values for chess figures...

[Alibaba]

Hi,

i saw in different chess engines different values for the chess figures.
What is best value for knight, Bishop, Rook and Queen in relation to a pawn?

Regards
Andi

[muxecoid]

No one really knows the exact values. In fact there is no such set of numbers cause it depends on position and play style.

In case of average position and average game style the best I can say is that the values of pieces are unlikely to be exact multiples of 0.25 pawns. Empirically determining the true value of pieces with centipawn accuracy will require more computational resources than we all have.

[Alibaba]

ok,

lets give a pawn 100 points.

How many would you give a rook and the queen?
Cleary it depends on the position, but lets talk about the basic values (which can be manipulated by a evaluation function...)...

Cheers
Andi

[hgm]

The accepted values for an 8x8 board are 100, 325, 325, 500, 975 for P, N, B, R, Q, and 50 bonus for the Bishop pair. Most programs perform better with a lighter Pawn, though, 90 or even 80. Of course 'Pawn' is not really a very constant concept. there are many different types of Pawns, and a white Pawn on g7 can be worth more than three white Pawns on h2, h3, h4 (when there is a black Pawn on h5). So 100 might be for a well-defended centralized Pawn (e4 or d4).

[Alibaba]

Thanks for your values.

I have some questions about it....
1.) Relation N to B:
clearly there are positions in which a N is more worth than a B but in lot of positions the bishop is stronger and especially in the endgame it can better stop free pawns of the opponent and this on both sides of the board...so should a bishop get a slightly higher value than an knight? lets say 10-15 points (if 100 is a pawn)

Clearly the bishop pair is more then the knight pair, but how much?
If a single bishop is more than a knight than 50 points seem a little bit to much... for my feeling...what about a bonus of 30-35.

2.) Relation of queen to rook
Cleary in most position 2 rooks are more than a queen, because the rooks can attack a piece/field 2 times....just 25 points seems not enought in my feeling...what about 50-60 points?

so if rook 500 then queen around 940-950

3.) Relation B/N to Q

3 B/N Figures have the same value than the queen. Is this correct?
Hm i thought 3 Figures are a little bit more than a queen...

if queens set (see relation R-Q) to 940-950 this would look good too


what do you think about this?

Regards
Andi

[zamar]

For starters I'd suggest to read:

http://home.comcast.net/~danheisman/Art ... alance.htm

It's of course not absolute truth, but good starting point for further discussion & research.

[jjh13]

Here is two aswers:

Hans Berliner (The System - A World Champion's Approach to Chess, p. 14):

Pawn, 1.0
Knight, 3.2
Bishop, 3.33
Rook, 5.1
Queen, 8.8

Larry Kaufman (The Evaluation of Material Imbalances):

Pawn, 1
Knight, 3 & 1/4
Bishop, 3 & 1/4
Rook, 5
Queen, 9 & 3/4

My thoughts:

If I understand if correctly, material values are "rules of thumbs" that should give a good indication of the average (probable) value of different pieces to the goal of winning the game. I think it is clear, that if we could go through a compete search tree, from the the start of the game to the end (we won't, I know...), and choose the best possible path, there would not be any need for material (or positional values) for the pieces. In other words, the "solving" of chess would not include the concepts of material and positional values.


Question 1: If the "true" value of a piece (= its value to winning the game) depends also on positional considerations (true value = basic value + positional value), i.e. the basic values are always relative to the positional "bonuses", is it meaningful, in the context of chess programs, to discuss the piece values independently of the whole evaluation function?

Question 2: Would it be possible to use, successfully, an evaluation function that would not give the pieces any material values but instead would use only positional concepts? Is it possible? Have someone already tried and failed?


(English is not my native language and I don't know much about chess or programming, so I apologize.)

[hgm]

1.) Relation N to B:
clearly there are positions in which a N is more worth than a B but in lot of positions the bishop is stronger and especially in the endgame it can better stop free pawns of the opponent and this on both sides of the board...so should a bishop get a slightly higher value than an knight? lets say 10-15 points (if 100 is a pawn)

The values I gave where the Kaufman base values, extracted by analyzing win probabilities in GM games with material imblance. Going byond piece values, and taking into account piece-interaction, the rule was that a single B and N are equal with 5 Pawns each, and that the Bishop is about 1/8 of a Pawn better with fewer Pawns. (I suppose it would also depend on where these Pawns were located.)

Clearly the bishop pair is more then the knight pair, but how much?
If a single bishop is more than a knight than 50 points seem a little bit to much... for my feeling...what about a bonus of 30-35.

But it isn't worth more, and 50 is almost exactly what I found as opening vaue of the B-pair in materially imbalanced comp-comp games. Both on 8x8 boards and on 10x8 boards (where the vaue difference between B and N is already 50 for the single piece).

2.) Relation of queen to rook
Cleary in most position 2 rooks are more than a queen, because the rooks can attack a piece/field 2 times....just 25 points seems not enought in my feeling...what about 50-60 points?
so if rook 500 then queen around 940-950

This is not so clear, and in my test with comp-comp games, two Rooks are completely slaughtered by a Queen. But likely the opening value for a
Rook is probably quite low, but we never notice it, because it only becomes available for trading when it gets reasonably developed. The empirical opening value of the rook was more like 475 in my tests. So the 500 is probably only reached in the presence of several open lines, or in the end-game.

3.) Relation B/N to Q

3 B/N Figures have the same value than the queen. Is this correct?
Hm i thought 3 Figures are a little bit more than a queen...

if queens set (see relation R-Q) to 940-950 this would look good too

Well, BNN would be a different matter than BBN.

[jwes]

ok,

lets give a pawn 100 points.

How many would you give a rook and the queen?
Cleary it depends on the position, but lets talk about the basic values (which can be manipulated by a evaluation function...)...

Cheers
Andi

The problem is that the proper material values are affected by other evaluation terms, e.g. a program that is good at evaluating pawn structures re strength of B vs N should have different material values for B and N from a program that is not.

[Sven]

The accepted values for an 8x8 board are 100, 325, 325, 500, 975 for P, N, B, R, Q, and 50 bonus for the Bishop pair. Most programs perform better with a lighter Pawn, though, 90 or even 80. Of course 'Pawn' is not really a very constant concept. there are many different types of Pawns, and a white Pawn on g7 can be worth more than three white Pawns on h2, h3, h4 (when there is a black Pawn on h5). So 100 might be for a well-defended centralized Pawn (e4 or d4).

What puzzles me is that some people want to change the material value of a Pawn from 100 to anything else (but still close to 100), at least under some conditions. In my opinion the whole evaluation function must rely on some basic unit of measurement, and the most common is "centipawns" (could also be "millipawns" but that is just about the same with a factor of 10). The most logical implication of evaluating a chess position in terms of "centipawns" is that there is one value that is *always* fixed, and that is the material value of a Pawn == 100 centipawns.

We do not say that one meter may sometimes have 101 centimeters, just because it is hot today. One meter is *always* 100 centimeters.

If we want to express different evaluations for pawns then we can simply replace this by something equivalent, just to avoid confusion. Examples:

- To express that pawns become slightly stronger towards the endgame, we could reduce the material values of the other pieces which are still relative to a pawn.

- To express that certain pawns are weaker than others based on their current position we can use the positional part of the evaluation.

Using a pawn material value different from 100 centipawns (1000 millipawns) makes understanding an evaluation function quite hard, since it is no longer clear whether the positional values are still measured in "centipawns" or not.

Sven