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'''[[Main Page|Home]] * [[Board Representation]] * [[Bitboards]] * [[Pawn Pattern and Properties]] * Dispersion and Distortion'''
[[FILE:SamuelBakLuna.jpg|border|right|thumb|link=http://chgs.elevator.umn.edu/asset/viewAsset/57f3b6787d58ae5f74bf8ba9#57f3b6d77d58ae5574bf8bb7|[[Arts#Bak|Samuel Bak]] - Luna <ref>[http://chgs.elevator.umn.edu/asset/viewAsset/57f3b6787d58ae5f74bf8ba9#57f3b6d77d58ae5574bf8bb7 Chess in the Art of Samuel Bak], [http://www.chgs.umn.edu/ Center for Holocaust & Genocide Studies], [https://en.wikipedia.org/wiki/University_of_Minnesota University of Minnesota]</ref> ]]
'''Dispersion''' and '''Distortion''',<br/>
are [[Hans Kmoch|Kmoch's]] terms <ref>[[Hans Kmoch]] ('''1959, 1990'''). ''Pawn Power in Chess''. New York: Dover, 1990. Previous ed.: New York: McKay, 1959. ISBN 0-486-26486-6</ref> <ref>[https://www.chess.com/forum/view/chess-equipment/pawn-power-in-chess-by-hans-kmoch-glossary-of-terms Pawn Power in Chess by Hans Kmoch - Glossary of Terms - Chess Forums] - [https://en.wikipedia.org/wiki/Chess.com Chess.com]</ref> for [[Pawn Structure|pawn structure]] [[Weak Pawns|weaknesses]] due to vertical or horizontal splitting caused by [[Captures|captures]] or [[Pawn Push|advancement]]. The proposed functions may be used via an additional scaling or indirection, f.i. to index a table with concrete penalties.
=Dispersion=
<span id="Dispersion"></span> '''Dispersion''' is [[Hans Kmoch|Kmoch's]] term for vertical splitting of pawns (most commonly, isolation) caused by captures. Having three or four [[Pawn Islands (Bitboards)|islands]] while the opponent has one or two - assuming about the same number of pawns for both sides - may be considered in evaluation. But this is also implicitly done by evaluating [[Double and Triple (Bitboards)|double- or triple]] and [[Isolated Pawns (Bitboards)#IsolanisSetWise|isolated]] or the balance of weak pawns in general. Some arbitrary dispersion measure, intended as index of a pre-calculated table for [[Evaluation|evaluation]] purpose.
<pre>
int dispersion(U64 pawns)
{
BYTE fileset = (BYTE) soutFill(pawns);
int ni = popCount(islandsEastFiles(fileset));
int np = popCount(wpawns);
return abs(3*ni*ni - np);
}
BYTE islandsEastFiles(BYTE f) {return f & ((f ^ (f >> 1));}
</pre>
The higher the worse.
<pre>
\ number if islands
\ 1 2 3 4
np \ 3 12 27 48
_____\________________
1 | 2 - - -
2 | 1 10 - -
3 | 0 9 24 -
4 | 1 8 23 44
5 | 2 7 22 43
6 | 3 6 21 42
7 | 4 5 20 41
8 | 5 4 19 40
</pre>
<span id="Distortion"></span>
=Distortion=
Distortion is [[Hans Kmoch|Kmoch's]] term for horizontal splitting of pawns caused by advances. One may use something like this based on [[Pawn Fills|rearfill]], xor and [[Population Count|population count]] to get an idea of distortion. It considers the rank-difference of two file-adjacent pawns (if any) as distortion penalty - the higher the worse. [[Isolated Pawns (Bitboards)IsolanisSetWise|Half-isolated]] or even [[Isolated Pawn|isolated pawns]] contribute a distortion penalty according to the size of their rearfill from 2 to 7 for each empty neighboring file, which discourages advancement of such pawns, interacting with terms considerring (half-) isolated pawns. Alternatively, for a "reverse" distortion penalty to encourage advancement of half-isolanis, one may use [[Pawn Fills|frontfill]] instead with a slightly different semantic is case of [[Doubled Pawn|doubled pawns]].
