I might post here some stupid theoretical conceptions of mine.
In order not to distract fellow forumers too much, as well as annoy the mods, I will stay compact within a single thread.
I am not very certain if I will post more than one topic, but there might be more throughout time.
Any interventions would only be very much appreciated.
Crazy theories
Moderators: hgm, Rebel, chrisw
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Lyudmil Tsvetkov
- Posts: 6052
- Joined: Tue Jun 12, 2012 12:41 pm
X-rayed
I think x-ray attacks of linear/sliding pieces are very important, especially in tactically rich positions. For me, having an x-ray term in the eval would definitely provide added value to proper position understanding.
I think scoring of x-ray attacks could be very simple.
[d]1r3rk1/2p2p1p/4p1p1/Rp1b4/8/1P4BP/1qP1QPP1/5RK1 w - - 0 1
For example, in the above diagram, several pieces x-ray attack enemy objects. When there is only one own or enemy object (pawn or piece) in between the attacker and the attacked piece, we could say that this is an x-ray attack once removed. An x-ray attack once removed might score 1/2 of the value for a direct attack, i.e., if the Bg3 attacking Rb8 in a direct attack would score some 9cps (1/50 the value of the attacked piece or whatever), now it should score some 4.5cps because of the c7 pawn. Other x-ray attacks once removed in the position are Rf1 attacking pf7, Rf8 attacking pf2, Ra5 attacking Bd5, Rb8 attacking pb3, Qb2 attacking Qe2 and Qe2 attacking Qb2.
In the case of the last attack one might wonder if it makes sense to consider x-ray attacks once removed of pieces of same power and capacity, but the problem could be resolved by taking into account if the object in between is own or enemy one. As having an enemy object in between is usually more propicious for the attacker, such an arrangement might score 20% higher. Thus, Qb2 will score 20% higher for attacking Qe2 on an x-ray.
X-ray attacks twice removed would be x-ray attacks with 2 own or enemy objects in between the attacker and the attacked object. Such attacks might score 1/4 of the usual value for a direct attack, so that if Qb2 attacking directly pf2 would score some 2cps, Qb2 on a twice removed x-ray attack against pf2 as in the actual position would score 0.5cps.
Of course, the most important x-ray attacks are those that are once removed, and I think they should be an obligatory element of a good program.
X-ray attacking the enemy king, as well as x-ray attacking squares of the enemy king shelter, are also very important, at least the attacks once removed, but also, in the case of attacking the king, the x-ray attacks removed more times.
[d]6k1/R4p1p/3pp1p1/4n3/8/1B4Q1/1B6/6K1 w - - 0 1
Looking at the above position, we have a couple of x-ray attacks upon the black king: Qg3 on a once removed attack against Kg8, Bb3 on a twice removed attack against Kg8. Once removed attack upon the king might score twice the value for a once removed attack upon the queen, while twice removed attack upon the king twice the value for a twice removed attack upon the enemy queen. (king considered 2 times more valuable than the queen)
In the same diagram, we have also a couple of x-ray attacks upon the enemy king shelter: Ra7 attacking g7 and h7 on a once removed x-ray, Bb2 attacking f6,g7 and h8 on a once removed x-ray. Values for such attacks might be 1/2 the usual values for directly attacking squares of the king shelter.
Very crazy indeed, but I think it makes some sense.
Any comments very much appreciated.
Best, Lyudmil
I think scoring of x-ray attacks could be very simple.
[d]1r3rk1/2p2p1p/4p1p1/Rp1b4/8/1P4BP/1qP1QPP1/5RK1 w - - 0 1
For example, in the above diagram, several pieces x-ray attack enemy objects. When there is only one own or enemy object (pawn or piece) in between the attacker and the attacked piece, we could say that this is an x-ray attack once removed. An x-ray attack once removed might score 1/2 of the value for a direct attack, i.e., if the Bg3 attacking Rb8 in a direct attack would score some 9cps (1/50 the value of the attacked piece or whatever), now it should score some 4.5cps because of the c7 pawn. Other x-ray attacks once removed in the position are Rf1 attacking pf7, Rf8 attacking pf2, Ra5 attacking Bd5, Rb8 attacking pb3, Qb2 attacking Qe2 and Qe2 attacking Qb2.
In the case of the last attack one might wonder if it makes sense to consider x-ray attacks once removed of pieces of same power and capacity, but the problem could be resolved by taking into account if the object in between is own or enemy one. As having an enemy object in between is usually more propicious for the attacker, such an arrangement might score 20% higher. Thus, Qb2 will score 20% higher for attacking Qe2 on an x-ray.
X-ray attacks twice removed would be x-ray attacks with 2 own or enemy objects in between the attacker and the attacked object. Such attacks might score 1/4 of the usual value for a direct attack, so that if Qb2 attacking directly pf2 would score some 2cps, Qb2 on a twice removed x-ray attack against pf2 as in the actual position would score 0.5cps.
Of course, the most important x-ray attacks are those that are once removed, and I think they should be an obligatory element of a good program.
X-ray attacking the enemy king, as well as x-ray attacking squares of the enemy king shelter, are also very important, at least the attacks once removed, but also, in the case of attacking the king, the x-ray attacks removed more times.
