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Dispersion and Distortion

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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|[[:Category:Samuel 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="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) {
=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]]
* [https://wannabe.guru.org/scott/hobbies/chess/ Monsoon/Typhoon Homepage] by [[Scott Gasch]]
* [https://en.wikipedia.org/wiki/Dispersion Dispersion from Wikipedia]

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