<pre>
int wDistortion(U64 wpawns) {
U64 fill = wRearFill(wpawns); // wFrontFill
U64 delta = (fill ^ (fill<<1)) & C64(0xfefefefefefefefe));
return popCount(delta);
}
</pre>
High distortion sample:
<pre>
wpawns rearFill rearFill << 1 xor & ~A-File
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 1 . 1 . 1 . . . 1 . 1 . 1 . . . . 1 . 1 . 1 . . 1 1 1 1 1 1
. . . . . . . . . . 1 . 1 . 1 . . . . 1 . 1 . 1 . . 1 1 1 1 1 1
1 . . . . . . . 1 . 1 . 1 . 1 . . 1 . 1 . 1 . 1 . 1 1 1 1 1 1 1
. . . . . . . . 1 . 1 . 1 . 1 . 1 1 . 1 . 1 . 1 . 1 1 1 1 1 1 1
. 1 . 1 . 1 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . . . . . . . .
. . . . . . . . 1 1 1 1 1 1 1 1 . 1 1 1 1 1 1 1 . . . . . . . .
26 bits sets
</pre>
=See also=
* [[Isolated Pawn]]
* [[Isolated Pawns (Bitboards)]]
* [[Pawn Islands]]
* [[Pawn Islands (Bitboards)]]
=External Links=
* [https://www.chess.com/forum/view/chess-equipment/pawn-power-in-chess-by-hans-kmoch-glossary-of-terms Pawn Power in Chess by Hans Kmoch - Glossary of Terms - Chess Forums] - [https://en.wikipedia.org/wiki/Chess.com Chess.com]
* [http://perl.guru.org/scott/hobbies/chess/ Monsoon/Typhoon Homepage] by [[Scott Gasch]]
* [https://en.wikipedia.org/wiki/Dispersion Dispersion from Wikipedia]
* [https://en.wikipedia.org/wiki/Distortion_%28disambiguation%29 Distortion (disambiguation) from Wikipedia]
=References=
<references />
'''[[Pawn Pattern and Properties|Up one Level]]'''
[[Category:Samuel Bak]][[Category:Hans Kmoch]]
[[FILE:SamuelBakLuna.jpg|border|right|thumb|link=http://chgs.elevator.umn.edu/asset/viewAsset/57f3b6787d58ae5f74bf8ba9#57f3b6d77d58ae5574bf8bb7|[[Arts#Bak|Samuel Bak]] - Luna <ref>[http://chgs.elevator.umn.edu/asset/viewAsset/57f3b6787d58ae5f74bf8ba9#57f3b6d77d58ae5574bf8bb7 Chess in the Art of Samuel Bak], [http://www.chgs.umn.edu/ Center for Holocaust & Genocide Studies], [https://en.wikipedia.org/wiki/University_of_Minnesota University of Minnesota]</ref> ]]
'''Dispersion''' and '''Distortion''',<br/>
are [[Hans Kmoch|Kmoch's]] terms <ref>[[Hans Kmoch]] ('''1959, 1990'''). ''Pawn Power in Chess''. New York: Dover, 1990. Previous ed.: New York: McKay, 1959. ISBN 0-486-26486-6</ref> <ref>[https://www.chess.com/forum/view/chess-equipment/pawn-power-in-chess-by-hans-kmoch-glossary-of-terms Pawn Power in Chess by Hans Kmoch - Glossary of Terms - Chess Forums] - [https://en.wikipedia.org/wiki/Chess.com Chess.com]</ref> for [[Pawn Structure|pawn structure]] [[Weak Pawns|weaknesses]] due to vertical or horizontal splitting caused by [[Captures|captures]] or [[Pawn Push|advancement]]. The proposed functions may be used via an additional scaling or indirection, f.i. to index a table with concrete penalties.
