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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Evaluation function | 2/2 | https://en.wikipedia.org/wiki/Evaluation_function | reference | science, encyclopedia | 2026-05-05T09:57:37.091312+00:00 | kb-cron |
c1 * material + c2 * mobility + c3 * king safety + c4 * center control + c5 * pawn structure + c6 * king tropism + ... Each of the terms is a weight multiplied by a difference factor: the value of white's material or positional terms minus black's.
The material term is obtained by assigning a value in pawn-units to each of the pieces. Mobility is the number of legal moves available to a player, or alternately the sum of the number of spaces attacked or defended by each piece, including spaces occupied by friendly or opposing pieces. Effective mobility, or the number of "safe" spaces a piece may move to, may also be taken into account. King safety is a set of bonuses and penalties assessed for the location of the king and the configuration of pawns and pieces adjacent to or in front of the king, and opposing pieces bearing on spaces around the king. Center control is derived from how many pawns and pieces occupy or bear on the four center spaces and sometimes the 12 spaces of the extended center. Pawn structure is a set of penalties and bonuses for various strengths and weaknesses in pawn structure, such as penalties for doubled and isolated pawns. King tropism is a bonus for closeness (or penalty for distance) of certain pieces, especially queens and knights, to the opposing king.
=== Piece-square tables === An important technique in evaluation since at least the early 1990s is the piece-square table (also called piece-value table). Each table is a set of 64 values corresponding to the squares of the chessboard. The most basic implementation of piece-square table consists of separate tables for each type of piece per player, which in chess results in 12 piece-square tables in total. The values in the tables are bonuses/penalties for the location of each piece on each space, and encode a composite of many subtle factors difficult to quantify analytically. In handcrafted evaluation functions, there are sometimes two sets of tables: one for the opening/middlegame, and one for the endgame; positions of the middle game are interpolated between the two.
=== Neural networks === While neural networks have been used in the evaluation functions of chess engines since the late 1980s, they did not become popular in computer chess until the late 2010s, as the hardware needed to train neural networks was not strong enough at the time, and fast training algorithms and network topology and architectures had not been developed yet. Neural network based evaluation functions generally consist of a neural network trained using reinforcement learning or supervised learning to accept a board state as input and output a real or integer value. Deep neural networks have been used, albeit infrequently, in computer chess after Matthew Lai's Giraffe in 2015 and Deepmind's AlphaZero in 2017 demonstrated the feasibility of deep neural networks in evaluation functions. The distributed computing project Leela Chess Zero was started shortly after to attempt to replicate the results of Deepmind's AlphaZero paper. Apart from the size of the networks, the neural networks used in AlphaZero and Leela Chess Zero also differ from those used in traditional chess engines in that they predict a distribution across subsequent moves (the policy head) in addition to the evaluation (the value head). Since deep neural networks are very large, engines using deep neural networks in their evaluation function usually require a graphics processing unit in order to efficiently calculate the evaluation function. The evaluation function used by most top engines is the efficiently updatable neural network (NNUE), a sparse and shallow neural network originally proposed for computer shogi in 2018 by Yu Nasu. In fact, the most basic NNUE architecture is simply the 12 piece-square tables described above, a neural network with only one layer and no activation functions. An efficiently updatable neural network architecture was first ported to chess in a Stockfish derivative called Stockfish NNUE, publicly released on May 30, 2020, and was incorporated into the official Stockfish engine on August 6, 2020.
=== Endgame tablebases ===
Chess engines frequently use endgame tablebases to quickly and accurately evaluate endgame positions.
== In Go == Historically, evaluation functions in Computer Go took into account both territory controlled, influence of stones, number of prisoners and life and death of groups on the board. However, modern go playing computer programs largely use deep neural networks in their evaluation functions, such as AlphaGo, Leela Zero, Fine Art, and KataGo, and output a win/draw/loss percentage rather than a value in number of stones.
== References ==
Slate, D and Atkin, L., 1983, "Chess 4.5, the Northwestern University Chess Program" in Chess Skill in Man and Machine 2nd Ed., pp. 93–100. Springer-Verlag, New York, NY. Ebeling, Carl, 1987, All the Right Moves: A VLSI Architecture for Chess (ACM Distinguished Dissertation), pp. 56–86. MIT Press, Cambridge, MA
== External links == Keys to Evaluating Positions GameDev.net - Chess Programming Part VI: Evaluation Functions