values for chess figures...

[hgm]

I agree it would be better to express the evluation in milliQueens than in centiPawns. But as a Chess player, I want my engine to display +3 when it is a Piece ahead, and +9 when it is a Queen ahead. Not +4 and +12 (say).

I think it would be much less desirable that being a piece ahead would be +3 in some engines and +5 in others, than that being a Pawn ahead is sometmes +0.8 and other times +1.2. The latter differences are in the positional range, and every Chess player knows one Pawn is not equal to the other.

Positional evaluation of Pawns is usually a strategic aspect of the position. I cannot move edge Pawns to the d file. A Queen, however, can move almost anywhere in two or three moves. So the difference between a good and a poor Queen really has a positional, transient character. But edge Pawns and central Pawns might as well have been different piece types, as changing that property requires exchange of material.

[Sven]

I agree it would be better to express the evluation in milliQueens than in centiPawns. But as a Chess player, I want my engine to display +3 when it is a Piece ahead, and +9 when it is a Queen ahead. Not +4 and +12 (say).

That is not realistic. When your engine is "a piece ahead" then the overall advantage does also depend on positional evaluation parts which might change the "+3.25" into "+2.5" or "+4.5" easily. When your engine is "a queen ahead" in an endgame where the enemy does neither have strong pawns nor any other counter attack then you may easily get displayed "+11" or "+12" instead of "+9.75", even with these old "standard" piece material values.

And what is even more important: your expectations "as a chess player" do not match the facts. Any evaluation displayed by a chess engine *has* to be seen individually, each engine has its own "eval space". We have some kind of "standards", like 0 = draw, or +32767 (+30000, +10000, ...) = "mate in 1", although even those are not really standardized. And we have the "common knowledge" saying that a minor piece is "about 3 pawns" worth and a queen "about 9 or 10 pawns". But today's strong engines work differently, this has been mentioned a couple of times in CCC. It is not unusual at all to have "minor = 4" and "queen = 12" today. But that does not make the values that other engines display less "correct". We should never put too much interpretation into the details of some values being displayed by an engine.

I think it would be much less desirable that being a piece ahead would be +3 in some engines and +5 in others, than that being a Pawn ahead is sometmes +0.8 and other times +1.2. The latter differences are in the positional range, and every Chess player knows one Pawn is not equal to the other.

As I said before: the "positional range" is much bigger than only +/- "0.2 pawns". And in my previous post I only referred to the material value of a pawn as the basic unit, while you are clearly talking about the positional part only.

Furthermore, what is the meaning of "+3" for an engine A that evaluates a pawn with 1.0, compared to "+3" from an engine B with pawn=0.8? My answer is simple: for engine A, "+3" means +300 centipawns but for B it is equal to +375 centipawns (3 / 0.8) since B does not have centipawns as basic unit. So what is B's "+3" display worth for you? You will probably say it's o.k. for you. I would say it is either kind of misleading, or even better, I would accept that there are two different relative values originating in two separate eval spaces, having the same absolute value by accident.

Positional evaluation of Pawns is usually a strategic aspect of the position. I cannot move edge Pawns to the d file. A Queen, however, can move almost anywhere in two or three moves. So the difference between a good and a poor Queen really has a positional, transient character. But edge Pawns and central Pawns might as well have been different piece types, as changing that property requires exchange of material.

An h-pawn becomes a g-pawn by capturing once. But as long as it is still an h-pawn you penalize it in the positional eval. This is to show that this h-pawn is currently in a weaker position than others. You could also maintain different piece types for that, just for the sake of different evaluation. But that makes things much more complex than necessary, including "promotion from edge-pawn to non-edge-pawn" ... I know you like that

Sven

[hgm]

Exactly! I do think such a capture is best considered as a promotion. In fact it is much more difficult to force it, than it would be to force a promotion. Insisting that an a-Pawn is the same piece as a b-Pawn is very much like insisting that a Queen really is a Pawn with a somewhat higher positional value. That the pieces have the same moves does not necessarily make them the same: in crazyhouse there are Queens that are promoted Pawns, and they are much more valuable as Queens that are premordial Queens, although they move the same. In xiangqi Pawns acquire extra moves when they cross the River, and many people consider this a promotion.

The actual vlue of a Pawn cannot be used as a standard for piece values, just like the distance between elbow and finger tips is not suitable as a length standard. You have to say which Pawn is used. I am pretty sure that even engines that value a Minor as 4 Pawns will have positions where deleting a single Pawn would gange the evaluation by 1/3 of what it would change by deleting the piece (e.g. a 7th-rank passer). We might as well declare such a Pawn as 'standard Pawn'. In fact piece values for humans have always been based on end-game values. And in simple end-games most Pawns are passers, or majorities can be easily converted to passers, so it makes sense that the value of a passer would be equated to 100 centi-Pawn.

[Sven]

Exactly! I do think such a capture is best considered as a promotion. In fact it is much more difficult to force it, than it would be to force a promotion. Insisting that an a-Pawn is the same piece as a b-Pawn is very much like insisting that a Queen really is a Pawn with a somewhat higher positional value. That the pieces have the same moves does not necessarily make them the same: in crazyhouse there are Queens that are promoted Pawns, and they are much more valuable as Queens that are premordial Queens, although they move the same. In xiangqi Pawns acquire extra moves when they cross the River, and many people consider this a promotion.

This is too much about other chess variants IMO. I know you like other variants, and there is no doubt that many others do as well, but here it is about evaluation of pieces in standard chess only. I would prefer not to mix that up. You clearly need different approaches to evaluate positions in other variants but I dont't think we should generalize too much and make standard chess "just one of many variants".