[d]6k1/R4p1p/3pp1p1/4n3/8/1B4Q1/1B6/6K1 w - - 0 1
Looking at the above position, we have a couple of x-ray attacks upon the black king: Qg3 on a once removed attack against Kg8, Bb3 on a twice removed attack against Kg8. Once removed attack upon the king might score twice the value for a once removed attack upon the queen, while twice removed attack upon the king twice the value for a twice removed attack upon the enemy queen. (king considered 2 times more valuable than the queen)
In the same diagram, we have also a couple of x-ray attacks upon the enemy king shelter: Ra7 attacking g7 and h7 on a once removed x-ray, Bb2 attacking f6,g7 and h8 on a once removed x-ray. Values for such attacks might be 1/2 the usual values for directly attacking squares of the king shelter.
Very crazy indeed, but I think it makes some sense.
Any comments very much appreciated.
Best, Lyudmil
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Lyudmil Tsvetkov
- Posts: 6052
- Joined: Tue Jun 12, 2012 12:41 pm
Flexible pawn structures
I think at least with groups of 3 pawns (3 connected pawns, might be part of a larger group, but no double pawns included) the notion of flexible pawn structures might be applied to good avail.
For me, a flexible pawn structure would be any group of 3 pawns with the characteristics that by any possible move of any of the pawns of the group most of the moves (i.e., at least 66%, but maybe even 100%) would lead to another structure that could be defined as 'good'.
Good structures would be those that provide some real added value, for example a chain of 3 pawns along one diagonal, a structure with an apex pawn (a pawn defended by 2 own pawns), because of being both sound and flexible, etc. Pawn structures that would lead to the formation of such good structures by most of the possible moves could be defined as 'flexible'. Flexible structures might be valuable, because they might be useful in predicting the possibilities for potential expansion of the existing pawn groups, thus having a direct influence on the game. Inflexible pawn structures on the other hand should be avoided if possible, as they would indicate that the group is likely to deteriorate into a worse pawn structure, or even fall apart.
Below some diagrams of flexible and inflexible pawn structures, consisting of 3 pawns.
Flexible pawn structures:
[d]6k1/8/8/8/2PPP3/8/8/6K1 w - - 0 1
3 horizontally adjacent pawns on the same rank, the structure is flexible, because, mainly, it would lead to a structure with an apex pawn (very useful), but also because the other 2 possible moves would not compromise the wholeness of the group, while a more advanced pawn would already be supported.
[d]6k1/8/8/3P4/2P1P3/8/8/6K1 w - - 0 1
A structure with an apex pawn, of course, the structure is valuable as it is, but also only a sinle move would lead to its falling apart, while 2 other possible moves would lead to the formation of a flexible structure.
[d]6k1/8/8/8/3PP3/2P5/8/6K1 w - - 0 1
2 pawns on a more advanced rank, and one on less advanced rank, the structure is flexible, because 2 of the possible moves would lead to the formation of either a chain, or another structure that is flexible (good, valuable).
Inflexible pawn structures:
[d]6k1/8/8/8/2P1P3/3P4/8/6K1 w - - 0 1
A structure with one root/base pawn. Of course, root/base pawns are bad, because vulnerable, and due some small penalty (maybe 5cps), and moreover, by 2 possible moves the group would fall apart.
[d]6k1/8/8/8/4P3/2PP4/8/6K1 w - - 0 1
2 pawns on a less advanced rank, with one pawn on a more advanced rank. The structure is inflexible, because by 2 possible moves it will either fall apart, or lead to the formation of a group with a root pawn (inflexible one).
[d]6k1/8/8/4P3/3P4/2P5/8/6K1 w - - 0 1
A chain of 3 pawns along the same diagonal. Of course, the chain would be due some nice bonus, as it thwarts the activity of the enemy pieces and is sound. That left aside, the structure ir obviously inflexible, as 2 of the possible moves would lead to its falling apart, while the third one to a structure that is inflexible.
I am not sure if inflexible pawn structures should be penalised, as with them there are usually other bonus or penalty points to be dispensed. But, definitely, flexible pawn structures should be incentivised in some way. I think 5-10-15 cps might be a good assessment of the value and potential usefulness of such structures.
Well, this was my brief outline. I think it was not very clear, it is not to me, and some issues with definitions might still stand out. However, I have no doubts at all concerning the added value of the above-mentioned flexible structures: they really mean something in the game, something tangible and useful, not to be easily discarded.
Best, Lyudmil
For me, a flexible pawn structure would be any group of 3 pawns with the characteristics that by any possible move of any of the pawns of the group most of the moves (i.e., at least 66%, but maybe even 100%) would lead to another structure that could be defined as 'good'.
Good structures would be those that provide some real added value, for example a chain of 3 pawns along one diagonal, a structure with an apex pawn (a pawn defended by 2 own pawns), because of being both sound and flexible, etc. Pawn structures that would lead to the formation of such good structures by most of the possible moves could be defined as 'flexible'. Flexible structures might be valuable, because they might be useful in predicting the possibilities for potential expansion of the existing pawn groups, thus having a direct influence on the game. Inflexible pawn structures on the other hand should be avoided if possible, as they would indicate that the group is likely to deteriorate into a worse pawn structure, or even fall apart.
Below some diagrams of flexible and inflexible pawn structures, consisting of 3 pawns.
