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[[FILE:SamuelBakIntruder.jpg|border|right|thumb|link=http://chgs.elevator.umn.edu/asset/viewAsset/57f3b6787d58ae5f74bf8ba9#57f3b6d77d58ae5574bf8bd0|[[:Category:Samuel Bak|Samuel Bak]] - Intruder <ref>[http://chgs.elevator.umn.edu/asset/viewAsset/57f3b6787d58ae5f74bf8ba9#57f3b6d77d58ae5574bf8bd0 Chess in the Art of Samuel Bak] [http://chgs.elevator.umn.edu/ Center for Holocaust & Genocide Studies], [[University of Minnesota]]</ref> ]]
The '''influence quantity''' of pieces is defined by their number of unique [[Moves|moves]] with respect to their [[Origin Square|from]]- and [[Target Square|to-square]] coordinates, the [https://en.wikipedia.org/wiki/Cardinality cardinality] of the set of all possible moves, or [[Mobility#TheValueofReachingaSquare|potential, global]] [[Mobility|mobility]] <ref>[[Dan Heisman]] ('''1990, 1999, 2010, 2015''').''[httphttps://www.danheisman.com/elements-of-positional-evaluation.html The Positional Elements of ChessPositional Evaluation]''. Russell Enterprises</ref>. It might be used to enumerate and [[Encoding Moves|encode]] all those moves, i.e. associating each move, per piece and in total, with a unique number for [[Hash Table#MinimalPerfectHashing|minimal perfect hashing]] opposed to intermittent [[Butterfly Boards|Butterfly boards]].
For instance a [[Pawn|pawn]] (including [[Promotions|promotions]]) has 48 (8*6) single pushes and 84 (2*7*6) [[Captures|captures]], plus 8 possible double pushes on each [[Files|file]], which results in a influence quantity of 140 of either white or black pawns.The influence quantities of all pieces are divisible by four times seven (28), excluding pawn and [[King|king]] even by sixteen times seven (112). While obviously the number of [[Queen|queen]] quantities is the sum of [[Rook|rook]]- and [[Bishop|bishop]] quantities, it is at the first glance somehow surprising that the rook quantity is the sum of bishop- and [[Knight|knight]] quantities.
* [[Mathematician#Coxeter|H. S. M. Coxeter]] ('''1940'''). ''Mathematical Recreations and Essays''. from the [http://www.gutenberg.org/ebooks/26839 original] by [[Mathematician#WWRouseBall|W. W. Rouse Ball]], [https://en.wikipedia.org/wiki/Macmillan_Publishers Macmillan]
* [[Jack Good]] ('''1968'''). ''A Five-Year Plan for Automatic Chess - Appendix F. The Value of the Pieces and Squares''. [http://www.doc.ic.ac.uk/~shm/MI/mi2.html Machine Intelligence Vol. 2]
* [[Dan Heisman]] ('''1990, 1999, 2010, 2015''').''[httphttps://www.danheisman.com/elements-of-positional-evaluation.html The Positional Elements of ChessPositional Evaluation]''. Russell Enterprises
* Peter Orantek ('''2008'''). ''[http://www.127jupiter.com/ Encyclopedia of Chess-Prehistory - Programming Language Chess]''.
