Editing Computer chess (section)

=== Leaf evaluation ===
{{main|Evaluation function}}
For most chess positions, computers cannot look ahead to all possible final positions. Instead, they must look ahead a few [[Ply (game theory)|plies]] and compare the possible positions, known as leaves. The algorithm that evaluates leaves is termed the "evaluation function", and these algorithms are often vastly different between different chess programs. Evaluation functions typically evaluate positions in hundredths of a pawn (called a centipawn), where by convention, a positive evaluation favors White, and a negative evaluation favors Black. However, some evaluation function output win/draw/loss percentages instead of centipawns.

Historically, handcrafted evaluation functions consider material value along with other factors affecting the strength of each side. When counting up the material for each side, typical values for pieces are 1 point for a [[pawn (chess)|pawn]], 3 points for a [[knight (chess)|knight]] or [[bishop (chess)|bishop]], 5 points for a [[rook (chess)|rook]], and 9 points for a [[queen (chess)|queen]]. (See [[Chess piece relative value]].) The [[king (chess)|king]] is sometimes given an arbitrarily high value such as 200 points ([[Claude Shannon#Shannon's computer chess program|Shannon's paper]]) to ensure that a checkmate outweighs all other factors {{Harvcol|Levy|Newborn|1991|pp=45}}. In addition to points for pieces, most handcrafted evaluation functions take many factors into account, such as pawn structure, the fact that a pair of bishops are usually worth more, centralized pieces are worth more, and so on. The protection of kings is usually considered, as well as the phase of the game (opening, middle or endgame). [[Machine learning]] techniques such as Texel turning, [[stochastic gradient descent]], or [[reinforcement learning]] are usually used to optimise handcrafted evaluation functions.

Most modern evaluation functions make use of [[Artificial neural network|neural networks]]. The most common evaluation function in use today is the [[efficiently updatable neural network]], which is a shallow neural network whose inputs are [[piece-square table]]s. Piece-square tables are a set of 64 values corresponding to the squares of the chessboard, and there typically exists a piece-square table for every piece and colour, resulting in 12 piece-square tables and thus 768 inputs into the neural network. In addition, some engines use [[deep neural networks]] in their evaluation function. Neural networks are usually trained using some [[reinforcement learning]] algorithm, in conjunction with [[supervised learning]] or [[unsupervised learning]].

The output of the evaluation function is a single scalar, quantized in centipawns or other units, which is, in the case of handcrafted evaluation functions, a weighted summation of the various factors described, or in the case of neural network based evaluation functions, the output of the head of the neural network. The evaluation putatively represents or approximates the value of the subtree below the evaluated node as if it had been searched to termination, i.e. the end of the game.  During the search, an evaluation is compared against evaluations of other leaves, eliminating nodes that represent bad or poor moves for either side, to yield a node which by convergence, represents the value of the position with best play by both sides.