Flexible pawn structures:
[d]6k1/8/8/8/2PPP3/8/8/6K1 w - - 0 1
3 horizontally adjacent pawns on the same rank, the structure is flexible, because, mainly, it would lead to a structure with an apex pawn (very useful), but also because the other 2 possible moves would not compromise the wholeness of the group, while a more advanced pawn would already be supported.
[d]6k1/8/8/3P4/2P1P3/8/8/6K1 w - - 0 1
A structure with an apex pawn, of course, the structure is valuable as it is, but also only a sinle move would lead to its falling apart, while 2 other possible moves would lead to the formation of a flexible structure.
[d]6k1/8/8/8/3PP3/2P5/8/6K1 w - - 0 1
2 pawns on a more advanced rank, and one on less advanced rank, the structure is flexible, because 2 of the possible moves would lead to the formation of either a chain, or another structure that is flexible (good, valuable).
Inflexible pawn structures:
[d]6k1/8/8/8/2P1P3/3P4/8/6K1 w - - 0 1
A structure with one root/base pawn. Of course, root/base pawns are bad, because vulnerable, and due some small penalty (maybe 5cps), and moreover, by 2 possible moves the group would fall apart.
[d]6k1/8/8/8/4P3/2PP4/8/6K1 w - - 0 1
2 pawns on a less advanced rank, with one pawn on a more advanced rank. The structure is inflexible, because by 2 possible moves it will either fall apart, or lead to the formation of a group with a root pawn (inflexible one).
[d]6k1/8/8/4P3/3P4/2P5/8/6K1 w - - 0 1
A chain of 3 pawns along the same diagonal. Of course, the chain would be due some nice bonus, as it thwarts the activity of the enemy pieces and is sound. That left aside, the structure ir obviously inflexible, as 2 of the possible moves would lead to its falling apart, while the third one to a structure that is inflexible.
I am not sure if inflexible pawn structures should be penalised, as with them there are usually other bonus or penalty points to be dispensed. But, definitely, flexible pawn structures should be incentivised in some way. I think 5-10-15 cps might be a good assessment of the value and potential usefulness of such structures.
Well, this was my brief outline. I think it was not very clear, it is not to me, and some issues with definitions might still stand out. However, I have no doubts at all concerning the added value of the above-mentioned flexible structures: they really mean something in the game, something tangible and useful, not to be easily discarded.
Best, Lyudmil
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Don
- Posts: 5106
- Joined: Tue Apr 29, 2008 4:27 pm
Re: X-rayed
Komodo has a couple of evaluation features that are based on tactical potential and less positional. So it's possible something could be done here.Lyudmil Tsvetkov wrote:I think x-ray attacks of linear/sliding pieces are very important, especially in tactically rich positions. For me, having an x-ray term in the eval would definitely provide added value to proper position understanding.
I think scoring of x-ray attacks could be very simple.
A problem in evaluation is what I'll call "relevance" which is important in evaluation functions. Relevance can be illustrated by the Rook to the 7th rule - there are cases when it's a meaningless rules, such as when the king is in the middle of the board and there are no pawns to attack on the 7th rank.
In this case, if a bishop attacks a rook through a pawn, and the pawn is part of a ram, it's not very relevant. There are many features that determine how relevant a given "potential" threat might be eventually. I think it might have a small positive effect if it can be calculated cheaply enough but these kinds of features seem to help really fast time controls a lot more and have little impact on long time controls. But it's worth taking a look.
[d]1r3rk1/2p2p1p/4p1p1/Rp1b4/8/1P4BP/1qP1QPP1/5RK1 w - - 0 1
For example, in the above diagram, several pieces x-ray attack enemy objects. When there is only one own or enemy object (pawn or piece) in between the attacker and the attacked piece, we could say that this is an x-ray attack once removed. An x-ray attack once removed might score 1/2 of the value for a direct attack, i.e., if the Bg3 attacking Rb8 in a direct attack would score some 9cps (1/50 the value of the attacked piece or whatever), now it should score some 4.5cps because of the c7 pawn. Other x-ray attacks once removed in the position are Rf1 attacking pf7, Rf8 attacking pf2, Ra5 attacking Bd5, Rb8 attacking pb3, Qb2 attacking Qe2 and Qe2 attacking Qb2.
In the case of the last attack one might wonder if it makes sense to consider x-ray attacks once removed of pieces of same power and capacity, but the problem could be resolved by taking into account if the object in between is own or enemy one. As having an enemy object in between is usually more propicious for the attacker, such an arrangement might score 20% higher. Thus, Qb2 will score 20% higher for attacking Qe2 on an x-ray.
X-ray attacks twice removed would be x-ray attacks with 2 own or enemy objects in between the attacker and the attacked object. Such attacks might score 1/4 of the usual value for a direct attack, so that if Qb2 attacking directly pf2 would score some 2cps, Qb2 on a twice removed x-ray attack against pf2 as in the actual position would score 0.5cps.
Of course, the most important x-ray attacks are those that are once removed, and I think they should be an obligatory element of a good program.
X-ray attacking the enemy king, as well as x-ray attacking squares of the enemy king shelter, are also very important, at least the attacks once removed, but also, in the case of attacking the king, the x-ray attacks removed more times.