=Dispersion=
<span id="Dispersion"></span> '''Dispersion''' is [[Hans Kmoch|Kmoch's]] term for vertical splitting of pawns (most commonly, isolation) caused by captures. Having three or four [[Pawn Islands (Bitboards)|islands]] while the opponent has one or two - assuming about the same number of pawns for both sides - may be considered in evaluation. But this is also implicitly done by evaluating [[Double and Triple (Bitboards)|double- or triple]] and [[Isolated Pawns (Bitboards)#IsolanisSetWise|isolated]] or the balance of weak pawns in general. Some arbitrary dispersion measure, intended as index of a pre-calculated table for [[Evaluation|evaluation]] purpose.
<pre>
int dispersion(U64 pawns)
{
BYTE fileset = (BYTE) soutFill(pawns);
int ni = popCount(islandsEastFiles(fileset));
int np = popCount(wpawns);
return abs(3*ni*ni - np);
}
BYTE islandsEastFiles(BYTE f) {return f & ((f ^ (f >> 1));}
</pre>
The higher the worse.
<pre>
\ number if islands
\ 1 2 3 4
np \ 3 12 27 48
_____\________________
1 | 2 - - -
2 | 1 10 - -
3 | 0 9 24 -
4 | 1 8 23 44
5 | 2 7 22 43
6 | 3 6 21 42
7 | 4 5 20 41
8 | 5 4 19 40
</pre>
<span id="Distortion"></span>
=Distortion=
Distortion is [[Hans Kmoch|Kmoch's]] term for horizontal splitting of pawns caused by advances. One may use something like this based on [[Pawn Fills|rearfill]], xor and [[Population Count|population count]] to get an idea of distortion. It considers the rank-difference of two file-adjacent pawns (if any) as distortion penalty - the higher the worse. [[Isolated Pawns (Bitboards)IsolanisSetWise|Half-isolated]] or even [[Isolated Pawn|isolated pawns]] contribute a distortion penalty according to the size of their rearfill from 2 to 7 for each empty neighboring file, which discourages advancement of such pawns, interacting with terms considerring (half-) isolated pawns. Alternatively, for a "reverse" distortion penalty to encourage advancement of half-isolanis, one may use [[Pawn Fills|frontfill]] instead with a slightly different semantic is case of [[Doubled Pawn|doubled pawns]].
<pre>
int wDistortion(U64 wpawns) {
U64 fill = wRearFill(wpawns); // wFrontFill
U64 delta = (fill ^ (fill<<1)) & C64(0xfefefefefefefefe));
return popCount(delta);
}
</pre>
High distortion sample:
<pre>
wpawns rearFill rearFill << 1 xor & ~A-File
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 1 . 1 . 1 . . . 1 . 1 . 1 . . . . 1 . 1 . 1 . . 1 1 1 1 1 1
. . . . . . . . . . 1 . 1 . 1 . . . . 1 . 1 . 1 . . 1 1 1 1 1 1
1 . . . . . . . 1 . 1 . 1 . 1 . . 1 . 1 . 1 . 1 . 1 1 1 1 1 1 1
. . . . . . . . 1 . 1 . 1 . 1 . 1 1 . 1 . 1 . 1 . 1 1 1 1 1 1 1
. 1 . 1 . 1 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . . . . . . . .
. . . . . . . . 1 1 1 1 1 1 1 1 . 1 1 1 1 1 1 1 . . . . . . . .
26 bits sets
</pre>
=See also=
* [[Isolated Pawn]]
* [[Isolated Pawns (Bitboards)]]
* [[Pawn Islands]]
* [[Pawn Islands (Bitboards)]]
=External Links=
* [https://www.chess.com/forum/view/chess-equipment/pawn-power-in-chess-by-hans-kmoch-glossary-of-terms Pawn Power in Chess by Hans Kmoch - Glossary of Terms - Chess Forums] - [https://en.wikipedia.org/wiki/Chess.com Chess.com]
* [http://perl.guru.org/scott/hobbies/chess/ Monsoon/Typhoon Homepage] by [[Scott Gasch]]
* [https://en.wikipedia.org/wiki/Dispersion Dispersion from Wikipedia]
* [https://en.wikipedia.org/wiki/Distortion_%28disambiguation%29 Distortion (disambiguation) from Wikipedia]
=References=
<references />
'''[[Pawn Pattern and Properties|Up one Level]]'''
[[Category:Samuel Bak]][[Category:Hans Kmoch]]
