PST-only Evaluation for MinimalChess 0.4

[lithander]

I have no idea what you guys are discussing here but it reinforces my belief that auto-tuning the evaluation is the way to go for me. =)

[hgm]

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.

This is not what Larry Kaufman claimed. Namely that the winning percentage for a Knight and a (lone) Bishop is exactly the same. Or, if you split the results by number of Pawns present, that it is exactly the same with 5 Pawns each, and that the B advantage very slightly decreases with the number of Pawns.

That redundancy argument is pure nonsense, BTW. There is in general no difference between having two identical pieces, or having two different pieces of the same value. Having color-bound pieces such that your power is not equally distributed over the square shades is a disadvantage, though, which appears to depend only very weakly on the power of the color-bound pieces (unless they get extremely weak). So there isn't so much a B-pair bonus, but more a lone-B (or, more accurately, odd-B) penalty.

[Desperado]

... Namely that the winning percentage for a Knight and a (lone) Bishop is exactly the same. ...

Maybe Larry Kaufmann said this, maybe not. I do not know it, but i know that there is enough evidence today that this statement is wrong.
A tuning algorithm will report something different. Testing values between 0...+30 normally result in a clear elo gain, especially in a evaluation,
that is "simple".

...That redundancy argument is pure nonsense. ...

Again, maybe, maybe not.
A reason would help much more to understand why. Even if my functionality argument is wrong, it is at least an argument!

What is your argument?

So, can you tell me what one rook can do what another rook can not do?
If you think of any interaction of pieces (of the same type), the interaction is not part of the material value itself.

If we think of two bishops of the same color (for one side), it might be more clear, what i like to express with redundant.

I agree with you that the pure number of pawns (independent on the position) do have an impact on the piece values,
because the number of pawns are already an indicator of the open/closed position attribute. We all know that sliding pieces,
feel well on open positions and knights are good in closed positions.
Of course you can choose a model to evaluate material combinations, instead of single piece values, but that is a different topic.

... BTW. There is in general no difference between having two identical pieces, or having two different pieces of the same value. Having color-bound pieces such that your power is not equally distributed over the square shades is a disadvantage, though, which appears to depend only very weakly on the power of the color-bound pieces (unless they get extremely weak). So there isn't so much a B-pair bonus, but more a lone-B (or, more accurately, odd-B) penalty.

Sorry for my bad english, but i said that a bishop-pair-bonus "compensates" it's weakness (meaning a single bishop). And adding a further penalty instead of a bonus would not help. Of course the restriction, that the area of a bishop is limited on the squares of the same color, is clearly a weakness (of the bishop type). The bishop pair corrects the defect of a single bishop. This characteristic is completely different to knight,rooks,queens. A knight can potentially always do what another knight is doing and so on...(imo that is redundant in its core function)

[hgm]

Maybe Larry Kaufmann said this, maybe not. I do not know it, but i know that there is enough evidence today that this statement is wrong.
A tuning algorithm will report something different. Testing values between 0...+30 normally result in a clear elo gain, especially in a evaluation,
that is "simple".

I don't know what kind of tuning you have in mind, but Texel tuning often gives piece values that perform disastrously worse than the classical values. And it of course is essential that the B-pair bonus was independently tunable.

Again, maybe, maybe not.
A reason would help much more to understand why. Even if my functionality argument is wrong, it is at least an argument!

What is your argument?

It is not an argument, but an observation. For instance, when you replace the Knights by Phoenixes, the result remains about 50%, showing Knights and Phoenixes are about equally valuable. And Knight + Phoenix vs 2 Knights or vs 2 Phoenixes also score about 50%. There just is no advantage from having two different pieces. Arguments are no substitute for facts.

So, can you tell me what one rook can do what another rook can not do?

I don't need to tell that anymore than that I have to give reasons for why grass is green. All I have to do is replace one Rook of one player by a piece that does something entirely different from a Rook but is about equally powerful (e.g. a Knight that can also can step one square diagonally), and play a number of games where both Rooks of one player are replaced by such pieces, and where only one Rook is replaced by such a piece. And then count the number of wins of each side. Then you will see that the 1+1 vs 2 result is just the average of the 2 vs 2 results, and that having the heterogeneous pair has no special advantage over what the average of the pair values predict.

If you think of any interaction of pieces (of the same type), the interaction is not part of the material value itself.

Thinking about piece values is not a viable approach. It usually leads to disastrously wrong values. Such as in the case of an Archbishop, where the imagined values are off by 200 cP.

If we think of two bishops of the same color (for one side), it might be more clear, what i like to express with redundant.

Well, they can form a battery, for example. It turns out that the value of a Bishop 'anti-pair' (i.e. on same square color) is worth almost exactly twice as much as a lone Bishop.

Of course you can choose a model to evaluate material combinations, instead of single piece values, but that is a different topic.

Awarding a B-pair bonus is a model that evaluates material combinations, rather than plain adding of piece values.

Sorry for my bad english, but i said that a bishop-pair-bonus "compensates" it's weakness (meaning a single bishop). And adding a further penalty instead of a bonus would not help.

I makes a difference whether you apply a penalty or award a bonus when you have more than 2 Bishops. E.g. when you have 2 light and 2 dark Bishops, how many pairs would you count? And how much better is this than having 3 light and 1 dark Bishop?

[Ras]

That redundancy argument is pure nonsense, BTW.

A bishop pair or bishop plus knight can enforce mate vs a lone king, but two knights or two bishops of the same colour cannot.

[hgm]

A bishop pair or bishop plus knight can enforce mate vs a lone king, but two knights or two bishops of the same colour cannot.

That is true, but mating potential seems to contribute awfully little to piece value. I guess the overhwelming majority of games ends in end-games with sufficiently many Pawns that mating potential of the pieces is irrelevant. Their value is mainly determined by how well they can guide Pawns to promotions (or stop opponent Pawns from promoting).

To Phoenixes (steps 1 orthogonally or jumps 2 diagonally) can force checkmate, even though they are equal. A Knight plus a Mortar (jumps 2 or 3 diagonally) cannot force checkmate, even though they are different (and all are 8-target leapers). It depends more on the individual manoeuvring capabilities of the pieces than on the combination. E.g. a Phoenix or a Modern Elephant (steps 1 or jumps 2 diagonally) can force mate in combination with almost anything else. (Because they can move from c1 to a1 in 3 moves, which is the critical feature on a rectangular board).

[Edit] What I forgot to point out is that it also depends on the board shape, and of course on how the royal piece moves. (E.g. in Knightmate even KRK is a draw.) On the Omea Chess board a pair of Knights can force checkmate (with orthodox Kings), while KBNK is a draw more often than not (because it is not possible to smoke the King out of the wrong corner). The relevant question is not what one Knight (or Rook, or whatever) can do that the other can not, but what two Knights can do what B+N cannot. (And in the Omega-Chess case the answer is: force checkmate).