What is a spearhead passer?
Obviously, a passer that is a spearhead of a long chain at the same time.
However, it does not make sense to consider all such passers, as passers and spearheads/inner chain pawns would already get their bonus in eval separately.
There is one special case that is very much worth considering and that will bring added value - this is when both of the own pawns following the passer spearhead in the chain behind are blocked by enemy pawns, i.e. the inner pawn defending the spearhead, as well as the next own pawn defending this inner pawn are blocked.
As this is the only reasonable way to give bonus to spearhead passers additionally, I will refer to it simply as bonus for spearhead passers.
[d]6k1/8/8/1Pp4p/2Pp2pP/3P1pP1/8/6K1 w - - 0 1
b5 and f3 are passer spearheads
in the case of b5, it is a spearhead of a long chain, the inner pawn defending b5, c4, is blocked, and the pawn defending this inner pawn, d3, is also blocked
in the case of f3, it is a spearhead of a long chain, the inner pawn defending it, g4, is blocked, and the pawn defending this inner pawn, h5, is also blocked
b5 is a spearhead passer on the 5th rank, while f3 is a spearhead passer on its 6th rank.
All spearhead passers deserve some nice bonus, maybe some 20cps additionally.
The condition that the 2 other own pawns following the spearhead passer in the long chain are blocked is absolutely necessary - this is what makes this particular passer especially strong, as in this case it is much more difficult to attack and destroy any of the pawns of the long chain, as they are blocked and less accessible, the enemy pawns blocking them provide them kind of shelter.
Spearhead passers happen on ranks 4 through 7, but it does not quite make sense to score such passers on the 4th rank, so you might just give the bonus for all spearhead passers on ranks 5,6 and 7.
Spearhead passers bonus might help engines see some piece sacrifices to create an advanced spearhead passer.
Maybe some remember the Carlsen spearhead passer on b3 from the Anand-Carlsen game.
I think this is a very true and very useful chess rule, but I have absolutely no clue if this would work in engines, as the associated lines are usually very deep, and engines mostly like seeing shallow to medium-deep lines.
Assorted tweaks
Moderator: Ras
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Lyudmil Tsvetkov
- Posts: 6052
- Joined: Tue Jun 12, 2012 12:41 pm
Spearhead levers
What is a spearhead lever?
Obviously, a spearhead of a long chain that is a lever at the same time, i.e. attacking an enemy pawn.
It is not good to be a spearhead and a lever at the same time, as this menaces destruction of the nice asset that is the spearhead. So spearhead levers, wherever found, are due some small penalty, maybe 5-7cps; or, you could give the bonus for the opponent pawn attacking the spearhead with a lever. The bonus is small, as this is very much tactically related, and besides ranks are not specified.
Spearhead levers are valid for all ranks, where found.
[d]8/1p6/2pp3p/3P2p1/2P2p2/1P3PP1/P6P/8 w - - 0 1
d5 is a spearhead lever for white, due some penalty; same is true for f4, due some penalty as a spearhead lever for black. Or, you could give the bonus to the respective attacking pawns, c6 and g3.
As you easily see above, when a spearhead is attacked, chances are it could be destroyed and the long chain in its present form perish with it.
Some might say, who needs that many terms, and that many feature combinations? It is not true, this is like bitboards, you create a bitboard to facilitate your work, and the same is true of eval features - specific eval features facilitate your work and make possible a wide range of combinations from which to choose and assess in testing.
Obviously, a spearhead of a long chain that is a lever at the same time, i.e. attacking an enemy pawn.
It is not good to be a spearhead and a lever at the same time, as this menaces destruction of the nice asset that is the spearhead. So spearhead levers, wherever found, are due some small penalty, maybe 5-7cps; or, you could give the bonus for the opponent pawn attacking the spearhead with a lever. The bonus is small, as this is very much tactically related, and besides ranks are not specified.
Spearhead levers are valid for all ranks, where found.
[d]8/1p6/2pp3p/3P2p1/2P2p2/1P3PP1/P6P/8 w - - 0 1
d5 is a spearhead lever for white, due some penalty; same is true for f4, due some penalty as a spearhead lever for black. Or, you could give the bonus to the respective attacking pawns, c6 and g3.
As you easily see above, when a spearhead is attacked, chances are it could be destroyed and the long chain in its present form perish with it.
