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[[FILE:Schach-Theorie.jpg|border|right|thumb|link=https://www.pinterest.de/pin/58476495131654514/| [[Arts#:Category:Wassily Kandinsky|Wassily Kandinsky]], - Schach-Theorie, 1937 <ref>[https://www.pinterest.de/pin/58476495131654514/ Vassily Kandinsky - Schach-Theorie | Art I love | Pinterest]</ref> ]]

a [https://en.wikipedia.org/wiki/Heuristic_(computer_science) heuristic function] to determine the [[Score|relative value]] of a [[Chess Position|position]], i.e. the chances of winning. If we could see to the end of the game in every line, the evaluation would only have values of -1 (loss), 0 (draw), and 1 (win), and the chess engine should search to depth 1 only to get the best move. In practice, however, we do not know the exact value of a position, so we must make an approximationwith the main purpose is to compare positions, and the chess engine now must search deeply and find the highest score position within a given period. Recently, there are two main ways to build an evaluation: traditional and multi-layer [[Neural Networks|neural networks]]. This page focuses on the traditional way considering explicit features of a [[Chess Position|chess position]].  Beginning chess players learn to do this starting with the [[Point Value|value]] of the [[Pieces|pieces]] themselves. Computer evaluation functions also use the value of the [[Material|material balance]] as the most significant aspect and then add other considerations.

It depends on the definition and [https://en.wikipedia.org/wiki/Linear_independence independence] of features and the acceptance of the [https://en.wikipedia.org/wiki/Axiom_of_choice axiom of choice] ([[Ernst Zermelo]] 1904), whether additive real number functions are linear or not <ref>[http://www.talkchess.com/forum/viewtopic.php?topic_view=threads&p=288501&t=29552 Re: Linear vs. Nonlinear EvalulationEvaluation] by [[Tord Romstad]], [[CCC]], August 27, 2009</ref> . Features are either related to single pieces ([[Material|material]]), their location ([[Piece-Square Tables|piece-square tables]]), or more sophisticated, considering interactions of multiple pawns and pieces, based on certain [[Evaluation Patterns|patterns]] or [[Chunking|chunks]]. Often several phases to first process simple features and after building appropriate data structures, in consecutive phases more complex features based on patterns and chunks are used.

Based on that, to distinguish [https://en.wikipedia.org/wiki/First-order first-order], [https://en.wikipedia.org/wiki/Second-order second-order], etc. terms, makes more sense than using the arbitrary terms linear vs. nonlinear evaluation <ref>[http://www.talkchess.com/forum/viewtopic.php?topic_view=threads&p=288564&t=29552 Re: Linear vs. Nonlinear EvalulationEvaluation] by [[Robert Hyatt]], [[CCC]], August 27, 2009</ref> . With respect to [[Automated Tuning|tuning]], one has to take care that features are independent, which is not always that simple. Hidden dependencies may otherwise make the evaluation function hard to maintain with undesirable nonlinear effects.

* [[Pawn Advantage, Win Percentage, and ELOElo]]

* [[Quantifying Evaluation featuresFeatures]] by [[Mark Watkins]]* [[Simplified evaluation functionEvaluation Function]]* [[PeSTO's Evaluation Function]]

* [https://en.wikipedia.org/wiki/Israel_Albert_Horowitz Israel Albert Horowitz], [https://en.wikipedia.org/wiki/Mott-Smith_Trophy Geoffrey Mott-Smith] ('''1960,1970,2012'''). ''[http://www.chess-game-strategies.com/point-count-chess.html Point Count Chess]''. [https://en.wikipedia.org/wiki/Samuel_Reshevsky Samuel Reshevsky] (Introduction), [[Sam Sloan]] (2012 Introduction), [http://www.amazon.com/Point-Count-Chess-Accurate-Winning/dp/4871874699/ref=sr_1_2?s=books&ie=UTF8&qid=1366734801&sr=1-2 Amazon] <ref>[https://www.stmintz.com/ccc/index.php?id=25046 Re: Books that help for evaluation] by [[Robert Hyatt]], [[CCC]], August 18, 1998</ref>

* [[Ron Atkin]] ('''1972'''). ''Multi-Dimensional Structure in the Game of Chess''. In [http://www.interaction-design.org/references/periodicals/international_journal_of_man-machine_studies_volume_4.html International Journal of Man-Machine Studies, Vol. 4]* [[Ron Atkin]], [[Ian H. Witten]] ('''1975'''). ''[http://www.bibsonomy.org/bibtex/2b91106ea980eb48aa505f6b54c130707/dblp A Multi-Dimensional Approach to Positional Chess]''. [http://www.interaction-design.org/references/periodicals/international_journal_of_man-machine_studies_volume_7.html International Journal of Man-Machine Studies, Vol. 7, No. 6]

* [[Eli David|Omid David]], [[Moshe Koppel]], [[Nathan S. Netanyahu]] ('''2008'''). ''Genetic Algorithms for Mentor-Assisted Evaluation Function Optimization'', ACM Genetic and Evolutionary Computation Conference ([http://www.sigevo.org/gecco-2008/ GECCO '08]), pp. 1469-1475, Atlanta, GA, July 2008.* [[Eli David|Omid David]], [[Jaap van den Herik]], [[Moshe Koppel]], [[Nathan S. Netanyahu]] ('''2009'''). ''Simulating Human Grandmasters: Evolution and Coevolution of Evaluation Functions''. [[ACM]] Genetic and Evolutionary Computation Conference ([http://www.sigevo.org/gecco-2009/ GECCO '09]), pp. 1483 - 1489, Montreal, Canada, July 2009.* [[Eli David|Omid David]] ('''2009'''). ''Genetic Algorithms Based Learning for Evolving Intelligent Organisms''. Ph.D. Thesis.

* [[Eli David|Omid David]], [[Moshe Koppel]], [[Nathan S. Netanyahu]] ('''2011'''). ''Expert-Driven Genetic Algorithms for Simulating Evaluation Functions''. Genetic Programming and Evolvable Machines, Vol. 12, No. 1, pp. 5--22, March 2011. » [[Genetic Programming]]

* [https://groups.google.com/group/rec.games.chess.computer/browse_frm/thread/77f10f072e907302 Evolutionary Evaluation] by [[Dan Daniel Homan]], [[Computer Chess Forums|rgcc]], September 09, 1997 » [[Automated Tuning]]

* [httphttps://wwwgithub.top-5000.nlcom/authorsgekomad/rebelchess-engine-eval-debugger GitHub - gekomad/chess840.htm#HW Evaluation in REBEL] by [[Ed Schroder|Ed Schröder]] » [[Rebel]]* [http://www.topchess-engine-5000.nl/eval.htm The value of an evaluation function] by [[Ed Schroder|Ed Schröder]] <ref>[http://www.talkchess.com/forum/viewtopic.php?t=44014 The value of an evaluation function] by [[Ed Schroder|Ed Schröder]], [[CCC]], June 11, 2012</ref>* [http://rebel13.nl/efs/index.html Rebel - The EFS project] from [httpdebugger://rebel13.nl/index.html Rebel Pure Nostalgica] by [[Ed Schroder|Ed Schröder]] <ref>[http://www.talkchess.com/forum/viewtopic.php?t=57087 (E)valuation (F)or (S)tartersChess engine web evaluator] by [[Ed Schroder|Ed SchröderGiuseppe Cannella]], [[CCC]], July 26, 2015</ref>