[d]6k1/R4p1p/3pp1p1/4n3/8/1B4Q1/1B6/6K1 w - - 0 1
Looking at the above position, we have a couple of x-ray attacks upon the black king: Qg3 on a once removed attack against Kg8, Bb3 on a twice removed attack against Kg8. Once removed attack upon the king might score twice the value for a once removed attack upon the queen, while twice removed attack upon the king twice the value for a twice removed attack upon the enemy queen. (king considered 2 times more valuable than the queen)
In the same diagram, we have also a couple of x-ray attacks upon the enemy king shelter: Ra7 attacking g7 and h7 on a once removed x-ray, Bb2 attacking f6,g7 and h8 on a once removed x-ray. Values for such attacks might be 1/2 the usual values for directly attacking squares of the king shelter.
Very crazy indeed, but I think it makes some sense.
Any comments very much appreciated.
Best, Lyudmil
Capital punishment would be more effective as a preventive measure if it were administered prior to the crime.
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Lyudmil Tsvetkov
- Posts: 6052
- Joined: Tue Jun 12, 2012 12:41 pm
Re: X-rayed
Hi Don.
Thanks for checking.
It is a feature of the position. It might be of a temporary nature, but I do not believe it disappears altogether; rather, in the course of the game it transposes into other eval terms in a logical way, or other eval terms (including positional and long range) transpose into it.
Thanks for checking.
It is a feature of the position. It might be of a temporary nature, but I do not believe it disappears altogether; rather, in the course of the game it transposes into other eval terms in a logical way, or other eval terms (including positional and long range) transpose into it.
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carldaman
- Posts: 2283
- Joined: Sat Jun 02, 2012 2:13 am
Re: Flexible pawn structures
Mobile/fluid/dynamic structures, whether they involve connected passers or pawn storms, are essential positional elements. I believe some of the biggest eval improvements in recent years have been in the area of handling passed pawns. Years ago, many engines had problems in advancing their mobile pawn masses, including passed pawns, which contributed to their overall endgame weakness.
However, *how* pawns are advanced is still extremely important. One weakness I see over an over among top engines is releasing the tension in the position too soon, sometimes immediately. All too often, promising flank attacks peter out into lifeless static pawn blockages. We see too many 'rams', and few 'levers' (terms from Hans Kmoch's Pawn Power in Chess -- a must-read for all, by the way). Overall, the engines' concepts of 'tension' and 'pawn breaks' need to be worked on.
In your diagrams, both the pawn chain and the apex formation could be subject to piece blockade, if opposing pieces are present, so care must be exercised as to how the pawns are advanced. I think top engines can handle piece blockade acceptably, since this implies a more open board, but locked-up pawn chains that close up the board, especially the center, are the biggest issue, since even the top engines struggle to plan ahead in closed positions. Progress in this area has been painfully slow.
Regards,
CL
However, *how* pawns are advanced is still extremely important. One weakness I see over an over among top engines is releasing the tension in the position too soon, sometimes immediately. All too often, promising flank attacks peter out into lifeless static pawn blockages. We see too many 'rams', and few 'levers' (terms from Hans Kmoch's Pawn Power in Chess -- a must-read for all, by the way). Overall, the engines' concepts of 'tension' and 'pawn breaks' need to be worked on.
In your diagrams, both the pawn chain and the apex formation could be subject to piece blockade, if opposing pieces are present, so care must be exercised as to how the pawns are advanced. I think top engines can handle piece blockade acceptably, since this implies a more open board, but locked-up pawn chains that close up the board, especially the center, are the biggest issue, since even the top engines struggle to plan ahead in closed positions. Progress in this area has been painfully slow.
Regards,
CL
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Lyudmil Tsvetkov
- Posts: 6052
- Joined: Tue Jun 12, 2012 12:41 pm
Complement!
I think complementary control of squares is one of the most important elements of chess, which, for some reason, is underestimated even by today's most advanced engines.
For me, there are a couple of manifestations of complementarity, which could be very useful, if properly applied, because they represent a real added value to existing eval terms.
Colour complementarity
Colour complementarity does indeed matter. I think it makes sense to establish the ratio of control of black and white squares for each side. (how many white and how many black squares do the pawns and pieces of one of the sides control) The closer the ratio to a perfect 50/50 split is, the better, as in this way the spread of control will be more optimal. Here you might introduce intervals. For example, in the interval from 50/50 to 60/40 split you assign some nice bonus (10-15cps), with no bonus outside this interval, and even a penalty when the split passes the boundary of 80/20.
[d]8/2n5/1p1p1pk1/1P1P2p1/2B1P1P1/5P2/5K2/8 w - - 0 1
Let us look at the above diagram. Why is black able to draw, when white is a full pawn up and has a bishop for a knight with play on both sides? Very simple (leaving aside fortress considerations, which are still largely based on complementarity): the ratio of control of black and white squares is very good for black, while very bad for black, which adds further points for black. Let's count what is the ratio of control for black and white (but kings might be left aside from considering this). The black pawns control 6 black squares (controlling would be counted with control of free squares, as well as squares occupied by own and enemy pawns and pieces): h4,f4, g5, e5,c5,a5, while the black knight also controls 6 white squares: a8,e8,a6,c6,b5,d5 - that is a perfect split, and some very nice bonus might be dispensed.
The ratio for white is disastrous. The white pawns control 8 white squares: a6,c6,e6,d5,f5,h5,e4,g4, while the white bishop another 6: b5,d3,e2,f1,b3,a2. So overall the white army controls 14 white squares and none black - that is a disastrous ratio, due a very big penalty.