Some might say, who needs that many terms, and that many feature combinations? It is not true, this is like bitboards, you create a bitboard to facilitate your work, and the same is true of eval features - specific eval features facilitate your work and make possible a wide range of combinations from which to choose and assess in testing.
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Lyudmil Tsvetkov
- Posts: 6052
- Joined: Tue Jun 12, 2012 12:41 pm
Spearhead backwardmakers
What is a backwardmaker?
The pawn that makes the enemy pawn backward, obviously.
So, technically, a backwardmaker would be the pawn that blocks the enemy pawn, defended by the backward pawn.
[d]8/1p6/2p5/2P5/3P4/4P3/8/8 w - - 0 1
above, c5 is a backwardmaker, it makes the enemy b7 pawn backward, by blocking the pawn, c6, that the enemy backward pawn defends.
However, c5 is also a special kind of backwardmaker - it is a sperhead of a long chain.
All spearhead backwardmakers deserve a small overbonus, maybe some 5cps.
The bonus is due for the fact, that the backward pawn is made weak not only by the spearhead itself, but by the whole long chain, as it very much resticts the access of enemy pieces to help with defending/unbackwarding the backward pawn.
Such funny concepts, but some of them might really work.
The pawn that makes the enemy pawn backward, obviously.
So, technically, a backwardmaker would be the pawn that blocks the enemy pawn, defended by the backward pawn.
[d]8/1p6/2p5/2P5/3P4/4P3/8/8 w - - 0 1
above, c5 is a backwardmaker, it makes the enemy b7 pawn backward, by blocking the pawn, c6, that the enemy backward pawn defends.
However, c5 is also a special kind of backwardmaker - it is a sperhead of a long chain.
All spearhead backwardmakers deserve a small overbonus, maybe some 5cps.
The bonus is due for the fact, that the backward pawn is made weak not only by the spearhead itself, but by the whole long chain, as it very much resticts the access of enemy pieces to help with defending/unbackwarding the backward pawn.
Such funny concepts, but some of them might really work.
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Lyudmil Tsvetkov
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- Joined: Tue Jun 12, 2012 12:41 pm
Re: Blocked spearheads
Hi Carl.
You are the proud author of the spearhead name, unless it has been known before you came up with it.
My situation is not cheerful at all - I am confined to this thread, maybe for the rest of my life, and no one knows if I will be able to open another thread on this forum.
It is nice to get some visits from time to time, although I am afraid they will be getting rarer and rarer.
Concerning pointed chains, man, Pawel got 2 or 3 elo from pointed chains, but you can get 50 elo from that, certainly you can, unfortunately, even if engines have this in their eval, first, you have to tune it very well, and second, as the associated lines are very deep, and not simply deep, and engines see only shallow to medium-depth lines, chances are we will have to wait for successful full scale pointed chain implementation until top engines improve significantly more their search and eval from the stage where they are now - and this might take years.
Engines score and play attacks well, as they are shallow, but when it comes to deep terms, serious difficulties arise.
This is true not only of pointed chains, but of many other eval terms.
You are the proud author of the spearhead name, unless it has been known before you came up with it.
My situation is not cheerful at all - I am confined to this thread, maybe for the rest of my life, and no one knows if I will be able to open another thread on this forum.
It is nice to get some visits from time to time, although I am afraid they will be getting rarer and rarer.
Concerning pointed chains, man, Pawel got 2 or 3 elo from pointed chains, but you can get 50 elo from that, certainly you can, unfortunately, even if engines have this in their eval, first, you have to tune it very well, and second, as the associated lines are very deep, and not simply deep, and engines see only shallow to medium-depth lines, chances are we will have to wait for successful full scale pointed chain implementation until top engines improve significantly more their search and eval from the stage where they are now - and this might take years.
Engines score and play attacks well, as they are shallow, but when it comes to deep terms, serious difficulties arise.
This is true not only of pointed chains, but of many other eval terms.
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Lyudmil Tsvetkov
- Posts: 6052
- Joined: Tue Jun 12, 2012 12:41 pm
Backwardfated storming pawns
Backwardfated storming pawns are always due some decent penalty, maybe 15cps or so, for the obvious fact that the existence of such a pawn in its quality of a storming pawn means that attacking with this pawn is close to impossible. Bearing in mind that the presence of such a pawn also indicates the presence of another own blocked storming pawn, quite frequently the entire attack will stall with such a backwardfated storming pawn.
It makes sense to evaluate such backwardfated storming pawns just on ranks 4 and 5, as on less advanced ranks they are not meaningful.
