PST-only Evaluation for MinimalChess 0.4

[Sven]

I don't question that. My point is, all that Henk and you are talking about is a matter of positional scoring of knights and bishops as single pieces, depending partially on properties like mobility or the color of squares occupied by friendly pawns.

And certainly you can have bad luck owning two weak bishops. The evaluation will assign penalties to both of them, and I think that should be enough. Additionally penalizing the fact that there is a pair of bishops that are both weak, and therefore scaling down the bishop pair bonus somehow that you would normally assign, is too much in my eyes and "redundant".

I also believe that having a pair of weak bishops should be evaluated higher than a weak knight and another weak knight or bishop, simply due to their higher potential for the future. And that would motivate me to always assign a bonus to a pair of bishops. Not as a positional bonus but as part of the material scoring, similar to certain kinds of material imbalance (which does not get scaled as well based on positional properties, that"s the way we handle "material" scoring).

[Ras]

Bishops are always somewhat weak initially because there are many pawns. The bishop pair is a long term investment for the endgame.

[Pio]

I don't question that. My point is, all that Henk and you are talking about is a matter of positional scoring of knights and bishops as single pieces, depending partially on properties like mobility or the color of squares occupied by friendly pawns.

The point is that you cannot say what the intrinsic value of a piece is since you could get rid of the piece values completely by just adding them to the PST for every piece-square-combination as an example.

And certainly you can have bad luck owning two weak bishops. The evaluation will assign penalties to both of them, and I think that should be enough. Additionally penalizing the fact that there is a pair of bishops that are both weak, and therefore scaling down the bishop pair bonus somehow that you would normally assign, is too much in my eyes and "redundant".

I don’t agree with you. The value of the bishop pair comes from that the opponent cannot put pieces on a certain colour and be safe and also from that you can use them as a pair next to each other thus being able to confine the opponents king. As soon as a bishop is weak both of those benefits become smaller and the bishop pair bonus should be penalised. Of course if you penalise it you should give your bishop pair a higher starting value than you have optimised it for so the average will be more or less the same.

I also believe that having a pair of weak bishops should be evaluated higher than a weak knight and another weak knight or bishop, simply due to their higher potential for the future. And that would motivate me to always assign a bonus to a pair of bishops. Not as a positional bonus but as part of the material scoring, similar to certain kinds of material imbalance (which does not get scaled as well based on positional properties, that"s the way we handle "material" scoring).

I agree with you to a certain extent. In the unlikely event both of the bishops can get out they will become stronger.

[Henk]

Bishops are always somewhat weak initially because there are many pawns. The bishop pair is a long term investment for the endgame.

Rooks are also weak. They are great in last part of the game.
And why not give a bonus for pair of rooks.

Also there are positions where one is better of without a pawn.
Pawn blocking (half) open files or diagonals. Or pawns occupying squares that would have been perfect for a knight.

Passed pawn in endgame more valuable than in first part.
Isolated pawns only become bad when in endgame.

[Sven]

A pair of rooks can be stronger than two single rooks in certain situations, you are right. Typically that is the case if they are doubled on an open file or on the 7th rank. But the bonus for that is usually limited to that moment, and it goes away when the doubling, or other reason for the bonus, has gone. So a pair of rooks is not an "investment into the future", as in case of a bishop pair.

[Sven]

I don't question that. My point is, all that Henk and you are talking about is a matter of positional scoring of knights and bishops as single pieces, depending partially on properties like mobility or the color of squares occupied by friendly pawns.

The point is that you cannot say what the intrinsic value of a piece is since you could get rid of the piece values completely by just adding them to the PST for every piece-square-combination as an example.

That is only an optimization to avoid accessing material scores and PST scores separately. The PST in that case still contains both material scores (unrelated to the piece position) and piece-square values.

And certainly you can have bad luck owning two weak bishops. The evaluation will assign penalties to both of them, and I think that should be enough. Additionally penalizing the fact that there is a pair of bishops that are both weak, and therefore scaling down the bishop pair bonus somehow that you would normally assign, is too much in my eyes and "redundant".

I don’t agree with you. The value of the bishop pair comes from that the opponent cannot put pieces on a certain colour and be safe and also from that you can use them as a pair next to each other thus being able to confine the opponents king. As soon as a bishop is weak both of those benefits become smaller and the bishop pair bonus should be penalised. Of course if you penalise it you should give your bishop pair a higher starting value than you have optimised it for so the average will be more or less the same.

You can certainly do it like that. But it would add a complexity for which I don't see any real benefit. Look at Stockfish, in material.cpp the bishop pair is evaluated as part of "material imbalance". It is a bit more complex than a simple constant bishop pair bonus since it takes into account the piece counts of all piece types (and I still need to wrap my head around it a bit more until I fully understand the implementation ), but it does not appear to use any information about the possible weakness of bishops resulting from their position, square colors of pawns etc.

[hgm]

In the material key you can consider Bishops and Pawns on different square shades as different piece types. For the Bishops it is useful to do that anyway, to easily disinguish maerial combinaions with like and unlike Bishops. But when you also do it for Pawns, it can also disinguish the good Bishop vs bad Bishop case. And make it dependent on wheher you have a pair or not, when tuning suggests that this matters.

[mvanthoor]

A pair of rooks can be stronger than two single rooks in certain situations, you are right. Typically that is the case if they are doubled on an open file or on the 7th rank. But the bonus for that is usually limited to that moment, and it goes away when the doubling, or other reason for the bonus, has gone. So a pair of rooks is not an "investment into the future", as in case of a bishop pair.

The one thing why you should try to keep a bishop pair is the reason that when the game progresses, it's more likely for the position to become open than to become closed. If a position is closed, it's often so from the opening, not due to the mid-game.

If you have the bishop pair, it is good to try and trade some pawns of the position is closed. It can even be beneficial to sacrifice a pawn to open up the position, especially if the opponent has two knights and you have two bishops. So, if you have the bishop pair, having more (semi-)open files is good, because that means less pawns.

(I'm now speaking from a chess player point of view, not from the point of an engine programmer.)

[Desperado]

Afaik pieces of a the same type are basically redundant for the general case. The reason is pretty simple, they provide the same functionality.
But that is not true for the bishops, because the board area they control is different. That is compensated with the bishop-pair-bonus.

Comparing the bishop with the knight for the general case, the bishop seems to be stronger than the knight too, on average.
The minor pieces have very different attributes (skills), so the positional impact is strong. Game statistics (computer chess) normally confirm that the winning percentage is higher, with a bishop than with a knight.

imho the general value is represented by the material score.

[Ras]

Game statistics (computer chess) normally confirm that the winning percentage is higher, with a bishop than with a knight.

I think that's because a knight is strongest if the position is rather blocked, but not too much so that also heavy pieces can play, and the knight has a strong outpost. That's something you have to work for, though. The bishop on the other hand becomes automatically stronger in the endgame, and that doesn't require that kind of work. It's particularly evident if pawns are on both queenside and kingside because the bishop can e.g. support an attack on one side while also defending on the other.