hgm wrote:
Would the dependence of piece values quoted there not simply be an effect of average mobility, which you would already incorporate automatically when you would incude a mobility term in your evaluation, rather than needing explicit treatment in a material table?
I think that it is useful to treat it explicitly (though I don't use tables for that, I just compute them on the fly), since it can be useful to help avoid bad trades when, e.g., your bishop is not very active in the "static" sense, but will become better later, while your opponent's knight is good now, but weaker in the endgame (too few pawns maybe).
Actually that bonus is not very high, it is just meant to give the engine some knowledge about the likely endings that can be reached from the position: and that should be the (main) role of the imbalance table, shouldn't it?
In it you find additional ideas like the values of pieces relative to the number of pawns (eg. less pawns result in more potential mobility for sliders)
Would the dependence of piece values quoted there not simply be an effect of average mobility, which you would already incorporate automatically when you would incude a mobility term in your evaluation, rather than needing explicit treatment in a material table?
As also already pointed out by Mauro Riccardi, it is more about the potential mobility of a piece in a certain material configuration on the board rather than the actual position. But probably it is not easy to seperate the two in an analysis of game results as was done by Kaufman. So if you use a combination of this material eval term and the dynamic mobility evaluation the values given in the paper might need scaling down.
Edmund wrote:As also already pointed out by Mauro Riccardi, it is more about the potential mobility of a piece in a certain material configuration on the board rather than the actual position. But probably it is not easy to seperate the two in an analysis of game results as was done by Kaufman. So if you use a combination of this material eval term and the dynamic mobility evaluation the values given in the paper might need scaling down.
The idea is that the search wouldl resolve that for you. If the low mobility of the piece is a transient effect, there wil be plenty branches where t develops its potential. And the presence of these branches will then make the engine decide to hang on to the piece, rather than trade it.
Edmund wrote:As also already pointed out by Mauro Riccardi, it is more about the potential mobility of a piece in a certain material configuration on the board rather than the actual position. But probably it is not easy to seperate the two in an analysis of game results as was done by Kaufman. So if you use a combination of this material eval term and the dynamic mobility evaluation the values given in the paper might need scaling down.
The idea is that the search wouldl resolve that for you. If the low mobility of the piece is a transient effect, there wil be plenty branches where t develops its potential. And the presence of these branches will then make the engine decide to hang on to the piece, rather than trade it.
This could be argued for every eval term. Still at very shallow depths or in quies nodes, where most captures happen, the approximate evaluation is much cheaper then the additional plies required to see the potential mobility of a piece.
Someone published a paper on a generalized heuristic for determining all wins involving NN vs. N, without having to use the tablebases at all. The algorithm was tested against the tablebase, and it was found to be 100% correct.
I forget who wrote the paper, but I think it was published between 2001 and 2004. You might want to look through this link:
...and download the PDF on that page which is a complete table of contents sorted by author. Look for "NN vs. N" in the paper titles and you may find it.
There may be some other ideas in this list you might want to explore.
This brings up the following question: as you add more pawns, does the knight gain in value relative to the bishop, as your data and my 1999 article suggest, or does the bishop pair lose value, as the reply by Mr. Georgiev suggests? Of course, both may be true (and probably are), but are both important or is one principle dominant? I have never been able to prove the validity of the bishop pair losing value with more pawns, but it seems right to me as a Grandmaster so I wonder if anyone else has proven it to be a valid term in a chess program (on top of the bishop/knight term)?
lkaufman wrote:This brings up the following question: as you add more pawns, does the knight gain in value relative to the bishop, as your data and my 1999 article suggest, or does the bishop pair lose value, as the reply by Mr. Georgiev suggests?
I have the knight's value start out at a maximum at the beginning of the game, and it decreases slightly as a function of the number of pawns on the board remaining. I also have the knight value increase on proximity to the enemy king. The idea being, if it can achieve a post on higher ranks on files closer and closer to the king, the pawn structure of must be such that it can support the outpost, and the opponent might not be able to drive it away. In these cases, the knight becomes very valuable, moreso than the Bishop, and close in value to a rook.
The "bishop pair" is a constant. What changes with pawn density are mobility values. You don't want to penalize a bishop pair, especially if one pawn break to the base of the opponent's pawn chain will suddenly unleash their fury.
lkaufman wrote:This brings up the following question: as you add more pawns, does the knight gain in value relative to the bishop, as your data and my 1999 article suggest, or does the bishop pair lose value, as the reply by Mr. Georgiev suggests? Of course, both may be true (and probably are), but are both important or is one principle dominant? I have never been able to prove the validity of the bishop pair losing value with more pawns, but it seems right to me as a Grandmaster so I wonder if anyone else has proven it to be a valid term in a chess program (on top of the bishop/knight term)?
There are two other factors that may hide this.
1. Positions with less pawns are generally more drawish (in the endgame).
2. Positions with pawns on both sides favor the bishop, and are more likely to occur with more pawns.
It may be better to let the mobility term take care of this.
Despite such general considerations, it is clear from testing by many people that on average, even after allowing for mobility etc., knights gain relative to bishops with more pawns. My question is whether this gain is the same for one knight vs. one bishop (without or without extra knights) as it is with one knight and one bishop (or two knights) vs. two bishops. This cannot be answered by general considerations, only by actual testing. Has anyone run such tests? My own were inconclusive.
