 1 [D]
You say "white has excellent winning chances".
Why?
Isn't the position a draw?

Code: Select all

35/58	33:40	 5.446.024k	2.695k	+0,18	Ra1-a8+ Kg8-f7 Ra8-h8 Kf7-e6

So you come up with a statement and make conclusions.
What if your statement is wrong?
Please refrain from giving other people a D.
Kind regards
Bernhard

[BBauer]

[D]8/5n2/3nk3/8/8/2R1B3/4K3/8 w - - 0 1 [D]
Did you know that the above position is a draw?
The 50 move rule kicks in.
Kind regards
Bernhard

[Lyudmil Tsvetkov]

I really appreciate your many posts concerning evaluation. Although I haven't read each one---there are quite a few, after all ---I've thought about many of them.

Now please don't take this the wrong way, but the main effect of your posts has been to convince me that this is not the way to go. Too many terms, too much hidden overlap (non-orthogonality), too many artifacts of the human approach to chess, motivated by our very limited search abilities.

At a fundamental level, it seems to me that evaluation comes down to mobility and attack. Even the material value of pieces is simply more or less an encapsulation of their mobilities. Admittedly this is overly simplistic (and focused on the opening and midgame), but a position is good for us if we can move to lots of squares and if we attack a lot of enemy material. After all, the goal of the game is to reduce the opponent's mobility to zero while simultaneously attacking his most valuable piece!

You've almost inspired me to revisit my primitive engine and, after improving the basic move generation and search, to focus on an evaluation based on mobility + attacking. Mostly as an academic exercise, since any engine I create would be just for fun (and also pretty weak).

Thanks Louis.

And I thought I posted just a few messages...

It depends on how you look upon it, I understand that very well. Different persons see different things. Nothing bad about that. But we are talking here how to perfect things. You are completely right, mobility is the most important thing (I would say immediately after space advantage ), but mobility comes in different ways: it comes with attacking, it comes with space, it comes with pawn features and it comes with imbalance evaluation. As mobility is reflected and substantiated in different ways, you can have a whole grasp of it only if you consider those different ways. And the more ways you consider, the closer you are to understanding mobility in-depth.

Now, I started hating that word - orthogonal. Lucas talks about orthogonality, Arjun talks about orthogonality, and now you also started doing this. You do not know what is orthogonal and what not until you test it. However, I completely agree that you do not need too many features in eval; but you need the most important ones. You can certainly get rid of unimportant terms.

I tell you again: the more terms you have in eval in a resonable way, the better, as they omit less possibilities of game development. This has been proven in engine history to be true, but people are always suspicious and unaccepting of new suggestions.

So you have an engine, hope to play a game against it one day.

Your messages and especially output also always inspire me.

There is a key point you miss here. These programs literally search millions (or even tens of millions) of nodes per second. Basically an exhaustive search although to a variable depth. Every evaluation term you add has to be 100% correct, because otherwise your huge search space is guaranteed to walk over those positions where it doesn't work.

As you add more terms, there are more and more unexpected interactions that will cause things to add (or subtract) in a completely unexpected way and produce a score that makes you drop a pawn (or worse) in the blink of an eye.

Most of us that have done this for a while agree that one can't get very far on a minimalistic evaluation, but also one can't get very far with an overly complex evaluation either, because it is so difficult to debug an evaluation where some times the terms work in a coordinated way, while at other times they diametrically oppose each other and lead you to think things are equal when they are anything bug.

The search space has gotten so big, your "more terms is better" can quickly and easily backfire and generate something so complex it is difficult for a human to make heads or tails as to what is going on inside the tree.

That is the challenge: to be able to keep track of and update more terms.

That is why it is more difficult to write a top-notch engine nowadays than it used to be in the past.

And probably that is why many people like to çopy, or, what would you call it alternatively, make use of the already available knowledge. (legality and morality not discussed here)

[Lyudmil Tsvetkov]

[D]8/5n2/3nk3/8/8/2R1B3/4K3/8 w - - 0 1 [D]
Did you know that the above position is a draw?
The 50 move rule kicks in.
Kind regards
Bernhard

Who cares about the 50 move rule?

FIDE should just change it.

Very simple, when specific positions requite more moves, you simply play further.

[Lyudmil Tsvetkov]

[D]6k1/1n6/3n2p1/7p/1P5P/6P1/8/R5K1 w - - 0 1 [D]
You say "white has excellent winning chances".
Why?
Isn't the position a draw?

Code: Select all

35/58	33:40	 5.446.024k	2.695k	+0,18	Ra1-a8+ Kg8-f7 Ra8-h8 Kf7-e6

So you come up with a statement and make conclusions.
What if your statement is wrong?
Please refrain from giving other people a D.
Kind regards
Bernhard

Man, I do not know if the position is possibly a draw in one of its endless ramifications. I said that white has good winning chances, although lagging behind in material. This illustrates the point that a pair of knights are due a redundancy penalty, what was my primary intention. It was intended as an illustration, so that people say, well, there might be something true about it.

I wonder which engine you have used (you did not mention it), but, in case you have used SF, you should know that this is one of the engines you should not use here, as as of late SF underestimates rooks in endgames and generally overestimates knights.

You might want to look at Houdini, Gull, etc., for this specific ending.

But, even if the true score is only 18cps white edge, this also supports my point, as in terms of material black leads by some 50cps, so you should explain where those 70cps difference in performance come from.