General control of complementary squares
General control of complementary squares could be defined as an optimal spread of control of squares across the board. For the purpose all squares controlled by a single piece or pawn will get 3cps bonus, squares controlled by 2 own pawns or pieces will get 2cps bonus, and squares controlled by 3 own pawns or pieces will get just 1cp bonus. Thus it would be better for a square to be controlled by as few pieces and pawns as possible.
[d]k7/3nb3/3p4/P3p1p1/1N2P3/3PB3/6K1/8 w - - 0 1
Looking at the above diagram: white is much better in terms of general control of complementary squares (it is not important how the game could end, this is just an illustration). Let us count. Only 2 squares on the board are controlled by 2 white pawns and pieces: b6 and d5 (4cps), the knight controls 5 squares that no other pawn or piece controls: a6,c6,a2,c2,d3, while the bishop another 9 that no other pawn or piece controls: d4,c5,a7,f2,g1,f4,g5,d2,c1. We have also 2 white pawns controlling such squares: e4 and f5. Thus the total for squares controlled only once becomes 3x16=48. Overall we have 52cps bonus for the white complementarity control.
For black we have only 6 squares controlled only once: b8,b6,d8,g5, d4,h4 (but h4 is also controlled on an x-ray by the bishop, so it depends, maybe x-ray control should be skipped here not to complicate things), and 5 squares controlled 2 times: c5,e5,f6,f8,f4. The total bonus would make 6x3 + 5x2 = 28cps. Thus, white is better in terms of complementary control of squares here by some 24cps. (a value not to easily neglect)
The conclusion is that white is much better here precisely because of complementarity.
Complementarity in terms of piece configurations
People call it imbalances, and I somehow distorted it to complementarity in terms of piece configurations.
But the basic idea is the same: an ensemble of different pieces might control the board in a better way precisely because different pieces might complement each other better.
Not to go into complications, I think the basic principle might be that each existing type of piece on the board would get a bonus (say 15-20cps). Simplistically, types could be defined as linear pieces (rooks and queen), diagonal pieces (bishops and queen) and a knight piece. Repetitions might also be introduced, as well as a pair of bishops type, but simplistically you could even skip that.
So, in general, the more types of pieces you have, the better.
[d]1r4r1/3k4/8/5N2/3B4/4N3/4K3/8 w - - 0 1
White is better here in terms of complementarity, it has 2 types of pieces - a diagonal piece and a knight piece, while black has only 1 type of piece - a linear piece. (+20cps for white)
[d]4q1k1/3b4/8/8/3Q4/4N3/8/6K1 w - - 0 1
A knight and queen complement each other better than a bishop and queen, controlling wider accessible range of squares. In the knight and queen you have 3 piece types: a linear and diagonal in the queen, and a knight type; in the bishop and queen you just have 2 piece types: a linear and a diagonal one. (+15cps for white simplistically)
[d]4q1k1/8/8/8/5N2/3B4/6N1/6K1 w - - 0 1
Equal in terms of complementarity, white has 2 piece types: diagonal and a knight, while black also has 2 piece types in the queen: linear and diagonal. (actually white is even worse, because the knight as a piece type repeats itself once for white with no repetitions of piece types for black; a repetition of types might subtract some 7cps)
[d]2r1q1k1/8/8/8/5N2/3B4/6N1/1R4K1 w - - 0 1
You simply add a rook each side, and things change considerably. Here white is already visibly better. White has 3 piece types: a linear, diagonal and a knight, while black remains with 2: linear and diagonal. Repetitions also do not favour black here, as the additional black rook already repeats the linear type in the queen. (+20cps for white)
For me, there are a couple of manifestations of complementarity, which could be very useful, if properly applied, because they represent a real added value to existing eval terms.
Colour complementarity
Colour complementarity does indeed matter. I think it makes sense to establish the ratio of control of black and white squares for each side. (how many white and how many black squares do the pawns and pieces of one of the sides control) The closer the ratio to a perfect 50/50 split is, the better, as in this way the spread of control will be more optimal. Here you might introduce intervals. For example, in the interval from 50/50 to 60/40 split you assign some nice bonus (10-15cps), with no bonus outside this interval, and even a penalty when the split passes the boundary of 80/20.
[d]8/2n5/1p1p1pk1/1P1P2p1/2B1P1P1/5P2/5K2/8 w - - 0 1
Let us look at the above diagram. Why is black able to draw, when white is a full pawn up and has a bishop for a knight with play on both sides? Very simple (leaving aside fortress considerations, which are still largely based on complementarity): the ratio of control of black and white squares is very good for black, while very bad for black, which adds further points for black. Let's count what is the ratio of control for black and white (but kings might be left aside from considering this). The black pawns control 6 black squares (controlling would be counted with control of free squares, as well as squares occupied by own and enemy pawns and pieces): h4,f4, g5, e5,c5,a5, while the black knight also controls 6 white squares: a8,e8,a6,c6,b5,d5 - that is a perfect split, and some very nice bonus might be dispensed.
The ratio for white is disastrous. The white pawns control 8 white squares: a6,c6,e6,d5,f5,h5,e4,g4, while the white bishop another 6: b5,d3,e2,f1,b3,a2. So overall the white army controls 14 white squares and none black - that is a disastrous ratio, due a very big penalty.
