values for chess figures...

[Sven]

As I already said, the proof is that without end game (e.g. in Crazyhouse) having Bishops in stead of Rooks does not increase you winning percentage. No amount of idle talk can change that.

Arguments like you are giving, like permeability of the attacked square, are already known not to work even for determining end-game values, as the values of Archbishop and Chancellor convincingly show.

As it is unavoidable that almost no Pawn will be evaluated as 100 cP, no matter what scale you employ, your initilal point also seems pointless. Not all Pawns are equally valuable, and only one can be worth 100 cP.

You continue to talk about other chess variants but you are unable to prove anything with that as far as standard chess is affected. There is zero relation, so please stop bringing arguments from fairy chess and stay on topic.

In standard chess, a rook is *usually* stronger than a knight and stronger than a bishop based on his extended abilities, and you can see that in middlegames as well as in endgames. I say *usually*, not *always*. Presence of more friendly pawns on average seems to help the knight and to impact the rook but how many pawns you have is not directly related to "middlegame vs endgame".

I hope at least you will agree immediately that a queen is *usually* much stronger than a rook already in middlegame of standard chess. It is obvious that the queen's combined abilities of rook and bishop are one part of the story here. Look how dangerous king attacks (middlegame!) are with the participation of a queen.

As to the "100 cP" point, you don't get what I say. How can I decrypt it for you?

1.0 == 100/100

Material values of engine A are pawn=100, knight=325, rook=500. How many centipawns is the exchange worth for A (only material)?

Engine B: pawn=90, knight=300, rook=450. Value of the exchange in centipawns?

Engine C: pawn=80, knight=320, rook=480. Value of the exchange in centipawns?

Answers:
A=175
B=167 (100 * (450-300) / 90)
C=200 (100 * (480-320) / 80)

So for C the exchange is worth relatively more than for A although the internal numbers suggest the opposite (C: 160 vs. A: 175). This is confusing.

In fact only A uses centipawns as basic unit of measurement while B and C use "points", or whatever you call it. You cannot say that B evaluates a knight as 300 centipawns because 300 is more than 300/100 * the value it assigns to a pawn. "centi" means 1/100, not 1/90. Translating the knight value of B into centipawns returns 333.

What you have in mind concerning different values of each single pawn is very much about positional evaluation. Nothing wrong with that but even there you need some basic unit to which all values refer. Taking an "average pawn value" as unit is arbitrary, you are right that milliQueen would be possible, too, but as soon as you decide what your unit is then you must be consistent and should not say that "1.0 units != 100/100 units" (where "unit" is one pawn in this case, not a centipawn, but that does not matter). It does not matter how many pawns in a given position do *actually* have a "material + positional" value of 100 cP because the definition of the overall basic unit "pawn" should be independent from positional aspects.

I can repeat that twice if you like ... should I?

Sven

[michiguel]

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.

Actually you have in science cases like that. The problems is the following: Generally, it's good to have as a "common currency" the value of the smallest unit of what your measuring. However, many times that reference point it not the most stable. Then, as a reference you try to pick the most stable (so the relative values of the rest do not keep swinging) and refer to it as if you were using the smallest unit. For instance, the element with the smalles atomic mass is Hydrogen (it should be one). However, the reference is Carbon, which is assigned an atomic mass of 12 by definition, so Hydrogen will have a value close to one (but not 1.0000!)

In chess, using a pawn as a reference point is a terrible idea because its value changes dramatically. Literally, a value of a Q may go (relative to different pawns) from 1 to 20. For fitting, tuning, and other purposes, it is better to fix the value of another piece such as a Knight. However, since a Knight it is not the smallest, it is convenient to assign the Knight some value close to three. That is pretty much what chemists/physicists have done with atomic masses.

Miguel

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

[hgm]

You continue to talk about other chess variants but you are unable to prove anything with that as far as standard chess is affected. There is zero relation, so please stop bringing arguments from fairy chess and stay on topic.

The point is that meaningful discussion is not possible as long as you believe nonsense like that. When someone tells me that he will run his car tomorrow, because he painted it agree with purple stripes and yellow spots on the hood, and that it is irrelevant that no car ever could use water for fuel, because non of these zillion cars in which it was tried was ever painted green with purple stripes and yellow spots on the hood... Well, than I can only shrug and turn away.

Arguments that are known to be false, don't autmatically become valid because you delare the cases where they were shown to fail as irrelevant. Water is no good as car fuel, no matter how much disdain you show for even-colored cars.

[Bill Rogers]

As to the value of the pieces I have always been inclined to accept the values that HGM has posted with one possible exception and that is if you have both bishops then they are worth 350 each otherwise only 325 of so.
I found the best values were somewhat based upon the number of attacking squares of each piece type in relation to each other and of the same types of pieces.
Bill

[muxecoid]

Given the set of all possible chess positions with material imbalance (normalized to avoid black/white mirroring) find a value set that will give 0.5 points as average result for all positions with equal material if played by equally strong players.

[hgm]

As to the value of the pieces I have always been inclined to accept the values that HGM has posted with one possible exception and that is if you have both bishops then they are worth 350 each otherwise only 325 of so.

Note that this is exactly what I said: a Bishop-pair bonus of 50. if you divide that up over two Bishops, they each get 25 extra.

The effective value of a piece depends on many factors, the number of attacked squares being only one of them. Other important factors are how easily their moves can be blocked, and forking power. For sliders and other riders the blockability correlates inversely with the permeability, which usually offsets the advantage in crowded positions. A good example is the Nightrider. It is worth more than a Rook throughout almost the entire game, despite the fact that the squares it covers are very permeable, with a Knight's jump between them. But that just means it penetrates deeper into the opponent's position. A Rook has on average more moves than a Nightrider on an empty board. But this is apparently no compensation for the fact that it attacks along two forward and two semi-forward rays, while the Roo has only one forrward attack. A Bishop has two...

