Moderators: hgm, Rebel, chrisw
I notice some have a value for the King, I agree with most that the King's value is infinite, but in the endgame, we must give it 3 or 4 points for "playing" value!Most masters will value the bishop pair extensively. Piece values fluctuate based on the position of the board. For instance, in certain positions it may favor knights, in more open terrain the bishops are favored. So humans players, good players, understand that 1 3 3 5, and 9 points are not quite accurate. I could write a lot more than what I wrote here - but just read what is already out there on the web.Sean Evans wrote:Hello,
Based on this piece value chart, what would be the best value for human chess and for computer chess?
I like Berliner's values
Cordially,
Sean
It would be nice to see a complete summary of Larry's values, and any refinements he's done.hgm wrote:The best values are of course the Kaufman values.
That Knight is practically equal to lone Bishop is pretty well verified. As Larry has shown, there is a small correction to the values depending on the number of Pawns.
Note that King=4 for its tactical value is a joke, however. It is not nearly that. It is hardly stonger than Knight, even in the end-game.
Piece values is only an approximate concept, however. In practice the value depends on the composition of the opposing army. You could never explain why 3 Queens lose so badly against 7 Knights by just adding piece values.
You do like the Kaufman values, because they are produced by some mathematical means, am i right?hgm wrote:The best values are of course the Kaufman values.
That Knight is practically equal to lone Bishop is pretty well verified. As Larry has shown, there is a small correction to the values depending on the number of Pawns
[....]
Piece values is only an approximate concept, however. In practice the value depends on the composition of the opposing army. You could never explain why 3 Queens lose so badly against 7 Knights by just adding piece values.
This is an example for what i have said above, It depends.hgm wrote:...
Note that King=4 for its tactical value is a joke, however. It is not nearly that. It is hardly stonger than Knight, even in the end-game.
Currently, two dimensional piece values are in use, to assess the endgame strength of pieces. You could attempt to improve on this, by adding some further dimension. It could solve the problem above.hgm wrote: You could never explain why 3 Queens lose so badly against 7 Knights by just adding piece values.
I would not say they were produced by mathematical means. I like them because they are empirically determined from real games, rather than conceived in the imagination of someone sitting at a desk.BeyondCritics wrote:You do like the Kaufman values, because they are produced by some mathematical means, am i right?
That just shows how unreliable and subjective (educated) guessing at piece values is. Another good example is the value of the Archbishop (B-N compound) known from Capablanca Chess. Values you could find on the internet ranged from 6.5 to 7.5, based on various arguments and insights. But in practice it is worth 8.75 (when Q=9.5), nearly as much as the Chancellor (R-N compound).But how can it be, that not even Fischer, Kasparov and Stockfish do agree on the values of such basic material features?
Well, that is how piece values are defined. As soon as you are evaluating aspects that depend on where the piece is located on the board, and how it is located compared to other pieces, you are talking about positional scores, wich are not part of the piece value.It is possible to calculate some statistic of material values with arbitrary high precision and this statistic could then truly be useful to forecast a game outcome, given _only_ some material signature.
Not really. You just have to be aware that evaluations based only on material always suck. King safety, Pawn structure, centralization, mobility should be taken into account, and do not follow from the material composition alone.The problem is, that in chess, positions with unbalanced material signature are so intricate, that nearly always one has to take into account other important positional factors. And the contributions of these factors could be extremly huge, up to two pawns!
And if this is so, it is concivable that the problem of assessing material values is problematic.
This is an unavoidable consequence that evaluation is just a heuristic. Game-theoretically the only thing that counts is whether a position is won, lost or drawn. Centi-Pawn advantages are just a figment of the imagination, a course approximation of the winning probability that reasonably correlates with the latter, but by no means gives a reliable indication in individual positions.Practically you can always subtract something from the material value and distribute it over these other important factors. And for simple positions you would then probably get away with that inaccurate values in any case.