[d]6k1/6p1/5p1p/7P/4P1P1/8/8/6K1 w - - 0 1
g4 backwardfated storming pawn above
As you see, playing g4-g5 is close to impossible, and thus the entire white attack has stalled. Please note, that this is not equivalent in most cases to both sides having one backwardfated pawn each, which would be tantamount to scoring all storming pawns blocked. For example above, white does not have at all a pawn on the f file.
[d]6k1/5p1p/5P1P/6P1/8/8/8/6K1 w - - 0 1
g5 backwardfated storming pawn - the white attack has stalled again as a whole
[d]6k1/7p/4p1p1/4P1P1/5P2/8/8/6K1 w - - 0 1
f4 backwardfated storming pawn
This is closely related to king safety and should be scored only in the mg.
I think that at least half of all available eval features in a good chess program should be related to king safety, as half of all possible chess lines are related to king safety. But, as far as I know, engines evaluate just a tiny portion of king safety elements.
Similarly, in a good chess program, 3/4 of all eval features should be scored only for the mg, as 3/4 or so of all available chess lines happen in the mg. In the mg you have many more reasonable eval features to score that do not exist at all in the eg, but, as far as I am aware, currently most engines have almost an equal number of parameters for the mg and eg.
It makes sense to evaluate such backwardfated storming pawns just on ranks 4 and 5, as on less advanced ranks they are not meaningful.
[d]6k1/6p1/5p1p/7P/4P1P1/8/8/6K1 w - - 0 1
g4 backwardfated storming pawn above
As you see, playing g4-g5 is close to impossible, and thus the entire white attack has stalled. Please note, that this is not equivalent in most cases to both sides having one backwardfated pawn each, which would be tantamount to scoring all storming pawns blocked. For example above, white does not have at all a pawn on the f file.
[d]6k1/5p1p/5P1P/6P1/8/8/8/6K1 w - - 0 1
g5 backwardfated storming pawn - the white attack has stalled again as a whole
[d]6k1/7p/4p1p1/4P1P1/5P2/8/8/6K1 w - - 0 1
f4 backwardfated storming pawn
This is closely related to king safety and should be scored only in the mg.
I think that at least half of all available eval features in a good chess program should be related to king safety, as half of all possible chess lines are related to king safety. But, as far as I know, engines evaluate just a tiny portion of king safety elements.
Similarly, in a good chess program, 3/4 of all eval features should be scored only for the mg, as 3/4 or so of all available chess lines happen in the mg. In the mg you have many more reasonable eval features to score that do not exist at all in the eg, but, as far as I am aware, currently most engines have almost an equal number of parameters for the mg and eg.
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Lyudmil Tsvetkov
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- Joined: Tue Jun 12, 2012 12:41 pm
Double bases
A base, or root pawn, is any undefended pawn defending an own pawn.
However, there are different kinds of base pawns, base pawns of a small chain of just 2 pawns, base pawns of a long chain, and base pawns defending 2 own pawns at the same time.
That last element, an undefended pawn defending 2 own pawns at the same time, is called a double base. If any base pawn is a bad feature in itself, as it is undefended and its capturing will lead to another own pawn becoming weak and undefended, a double base pawn is a much bigger weakness, as, apart from being undefended, its destruction will leave behind 2 own undefended pawns, and besides, the presence of such a double base means that quite frequently, if the square in front of the pawn is empty, this will be a hole where enemy pieces might land on outposts.
So that, if possible, such double bases should be avoided. However, there is one trick to scoring such pawns. As double bases defend 2 strong advanced pawns if on rank 4 and above, and it is not easy to decide if such an advanced base is already a weakness, it makes very much sense to score such double bases only on ranks 2 and 3.
Any double base found on rank 2 or 3 might get some 5-8cps additional penalty.
[d]6k1/8/8/8/5P1P/1P1P2P1/2P5/6K1 w - - 0 1
double base on the 2nd rank on c2; double base on the 3rd rank on g3
I think that it makes very much sense to have specific eval for different kinds of undefended pawns, as there are many types of undefended pawns, that exhibit different degrees of weakness. For example, isolated pawns are undefended pawns, vertically isolated pawns are undefended pawns, duos are undefended pawns in most cases, base pawns are undefended pawns, etc. It is difficult to believe that all those pawns are due an equal penalty.
PS. I very much hope I have not mentioned this before; I think I mentioned base pawns in general, but not double bases.