[hgm]

[d]2bq2k1/pppppppp/8/8/8/8/PPPPPPPP/1N1Q2K1 w - - 0 1
Anyone doubting in the redundancy theory should look at the above position.

Indeed, they should look at the above position, play it some 10,000 times between equally strong opponents, (possibly permuting the back-rank pieces to force game diversity), and then compare the result with that for the same position(s) without Queens. Then they would know if the extra Queen is worth more to white than to black.

Point is that you have not done that at all, and that anything you say about it is just a fabrication of your imagination.

[d]8/5n2/3nk3/8/8/2R1B3/4K3/8 w - - 0 1
Another proof for the redundancy of knights. Did you know that this is won ... in 222 moves for white?

How is this proof for Knight redundancy? The hypothesis that Bishops are stronger than Knights when not hindered by Pawns (as is already extensively discussed in Larry Kaufman's paper on empirical piece values), plus the obvious fact that Rooks are stronger than Knights, is by itself perfectly capable of explaining this 'cursed win'. This position gives exactly zero evidence for Knight redundancy. It only tells us that Knights are pretty weak pieces.

Redundancy can never be demonstrated from single positions. It only can be demonstrated from comparing positions that have an extra pair of pieces to an equivalent position that has not. You would have (the beginning of) a case if BRNKNN was won, and KRKN (deleting a Knight on each side) was draw. Only the beginning of a case, because piece values are in general not determined by how well the pieces perform in Pawnless endings, but by how well they combat and support Pawns. To make a real case you would not only have to see what extra Knights do to KRKN, but what they do to a representative mix of material combinations where one side already has a Knight (so that the second Knight is 'redundant'), and the other has not. With KRBKNN there aren't even equal pieces on each side that you could delete...

[ZirconiumX]

Lyudmil,

I feel you are missing something quite obvious. Every engine that implements a bishop pair bonus has an implicit knight redundancy term, as two knights are penalised by not being given a bonus.

There is no need to make this implicit bonus any larger than it already is, in my view.

Matthew:out

[Lyudmil Tsvetkov]

[d]2bq2k1/pppppppp/8/8/8/8/PPPPPPPP/1N1Q2K1 w - - 0 1
Anyone doubting in the redundancy theory should look at the above position.

Indeed, they should look at the above position, play it some 10,000 times between equally strong opponents, (possibly permuting the back-rank pieces to force game diversity), and then compare the result with that for the same position(s) without Queens. Then they would know if the extra Queen is worth more to white than to black.

Point is that you have not done that at all, and that anything you say about it is just a fabrication of your imagination.

[d]8/5n2/3nk3/8/8/2R1B3/4K3/8 w - - 0 1
Another proof for the redundancy of knights. Did you know that this is won ... in 222 moves for white?

How is this proof for Knight redundancy? The hypothesis that Bishops are stronger than Knights when not hindered by Pawns (as is already extensively discussed in Larry Kaufman's paper on empirical piece values), plus the obvious fact that Rooks are stronger than Knights, is by itself perfectly capable of explaining this 'cursed win'. This position gives exactly zero evidence for Knight redundancy. It only tells us that Knights are pretty weak pieces.

Redundancy can never be demonstrated from single positions. It only can be demonstrated from comparing positions that have an extra pair of pieces to an equivalent position that has not. You would have (the beginning of) a case if BRNKNN was won, and KRKN (deleting a Knight on each side) was draw. Only the beginning of a case, because piece values are in general not determined by how well the pieces perform in Pawnless endings, but by how well they combat and support Pawns. To make a real case you would not only have to see what extra Knights do to KRKN, but what they do to a representative mix of material combinations where one side already has a Knight (so that the second Knight is 'redundant'), and the other has not. With KRBKNN there aren't even equal pieces on each side that you could delete...

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.

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.

[d]4q3/5n2/3nk3/8/8/2R1B3/4K3/4Q3 w - - 0 1
You might also want to take a look at the below position. It is the same as the main RB vs NN endgame, but you add one queen each side. I bet here already black's drawing chances are much better. Why? Simply because if black still has the full redundancy of the knights, white already gets 2 more partial redundancies that did not exist earlier, namely the partial redundancy of Q and R as linear pieces and the partial redundancy of Q and B as diagonal pieces.

OK, you can not check a million database or play hundred thousand games to check the theory of redundancy, but you can certainly compare the below 2 positions that are relatively simple. Are there differences in score for the 2 positions and what they are attributed to?

[d]8/5n2/3nk3/8/8/2R1B3/4K3/8 w - - 0 1
[d]4q3/5n2/3nk3/8/8/2R1B3/4K3/4Q3 w - - 0 1

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.

[Lyudmil Tsvetkov]

Lyudmil,

I feel you are missing something quite obvious. Every engine that implements a bishop pair bonus has an implicit knight redundancy term, as two knights are penalised by not being given a bonus.

There is no need to make this implicit bonus any larger than it already is, in my view.

Matthew:out

The pair of bishops bonus is due in BB vs BN, as well as in BB vs NN, but in the first case a win is much more difficult, if possible, while in the second almost assured.

There are thousands of combinations between different pieces in imbalances, in some you have a single knight, in other a pair of knights, and you have to be able to evaluate correctly for all cases.

[hgm]

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.