Another good example that shows how drastically piece values are altered when there is no promise of an end-game is of course the Knights vs Queens position:
[d]1q1qk1q1/3ppp2/8/8/8/1NN2NN1/3PPP2/2NNKN2 w - -
The Queens are slaughtered, because they have no easy way to trade down to an end-game. So the Knights can exploit their higher middle-game value compared to Queen indefinitely. so 7 Knights (classical piece value 21) beat 3 Queens (classical value 27) easily.

[Sven]

You continue to talk about other chess variants but you are unable to prove anything with that as far as standard chess is affected. There is zero relation, so please stop bringing arguments from fairy chess and stay on topic.

The point is that meaningful discussion is not possible as long as you believe nonsense like that. When someone tells me that he will run his car tomorrow, because he painted it agree with purple stripes and yellow spots on the hood, and that it is irrelevant that no car ever could use water for fuel, because non of these zillion cars in which it was tried was ever painted green with purple stripes and yellow spots on the hood... Well, than I can only shrug and turn away.

Arguments that are known to be false, don't autmatically become valid because you delare the cases where they were shown to fail as irrelevant. Water is no good as car fuel, no matter how much disdain you show for even-colored cars.

So you "know" that my arguments are false. Fine. Who else "knows" that?

Can you explain why you think that statements about other chess variants can prove anything about standard chess? I can accept that standard chess is kind of a "subset" of FRC just because the rules are the same (except for FRC castling) and the main difference is that there are more possible starting positions. But all those other variants with additional pieces, different ways of moving, additional/different rules are really something else than standard chess.

Please, don't call that "nonsense". You want a meaningful discussion, so please discuss, but don't say "I am right and your arguments are known to be false". Show me your proof, I haven't seen it yet. But don't try to explain chess to me.

I have the impression that you regard a chess engine as a program that is able to play many different chess variants, where standard chess is just one of them. I accept that you have fun with that, and you share that with many other programmers and users. But please accept that there is also a very different viewpoint, where a chess engine is specialized for playing standard chess only (and perhaps FRC). In the latter case, there is no need for a generalized approach where standard chess is one special case. The approach is different.

Please don't forget that there is a world outside your world.

Sven

[Sven]

As to the value of the pieces I have always been inclined to accept the values that HGM has posted with one possible exception and that is if you have both bishops then they are worth 350 each otherwise only 325 of so.
I found the best values were somewhat based upon the number of attacking squares of each piece type in relation to each other and of the same types of pieces.
Bill

I can roughly accept your statements. However, it seems you have missed some parts of my current discussion with HGM in this thread. The discussion was never about "values that HGM has posted", and also it was never about the pair of bishops. It was about

1) usage of centipawns as basic evaluation unit while setting the material value of a pawn to anything different from 100 cP (which I do not call "incorrect" but just "confusing"), and

2) the question whether classical material values of pieces are mainly based on winning probabilities in the endgame (as originally stated by HGM) or also on piece properties in the middlegame (which is my viewpoint). Part of that discussion was also my example about the value of the exchange, with presence of bishop pair excluded explicitly.

Sven

[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.

Actually you have in science cases like that. The problems is the following: Generally, it's good to have as a "common currency" the value of the smallest unit of what your measuring. However, many times that reference point it not the most stable. Then, as a reference you try to pick the most stable (so the relative values of the rest do not keep swinging) and refer to it as if you were using the smallest unit. For instance, the element with the smalles atomic mass is Hydrogen (it should be one). However, the reference is Carbon, which is assigned an atomic mass of 12 by definition, so Hydrogen will have a value close to one (but not 1.0000!)

I do not say that using "pawn=90" is wrong. I just say that an engine with such a definition does not use "centipawns" as basic unit because "centi" means 1/100 and 90/100 != 1.0 (is that accepted here? ), and that it is confusing to do so because, for instance, a value of "rook=500" with "pawn=90" falsely pretends that a rook were worth 5 pawns in that program although in fact it is more than 5,5.

In chess, using a pawn as a reference point is a terrible idea because its value changes dramatically. Literally, a value of a Q may go (relative to different pawns) from 1 to 20. For fitting, tuning, and other purposes, it is better to fix the value of another piece such as a Knight. However, since a Knight it is not the smallest, it is convenient to assign the Knight some value close to three. That is pretty much what chemists/physicists have done with atomic masses.

If you say you want to fix the value of a knight then this is fine for me. In that case, please explain what you mean by "fixing". My understanding would be to define a fixed constant for the material value of an "average knight", say 325, and define your basic eval unit as "knight/325".

Also, based on what I wrote above I see nothing "convenient" in setting the knight value close to three while setting the pawn to something like 0.9, it is just one form of window-dressing - unless you explicitly set your unit to "knight/3xx" instead of "centipawns".

Sven

[Aaron Becker]

I think this is sort of a pointless distinction because, as Miguel points out, the value of a pawn varies a lot with the position. Therefore specifying the value of a pawn is a somewhat fuzzy endeavor. It's impossible to insist on "one pawn = 100 evaluation units" once you acknowledge that the value of a pawn is not a constant.

In daydreamer, I think on average pawns are worth about 100 if you discard passer bonuses. However, their value varies based on game phase, location, pawn structure, etc. There's not any place in the code that says "Pawn = 100". Their base value is 85 in the midgame and 115 in the endgame. I guess you could say that this is confusing, but at least it acknowledges that pawn values aren't static over the course of a game.