However, there are different kinds of base pawns, base pawns of a small chain of just 2 pawns, base pawns of a long chain, and base pawns defending 2 own pawns at the same time.
That last element, an undefended pawn defending 2 own pawns at the same time, is called a double base. If any base pawn is a bad feature in itself, as it is undefended and its capturing will lead to another own pawn becoming weak and undefended, a double base pawn is a much bigger weakness, as, apart from being undefended, its destruction will leave behind 2 own undefended pawns, and besides, the presence of such a double base means that quite frequently, if the square in front of the pawn is empty, this will be a hole where enemy pieces might land on outposts.
So that, if possible, such double bases should be avoided. However, there is one trick to scoring such pawns. As double bases defend 2 strong advanced pawns if on rank 4 and above, and it is not easy to decide if such an advanced base is already a weakness, it makes very much sense to score such double bases only on ranks 2 and 3.
Any double base found on rank 2 or 3 might get some 5-8cps additional penalty.
[d]6k1/8/8/8/5P1P/1P1P2P1/2P5/6K1 w - - 0 1
double base on the 2nd rank on c2; double base on the 3rd rank on g3
I think that it makes very much sense to have specific eval for different kinds of undefended pawns, as there are many types of undefended pawns, that exhibit different degrees of weakness. For example, isolated pawns are undefended pawns, vertically isolated pawns are undefended pawns, duos are undefended pawns in most cases, base pawns are undefended pawns, etc. It is difficult to believe that all those pawns are due an equal penalty.
PS. I very much hope I have not mentioned this before; I think I mentioned base pawns in general, but not double bases.
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Lyudmil Tsvetkov
- Posts: 6052
- Joined: Tue Jun 12, 2012 12:41 pm
Pair of unopposed duos on the 4th rank
A pair of unopposed duos on the 4th rank is always due some nice bonus, maybe some 20cps.
This should be given only for the mg, as in the eg this quite frequently might indicate the presence of passers, that will be sufficiently evaluated.
[d]6k1/1p6/p3p3/6pp/2PP4/8/P4P2/6K1 w - - 0 1
c4 and d4 for white and h5 and g5 for black are both pairs of unopposed duos on the 4th rank. Please note that each of the duo pawns is unopposed.
Such pairs of unopposed duos on the 4th rank are simply stronger or much stronger than what it outwardly appears. Chances are, that you not only have 2 candidate passers for white, but much more, as in the usual case less than half of the candidate passers on the 4th rank will make it to a passer status soon, while a pair of unopposed duos will almost certainly very quickly create a full passer one way or the other, full and advanced at that.
Similarly for black, the h5 and g5 pawns are stronger than what might seem: chances are that, while advancing, the black duo not only will have a more advanced passer on the h file, but will also have the opportunity to decide where, on which file to create it - g or h. So such pawns are very flexible and very versatile indeed.
It does not make sense to evaluate such duos on less advanced ranks than the 4th, as there they threaten nothing, while on more advanced ranks those will already be passers.
Well, I did not quite like the way I formulated this rule, there is something I still do not understand about that, but simultaneously, without fully understanding it, I am fully convinced that such unopposed duo pairs are really a tremendous force in the mg.
This should be given only for the mg, as in the eg this quite frequently might indicate the presence of passers, that will be sufficiently evaluated.
[d]6k1/1p6/p3p3/6pp/2PP4/8/P4P2/6K1 w - - 0 1
c4 and d4 for white and h5 and g5 for black are both pairs of unopposed duos on the 4th rank. Please note that each of the duo pawns is unopposed.
Such pairs of unopposed duos on the 4th rank are simply stronger or much stronger than what it outwardly appears. Chances are, that you not only have 2 candidate passers for white, but much more, as in the usual case less than half of the candidate passers on the 4th rank will make it to a passer status soon, while a pair of unopposed duos will almost certainly very quickly create a full passer one way or the other, full and advanced at that.
Similarly for black, the h5 and g5 pawns are stronger than what might seem: chances are that, while advancing, the black duo not only will have a more advanced passer on the h file, but will also have the opportunity to decide where, on which file to create it - g or h. So such pawns are very flexible and very versatile indeed.
It does not make sense to evaluate such duos on less advanced ranks than the 4th, as there they threaten nothing, while on more advanced ranks those will already be passers.