The actual vlue of a Pawn cannot be used as a standard for piece values, just like the distance between elbow and finger tips is not suitable as a length standard.

I did never say that. But I said that one meter is always 100 centimeter. And I add that 1.0 is always 100 percent, never 90 or 110 percent.

In fact piece values for humans have always been based on end-game values.

Have you ever asked some stronger human players about this? I heavily doubt your statement. There are endgames where two connected passers win against a rook, or even one edge pawn draws against a queen. And some kind of "equality" of a minor piece and three pawns is surely not based on endgames only.

I think that middlegame situations have influenced that traditional "1-3-3-5-9" scheme as well. Look at the value of the exchange: while in most cases one pawn does not fully compensate it, usually two pawns are sufficient, and are sometimes even superior. I know this is a complex task which has been discussed many times elsewhere, but here my point is that often you can already see in the middlegame whether there is some compensation for material or not. A clear advantage in the middlegame also shows up by helping the stronger side to further improve its position. Compensation also means it's not easy to win. So the material values clearly do have their roots also in middlegame.

And in simple end-games most Pawns are passers, or majorities can be easily converted to passers, so it makes sense that the value of a passer would be equated to 100 centi-Pawn.

In most endgames most pawns are not passers. And in the average case it is not easy to convert a majority into a passer. The "average pawn" cannot be described as a passer, that would be very inadequate IMO.

Sven

[hgm]

Well, like it or not, standard Chess is just one of many variants. And a pretty insignificant one on a World scale. About 10 times as many people play Xiangqi...

I strongly doubt that a Rook has any advantage over a Bishop in the middle game. In fact, the Bishop might have the upper hand. Only by virtue of the fact that there is a very high chance that the imbalance can be conserved until the end-game, and the latter will unavoidably come, do middle-game positions with Rook vs Bishop have the better winning chances.

But in crazyhouse, where there will never be an end-game, the piece values ae more like Q ~ N > R ~ B.

[Hood]

Hi,
thanks for the discussion.
That is usefull for OTB players too.
It would be interesting how the values of pieces are evaluating during a game in program. Lets assume pawn as 1.00.

rgds Hood

[Sven]

Well, like it or not, standard Chess is just one of many variants. And a pretty insignificant one on a World scale. About 10 times as many people play Xiangqi...

Possibly "insignificant on a World scale" but not here in CCC. And within this thread, everything else but standard chess has clearly zero significance.

I strongly doubt that a Rook has any advantage over a Bishop in the middle game. In fact, the Bishop might have the upper hand. Only by virtue of the fact that there is a very high chance that the imbalance can be conserved until the end-game, and the latter will unavoidably come, do middle-game positions with Rook vs Bishop have the better winning chances.

I hope that most strong human chess players confirm that this is totally wrong.

A rook is able to attack each square (and therefore each piece) on the board, and it mostly depends on a rook's actual mobility whether he can really do so in a given position. A bishop, even with optimal mobility, can only attack half of all squares (pieces).

A rook on 7th rank is dangerous for enemy pawns and also the king. There is no equivalent concept for a bishop. One reason for that difference is that a rook can hold down a king on its base rank while a bishop can't (the squares attacked by a bishop are somewhat "permeable").

A rook can give mate on a weak back rank. A bishop can't.

A rook can help to push friendly pawns forward (not only passers, not only in endgame) and can control enemy pawns. Both abilities are very limited or non-existent for a bishop.

There are many more examples showing the *middlegame* strength of a rook vs a bishop. You may clearly show a few abilities favoring a bishop but there are only very few. Note that we are *not* talking about bishop pairs.

But in crazyhouse, where there will never be an end-game, the piece values ae more like Q ~ N > R ~ B.

Irrelevant here, see above.

Sven

[hgm]

Unfortunately for your argument Bishops do come in pairs in standard chess. So if you gain the exchange, you Rooks will have to face Bishop pair. On crowded boards the Rooks will never be able to reach 7th rank.

Your arguments are not convincing, or simply wrong.

[Sven]

Unfortunately for your argument Bishops do come in pairs in standard chess. So if you gain the exchange, you Rooks will have to face Bishop pair. On crowded boards the Rooks will never be able to reach 7th rank.

Your arguments are not convincing, or simply wrong.

Thanks for that lesson, Harm G.M.

I simply do not know what you are talking about. I explicitly said I'm *not* talking about presence of bishop pairs. The situation of exchange vs bishop pair is different from exchange without bishop pair. You bring up exceptional cases where it is most important to start with the normal cases first. It is quite frequent that some bishops leave the board before one side wins the exchange. (I do not say that happens always but you appear to think the opposite always happens.) You seem to have the opening in mind where most pieces are still on board, but that's only a small fraction of middlegame positions, if we can even call opening part of middlegame.

On "crowded" boards you may or may not have open files. If you have some then it is not unlikely that one side gains control over an open file (another advantage of the rook: it can control an open file which can be stronger than controlling an "open" diagonal due to the "permeability" I already mentioned, and also because it is easier to close again a diagonal than to close an open file), often followed by a 7th rank attack.

You do not explain why you think my arguments are wrong. Maybe you have no explanation?

So for all others to follow again: my point was that

1) if a program uses a fraction of the material value of an "average" pawn as basic measurement unit for its evaluation function, e.g. centipawns, then it is counterintuitive and may be confusing if the same program uses a material value different from 100 (centipawns) for a pawn, simply because 1.0 is always 100/100; and

2) in reply to a remark from HGM, material value settings like the traditional 1-3-3-5-9 are *not* based only on endgame positions but are already valid during middlegame since they do also reflect the different abilities of pieces, not only winning probabilities in endgames.

Sven

[hgm]

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.