General control of complementary squares
General control of complementary squares could be defined as an optimal spread of control of squares across the board. For the purpose all squares controlled by a single piece or pawn will get 3cps bonus, squares controlled by 2 own pawns or pieces will get 2cps bonus, and squares controlled by 3 own pawns or pieces will get just 1cp bonus. Thus it would be better for a square to be controlled by as few pieces and pawns as possible.
[d]k7/3nb3/3p4/P3p1p1/1N2P3/3PB3/6K1/8 w - - 0 1
Looking at the above diagram: white is much better in terms of general control of complementary squares (it is not important how the game could end, this is just an illustration). Let us count. Only 2 squares on the board are controlled by 2 white pawns and pieces: b6 and d5 (4cps), the knight controls 5 squares that no other pawn or piece controls: a6,c6,a2,c2,d3, while the bishop another 9 that no other pawn or piece controls: d4,c5,a7,f2,g1,f4,g5,d2,c1. We have also 2 white pawns controlling such squares: e4 and f5. Thus the total for squares controlled only once becomes 3x16=48. Overall we have 52cps bonus for the white complementarity control.
For black we have only 6 squares controlled only once: b8,b6,d8,g5, d4,h4 (but h4 is also controlled on an x-ray by the bishop, so it depends, maybe x-ray control should be skipped here not to complicate things), and 5 squares controlled 2 times: c5,e5,f6,f8,f4. The total bonus would make 6x3 + 5x2 = 28cps. Thus, white is better in terms of complementary control of squares here by some 24cps. (a value not to easily neglect)
The conclusion is that white is much better here precisely because of complementarity.
Complementarity in terms of piece configurations
People call it imbalances, and I somehow distorted it to complementarity in terms of piece configurations.
But the basic idea is the same: an ensemble of different pieces might control the board in a better way precisely because different pieces might complement each other better.
Not to go into complications, I think the basic principle might be that each existing type of piece on the board would get a bonus (say 15-20cps). Simplistically, types could be defined as linear pieces (rooks and queen), diagonal pieces (bishops and queen) and a knight piece. Repetitions might also be introduced, as well as a pair of bishops type, but simplistically you could even skip that.
So, in general, the more types of pieces you have, the better.
[d]1r4r1/3k4/8/5N2/3B4/4N3/4K3/8 w - - 0 1
White is better here in terms of complementarity, it has 2 types of pieces - a diagonal piece and a knight piece, while black has only 1 type of piece - a linear piece. (+20cps for white)
[d]4q1k1/3b4/8/8/3Q4/4N3/8/6K1 w - - 0 1
A knight and queen complement each other better than a bishop and queen, controlling wider accessible range of squares. In the knight and queen you have 3 piece types: a linear and diagonal in the queen, and a knight type; in the bishop and queen you just have 2 piece types: a linear and a diagonal one. (+15cps for white simplistically)
[d]4q1k1/8/8/8/5N2/3B4/6N1/6K1 w - - 0 1
Equal in terms of complementarity, white has 2 piece types: diagonal and a knight, while black also has 2 piece types in the queen: linear and diagonal. (actually white is even worse, because the knight as a piece type repeats itself once for white with no repetitions of piece types for black; a repetition of types might subtract some 7cps)
[d]2r1q1k1/8/8/8/5N2/3B4/6N1/1R4K1 w - - 0 1
You simply add a rook each side, and things change considerably. Here white is already visibly better. White has 3 piece types: a linear, diagonal and a knight, while black remains with 2: linear and diagonal. Repetitions also do not favour black here, as the additional black rook already repeats the linear type in the queen. (+20cps for white)
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Lyudmil Tsvetkov
- Posts: 6052
- Joined: Tue Jun 12, 2012 12:41 pm
Intensity of interaction
Intensity of interaction is another eval term that might not be very popular.
Intensity of interaction could be defined as 2 or more own pieces controlling one and the same square. Often this is important because it enables the side with a good interaction potential to have access to squares that would otherwise be inaccessible, and sometimes such squares might be very meaningful. I think with intensity of interaction squares that are controlled by an enemy pawn or a piece of lower power than both of the interacting pieces should not be included into the computation.
Basically, each square controlled by 2 or more own pieces might get a bonus equal to 1/100 the sum of the values of the controlling pieces. For example, a bishop and a knight controlling certain square would score some 6cps, a bishop and a rook some 7.5cps, a queen and a rook some 13.5cps, etc. A square controlled by a knight, bishop and a rook simultaneously would score some 10.5cps.
[d]6k1/5p2/pn2bqp1/1r3p2/8/P3QN1P/5PP1/3RB1K1 b - - 0 1
For example, on the above position, black has a very good intensity of interaction potential for the squares b3, d5 and c4, while white has an excellent interaction square in the face of d4. Which side will have the advantage here is not so important, but there are positions where this term will definitely make some difference.
Intensity of interaction is extremely important especially in endgames with arising imbalances, where often the potential for the side with the bigger number of pieces of lower power will be a decisive factor in determining the outcome of the game. In such situations the relevant term values might be increased 3 to 5 times to reflect its realistic weight.