Well, I did not quite like the way I formulated this rule, there is something I still do not understand about that, but simultaneously, without fully understanding it, I am fully convinced that such unopposed duo pairs are really a tremendous force in the mg.
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Lyudmil Tsvetkov
- Posts: 6052
- Joined: Tue Jun 12, 2012 12:41 pm
Blocked/unblocked chain/defended pawns
Well, as said, chain eval is rich, and blocked chain eval is also rich and pertinent.
It makes very much sense to score chain/defended pawns in terms of whether the respective pawn is blocked by an enemy pawn or not. Of course, a blocked pawn, no matter what the pawn is, generally means that the condition of this pawn becomes more durable or permanent. This will mean that the respective pawn values should be overincreased or overdecreased in respect of whether such a pawn is a strength or a weakness.
For strong pawns, that score a bonus, the blocked condition means that the bonus for the pawn should be increased, while for weak pawns, that score a penalty, the blocked condition means the penalty should be further increased.
As strong pawns, scoring a bonus, chain/defended pawns naturally increase their value and bonus when blocked by enemy pawns. This is true of all chain pawns, any defended pawns, an apex/twice defended pawn, spearheads of long chains, and even inner pawns of long chains. So, whenever you find a blocked defended pawn, you might increase the respective chain bonus by some 10% or so.
Of course, this will be especially useful for engines that score defended pawns in terms of ranks, as in this case the more advanced defended pawn, when blocked, will even further increase its bonus to the detriment of a less advanced enemy defended pawn, if also blocked.
[d]6k1/5pp1/2p5/1pP2P2/1P4P1/8/8/6K1 w - - 0 1
c5 is due a bigger bonus than f5, although both pawns are defended, on the same rank, and equally central files. c5 is simply stronger than f5, as its condition is more permanent.
black b5 also deserves bigger bonus, as it is blocked by white b4 pawn, but, as the defended pawns are scored in terms of ranks, when you increase the bonus for both white c5 and black b5 pawns by 10%, the white pawn will get a relatively higher increase, as it is on the 5th rank, while b5 is on its 4th rank
[d]6k1/5p2/1p3Pp1/pP4P1/P1P4P/8/8/6K1 w - - 0 1
blocked apex pawn on b5 - stronger than if the pawn had not been blocked
blocked spearhead on f6 - stronger than if the pawn had not been blocked
Now, I am absolutely certain scoring chain/defended pawns in terms of blocked and not blocked is the right and working approach. However, I am even more certain that it is extremely difficult to implement this in an chess engine: first you will have to split the eval for chain pawns in 2 large groups of blocked and unblocked chain pawns, and only then tune and untune to oblivion, a task tantamount to impossible in an already well-tuned engine.
There is certainly a way to tune it, but you will need capabilities no autotuner or human currently possess. Only way to succeed is be lucky.
It makes very much sense to score chain/defended pawns in terms of whether the respective pawn is blocked by an enemy pawn or not. Of course, a blocked pawn, no matter what the pawn is, generally means that the condition of this pawn becomes more durable or permanent. This will mean that the respective pawn values should be overincreased or overdecreased in respect of whether such a pawn is a strength or a weakness.
For strong pawns, that score a bonus, the blocked condition means that the bonus for the pawn should be increased, while for weak pawns, that score a penalty, the blocked condition means the penalty should be further increased.
As strong pawns, scoring a bonus, chain/defended pawns naturally increase their value and bonus when blocked by enemy pawns. This is true of all chain pawns, any defended pawns, an apex/twice defended pawn, spearheads of long chains, and even inner pawns of long chains. So, whenever you find a blocked defended pawn, you might increase the respective chain bonus by some 10% or so.
Of course, this will be especially useful for engines that score defended pawns in terms of ranks, as in this case the more advanced defended pawn, when blocked, will even further increase its bonus to the detriment of a less advanced enemy defended pawn, if also blocked.