Empirical fact is that when you are in a late end-game, and have two Kings (one of them designated as non-royal, i.e. expendable) and the opponent a Knight and one extra Pawn, and you put these on the board in many different constellations without giving an obvious large advantage to either side (e.g. no connected passers on 7th rank, but rather all Pawns on their own half, and tactically quiet), the side with the extra King almost always loses.So for me, the guess of 4 makes sense somehow.
Not sure what you mean by 'two-dimensional piece values'. I have never heard of such a thing.Currently, two dimensional piece values are in use, to assess the endgame strength of pieces. You could attempt to improve on this, by adding some further dimension. It could solve the problem above.
I think it is an intrinsic problem. For the sake of clarity, take one simple example. Imagine a hypothetical fairy game with pawns and a single piece A only and with only 2 equally likely (whatever that means!) scenarios possible. In Scenario 1 the piece A is always comparable to having exactly 4 pawns. In Scenario 2 A is always worth 5 pawns. According to your definition, the intrinsic value of the piece A _must_ be 4.5. You then have to adjust this value for every single position.hgm wrote:I would not say they were produced by mathematical means. I like them because they are empirically determined from real games, rather than conceived in the imagination of someone sitting at a desk.BeyondCritics wrote:You do like the Kaufman values, because they are produced by some mathematical means, am i right?
That just shows how unreliable and subjective (educated) guessing at piece values is. Another good example is the value of the Archbishop (B-N compound) known from Capablanca Chess. Values you could find on the internet ranged from 6.5 to 7.5, based on various arguments and insights. But in practice it is worth 8.75 (when Q=9.5), nearly as much as the Chancellor (R-N compound).But how can it be, that not even Fischer, Kasparov and Stockfish do agree on the values of such basic material features?
Well, that is how piece values are defined. As soon as you are evaluating aspects that depend on where the piece is located on the board, and how it is located compared to other pieces, you are talking about positional scores, wich are not part of the piece value.It is possible to calculate some statistic of material values with arbitrary high precision and this statistic could then truly be useful to forecast a game outcome, given _only_ some material signature.
Not really. You just have to be aware that evaluations based only on material always suck. King safety, Pawn structure, centralization, mobility should be taken into account, and do not follow from the material composition alone.The problem is, that in chess, positions with unbalanced material signature are so intricate, that nearly always one has to take into account other important positional factors. And the contributions of these factors could be extremly huge, up to two pawns!
And if this is so, it is concivable that the problem of assessing material values is problematic.This is an unavoidable consequence that evaluation is just a heuristic. Game-theoretically the only thing that counts is whether a position is won, lost or drawn. Centi-Pawn advantages are just a figment of the imagination, a course approximation of the winning probability that reasonably correlates with the latter, but by no means gives a reliable indication in individual positions.Practically you can always subtract something from the material value and distribute it over these other important factors. And for simple positions you would then probably get away with that inaccurate values in any case.
.
Did you tested that? In this case my apologizes, you are truly more of an expert here.hgm wrote:Empirical fact is that when you are in a late end-game, and have two Kings (one of them designated as non-royal, i.e. expendable) and the opponent a Knight and one extra Pawn, and you put these on the board in many different constellations without giving an obvious large advantage to either side (e.g. no connected passers on 7th rank, but rather all Pawns on their own half, and tactically quiet), the side with the extra King almost always loses.So for me, the guess of 4 makes sense somehow.
If that observation is compatible with the piece value of a King being 4, I wouldn't know what piece value means.
Sorry for me being so imprecise. I was refering to "tapered eval". They are working with a two dimensional vector and just in the last moment the vector valued assessment collapses into some scalar.hgm wrote:Not sure what you mean by 'two-dimensional piece values'. I have never heard of such a thing.Currently, two dimensional piece values are in use, to assess the endgame strength of pieces. You could attempt to improve on this, by adding some further dimension. It could solve the problem above.