[d]8/3n2k1/5n2/1P6/2Pb4/1Q6/6K1/8 w - - 0 1
I think I already posted a similar position. It is precisely the interaction potential of black (the mutual control of the squares c5 and b6 by the bishop and the knight) that makes it possible for the game to end in a draw. The white passers can not advance, so they are pretty much meaningless. Thus, in such constellations it is always recommended to have an abundant control of the squares in front of the enemy passers. Such squares might further increase the bonus points for the term.
[d]8/6k1/2r1r3/8/P5P1/3Q4/6K1/8 w - - 0 1
Again, I do not know how many engines will recognize this instantly, but this is a draw. The white king can not penetrate behind the 6th rank to try to support the queen in mating the enemy king, while both white separate passers can not advance past the 5th rank, as squares in front of the passers are firmly controlled by the black rooks (a6 and g6). In this case intensity of interaction takes the form of control and x-ray control of the squares in front of the passers (a6 and g6 are stop squares). In this specific case x-ray control is really important to properly understand the position; also suggesting that the general notion of x-ray is not devoid of some genuine interest.
Intersections of pawns and pieces are a variety of the interaction term with some relevance. Intersections of pawns and pieces might be scored in the same way, 1/100 the sum of the pawn and the piece values, some 4cps in the case of an intersection of a pawn and bishop or knight, 5.5 cps in the case of an intersection of pawn and rook, etc. But only intersections of pawns and minors on squares into the enemy camp might be counted, as those could be potential outposts, as well as intersections of pawns and rooks on open files, where they could be useful in determining which side will prevail in the struggle for controlling the file.
[d]6k1/6b1/8/8/1p3n2/7p/8/6K1 b - - 0 1
c3 and g2 are important intersection squares for black
[d]1r1r4/5k1p/3p2p1/p1pP1p2/P4P2/2P3P1/5K1P/1R2R3 w - - 0 1
The position outwardly looks completely even, but that is not so. The difference is made by the b5 intersection square on the b open file (I think here the value might be even double the usual), where the white rook can land with some effect, while at the same time black does not have at its disposal such a square, as b4 is controlled by c3. Thus, after 1.Rb5 white can expect to gain control of the open file and even hope for a win (exchaning the rooks will create a probably dangerous protected passer). Beside that, white has another good landing square enabled by interaction - e6.
Best, Lyudmil
PS. I forgot to tell you, but of course, any comments very much appreciated.
Intensity of interaction could be defined as 2 or more own pieces controlling one and the same square. Often this is important because it enables the side with a good interaction potential to have access to squares that would otherwise be inaccessible, and sometimes such squares might be very meaningful. I think with intensity of interaction squares that are controlled by an enemy pawn or a piece of lower power than both of the interacting pieces should not be included into the computation.
Basically, each square controlled by 2 or more own pieces might get a bonus equal to 1/100 the sum of the values of the controlling pieces. For example, a bishop and a knight controlling certain square would score some 6cps, a bishop and a rook some 7.5cps, a queen and a rook some 13.5cps, etc. A square controlled by a knight, bishop and a rook simultaneously would score some 10.5cps.
[d]6k1/5p2/pn2bqp1/1r3p2/8/P3QN1P/5PP1/3RB1K1 b - - 0 1
For example, on the above position, black has a very good intensity of interaction potential for the squares b3, d5 and c4, while white has an excellent interaction square in the face of d4. Which side will have the advantage here is not so important, but there are positions where this term will definitely make some difference.
Intensity of interaction is extremely important especially in endgames with arising imbalances, where often the potential for the side with the bigger number of pieces of lower power will be a decisive factor in determining the outcome of the game. In such situations the relevant term values might be increased 3 to 5 times to reflect its realistic weight.
[d]8/3n2k1/5n2/1P6/2Pb4/1Q6/6K1/8 w - - 0 1
I think I already posted a similar position. It is precisely the interaction potential of black (the mutual control of the squares c5 and b6 by the bishop and the knight) that makes it possible for the game to end in a draw. The white passers can not advance, so they are pretty much meaningless. Thus, in such constellations it is always recommended to have an abundant control of the squares in front of the enemy passers. Such squares might further increase the bonus points for the term.
[d]8/6k1/2r1r3/8/P5P1/3Q4/6K1/8 w - - 0 1
Again, I do not know how many engines will recognize this instantly, but this is a draw. The white king can not penetrate behind the 6th rank to try to support the queen in mating the enemy king, while both white separate passers can not advance past the 5th rank, as squares in front of the passers are firmly controlled by the black rooks (a6 and g6). In this case intensity of interaction takes the form of control and x-ray control of the squares in front of the passers (a6 and g6 are stop squares). In this specific case x-ray control is really important to properly understand the position; also suggesting that the general notion of x-ray is not devoid of some genuine interest.
Intersections of pawns and pieces are a variety of the interaction term with some relevance. Intersections of pawns and pieces might be scored in the same way, 1/100 the sum of the pawn and the piece values, some 4cps in the case of an intersection of a pawn and bishop or knight, 5.5 cps in the case of an intersection of pawn and rook, etc. But only intersections of pawns and minors on squares into the enemy camp might be counted, as those could be potential outposts, as well as intersections of pawns and rooks on open files, where they could be useful in determining which side will prevail in the struggle for controlling the file.