[d]6k1/5pp1/2p5/1pP2P2/1P4P1/8/8/6K1 w - - 0 1
c5 is due a bigger bonus than f5, although both pawns are defended, on the same rank, and equally central files. c5 is simply stronger than f5, as its condition is more permanent.
black b5 also deserves bigger bonus, as it is blocked by white b4 pawn, but, as the defended pawns are scored in terms of ranks, when you increase the bonus for both white c5 and black b5 pawns by 10%, the white pawn will get a relatively higher increase, as it is on the 5th rank, while b5 is on its 4th rank
[d]6k1/5p2/1p3Pp1/pP4P1/P1P4P/8/8/6K1 w - - 0 1
blocked apex pawn on b5 - stronger than if the pawn had not been blocked
blocked spearhead on f6 - stronger than if the pawn had not been blocked
Now, I am absolutely certain scoring chain/defended pawns in terms of blocked and not blocked is the right and working approach. However, I am even more certain that it is extremely difficult to implement this in an chess engine: first you will have to split the eval for chain pawns in 2 large groups of blocked and unblocked chain pawns, and only then tune and untune to oblivion, a task tantamount to impossible in an already well-tuned engine.
There is certainly a way to tune it, but you will need capabilities no autotuner or human currently possess. Only way to succeed is be lucky.
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Lyudmil Tsvetkov
- Posts: 6052
- Joined: Tue Jun 12, 2012 12:41 pm
Backward pawns with minors
A very simple rule: increase, maybe even double the penalty for any backward pawn the opponent has, when you have 2 more minors than the opponent.
Why so?
Well, simply minors have the ability to make enemy backward pawns even weaker, backwardfated almost, when the opponent has 2 minors less.
[d]3r3r/1p2kp2/3p2p1/2p3P1/2P1N1B1/2NKPP2/1P6/8 w - - 0 1
guess who has the advantage above?
equal material, but, as white has 2 minors more than black, the penalty for both black d6 and f7 backward pawns should be increased/doubled, so actually white has a significant advantage above
as you see, d6 and f7 absolutely can not move, so they are out of the game for the moment
This influences only the enemy's backward pawns, and not yours.
I think this is a very good and very positional chess rule, that is true that is not the most frequent, but still happens from time to time. For example, this could occur in imbalances like 2 minors vs rook, minors vs queen, rook and minors vs queen, 3 minors vs 2 rooks, etc. It would be nice to see your engine picking the right lines and handling this correctly, especially picking the right lines, as handling is easier.
Why so?
Well, simply minors have the ability to make enemy backward pawns even weaker, backwardfated almost, when the opponent has 2 minors less.
[d]3r3r/1p2kp2/3p2p1/2p3P1/2P1N1B1/2NKPP2/1P6/8 w - - 0 1
guess who has the advantage above?
equal material, but, as white has 2 minors more than black, the penalty for both black d6 and f7 backward pawns should be increased/doubled, so actually white has a significant advantage above
as you see, d6 and f7 absolutely can not move, so they are out of the game for the moment
This influences only the enemy's backward pawns, and not yours.
I think this is a very good and very positional chess rule, that is true that is not the most frequent, but still happens from time to time. For example, this could occur in imbalances like 2 minors vs rook, minors vs queen, rook and minors vs queen, 3 minors vs 2 rooks, etc. It would be nice to see your engine picking the right lines and handling this correctly, especially picking the right lines, as handling is easier.
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Lyudmil Tsvetkov
- Posts: 6052
- Joined: Tue Jun 12, 2012 12:41 pm
Chainwise defended doubled pawn
What is a chainwise defended doubled pawn?
Well, a doubled pawn, that is defended by a pawn, which is in turn defended by another own pawn on the same file as the doubled pawn.
[d]6k1/2pp4/1p6/3P4/2P5/3P4/8/6K1 w - - 0 1
above, d5 is a chainwise defended doubled pawn - it is defended by c4, which is in turn defended by d3, that is on the same file as d5
Such pawns are due some 7cps or so overbonus.
Why so?
Well, although you score 2 defended pawns above, d5 and c4, the whole structure is even stronger, as it is kind of an ugly long chain. Of course, the doubled pawn penalty will diminish the importance of the structure, but still it is very strong and not bad to have.
You will say - stupid - no, sometimes details make the difference.
Well, a doubled pawn, that is defended by a pawn, which is in turn defended by another own pawn on the same file as the doubled pawn.
[d]6k1/2pp4/1p6/3P4/2P5/3P4/8/6K1 w - - 0 1
above, d5 is a chainwise defended doubled pawn - it is defended by c4, which is in turn defended by d3, that is on the same file as d5
Such pawns are due some 7cps or so overbonus.
Why so?
Well, although you score 2 defended pawns above, d5 and c4, the whole structure is even stronger, as it is kind of an ugly long chain. Of course, the doubled pawn penalty will diminish the importance of the structure, but still it is very strong and not bad to have.
You will say - stupid - no, sometimes details make the difference.