Changes

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.