[d]6k1/6b1/8/8/1p3n2/7p/8/6K1 b - - 0 1
c3 and g2 are important intersection squares for black
[d]1r1r4/5k1p/3p2p1/p1pP1p2/P4P2/2P3P1/5K1P/1R2R3 w - - 0 1
The position outwardly looks completely even, but that is not so. The difference is made by the b5 intersection square on the b open file (I think here the value might be even double the usual), where the white rook can land with some effect, while at the same time black does not have at its disposal such a square, as b4 is controlled by c3. Thus, after 1.Rb5 white can expect to gain control of the open file and even hope for a win (exchaning the rooks will create a probably dangerous protected passer). Beside that, white has another good landing square enabled by interaction - e6.
Best, Lyudmil
PS. I forgot to tell you, but of course, any comments very much appreciated.
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Lyudmil Tsvetkov
- Posts: 6052
- Joined: Tue Jun 12, 2012 12:41 pm
Re: Flexible pawn structures
Thanks, Carl, for keeping the discussion alive again.carldaman wrote:Mobile/fluid/dynamic structures, whether they involve connected passers or pawn storms, are essential positional elements. I believe some of the biggest eval improvements in recent years have been in the area of handling passed pawns. Years ago, many engines had problems in advancing their mobile pawn masses, including passed pawns, which contributed to their overall endgame weakness.
However, *how* pawns are advanced is still extremely important. One weakness I see over an over among top engines is releasing the tension in the position too soon, sometimes immediately. All too often, promising flank attacks peter out into lifeless static pawn blockages. We see too many 'rams', and few 'levers' (terms from Hans Kmoch's Pawn Power in Chess -- a must-read for all, by the way). Overall, the engines' concepts of 'tension' and 'pawn breaks' need to be worked on.
In your diagrams, both the pawn chain and the apex formation could be subject to piece blockade, if opposing pieces are present, so care must be exercised as to how the pawns are advanced. I think top engines can handle piece blockade acceptably, since this implies a more open board, but locked-up pawn chains that close up the board, especially the center, are the biggest issue, since even the top engines struggle to plan ahead in closed positions. Progress in this area has been painfully slow.
Regards,
CL
Yeah, humans are stronger where there is nothing to see, and engines where there are many things to see
That is right, in order to be correct, you must specify, and specify, and specify... My suggestion was just a brief outline. However, it makes sense to:
- assign 1/2 bonus points where some of the pawns of such a structure is part of the king shelter, or even leave those aside; the logic is evident, you should exercise restraint with pawn shelter
- assign 2/3 bonus when one of the pawns of the structure is blocked (fixed/rammed/locked, whatever) - in the cases where this is possible
- assign 1/3 bonus when 2 of the pawns of the structure are blocked (where relevant), etc.
But even then you will have to check and recheck, specify further, etc., not to mention making workable a whole set of terms. The good thing for whole sets is, as I understand it, that you could be able to find the right decision by combining 2 wrong ones, and that is what makes possible all those tuning experiments with an enormous amount of parameters. What matters is the end value, but it is more probable to have a more precise end value by tuning a larger set of terms than a smaller ones. That is why, in my understanding, multitude of terms (even better quality ones) is important.
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Lyudmil Tsvetkov
- Posts: 6052
- Joined: Tue Jun 12, 2012 12:41 pm
Re: Flexible pawn structures
And something else, concerning evaluation bugs.
[d]6k1/8/8/8/3PP3/2P2P2/8/6K1 w - - 0 1
Suppose that a structure with 2 pawns that are more advanced and one less advanced really deserves a bonus for flexibility. Then, on the above diagram, how many bonus points would you dispense, as there seem to be 2 such structures: c3-d4-e4, and f3-e4-d4? Would you dispense 2, or probably just one, under an additional rule that none of the pawns of such a structure should duplicate another flexible structure? The end result would be different in both cases, you might be imprecise and end up introducing an eval bug. So a seemingly good idea might end up nowhere, while a really stupid idea work because of a 'beneficial' bug that would straighten things up.
Or even worse, supposing 3 adjacent pawns on the same rank are really due some flexibility bonus (which might be questionable), should you dispense a whole lot of bonus points for the multitude of horizontally adjacent pawns in the initial position? Quite probably you should leave aside this case when the pawns are on the second rank. But you need to specify and define correctly, otherwise an eval bug is introduced for sure. And this time it will be a nasty one.
That is why many good evaluation ideas end up nowhere.
[d]6k1/8/8/8/3PP3/2P2P2/8/6K1 w - - 0 1
Suppose that a structure with 2 pawns that are more advanced and one less advanced really deserves a bonus for flexibility. Then, on the above diagram, how many bonus points would you dispense, as there seem to be 2 such structures: c3-d4-e4, and f3-e4-d4? Would you dispense 2, or probably just one, under an additional rule that none of the pawns of such a structure should duplicate another flexible structure? The end result would be different in both cases, you might be imprecise and end up introducing an eval bug. So a seemingly good idea might end up nowhere, while a really stupid idea work because of a 'beneficial' bug that would straighten things up.
Or even worse, supposing 3 adjacent pawns on the same rank are really due some flexibility bonus (which might be questionable), should you dispense a whole lot of bonus points for the multitude of horizontally adjacent pawns in the initial position? Quite probably you should leave aside this case when the pawns are on the second rank. But you need to specify and define correctly, otherwise an eval bug is introduced for sure. And this time it will be a nasty one.
That is why many good evaluation ideas end up nowhere.