An evaluation function, also known as a heuristic evaluation function or static evaluation function, is a function used by game-playing computer programs to estimate the value or goodness of a position (usually at a leaf or terminal node) in a game tree. Most of the time, the value is either a real number or a quantized integer, often in nths of the value of a playing piece such as a stone in go or a pawn in chess, where n may be tenths, hundredths or other convenient fraction, but sometimes, the value is an array of three values in the unit interval, representing the win, draw, and loss percentages of the position.

There do not exist analytical or theoretical models for evaluation functions for unsolved games, nor are such functions entirely ad-hoc. The composition of evaluation functions is determined empirically by inserting a candidate function into an automaton and evaluating its subsequent performance. A significant body of evidence now exists for several games like chess, shogi and go as to the general composition of evaluation functions for them.

Games in which game playing computer programs employ evaluation functions include chess, go, shogi (Japanese chess), othello, hex, backgammon, and checkers. In addition, with the advent of programs such as MuZero, computer programs also use evaluation functions to play video games, such as those from the Atari 2600. Some games like tic-tac-toe are strongly solved, and do not require search or evaluation because a discrete solution tree is available.

A tree of such evaluations is usually part of a search algorithm, such as Monte Carlo tree search or a minimax algorithm like alpha–beta search. The value is presumed to represent the relative probability of winning if the game tree were expanded from that node to the end of the game. The function looks only at the current position (i.e. what spaces the pieces are on and their relationship to each other) and does not take into account the history of the position or explore possible moves forward of the node (therefore static). This implies that for dynamic positions where tactical threats exist, the evaluation function will not be an accurate assessment of the position. These positions are termed non-quiescent; they require at least a limited kind of search extension called quiescence search to resolve threats before evaluation. Some values returned by evaluation functions are absolute rather than heuristic, if a win, loss or draw occurs at the node.

There is an intricate relationship between search and knowledge in the evaluation function. Deeper search favors less near-term tactical factors and more subtle long-horizon positional motifs in the evaluation. There is also a trade-off between efficacy of encoded knowledge and computational complexity: computing detailed knowledge may take so much time that performance decreases, so approximations to exact knowledge are often better. Because the evaluation function depends on the nominal depth of search as well as the extensions and reductions employed in the search, there is no generic or stand-alone formulation for an evaluation function. An evaluation function which works well in one application will usually need to be substantially re-tuned or re-trained to work effectively in another application.^{[citation needed]}

In computer chess, larger evaluations indicate a material imbalance or positional advantage or that a win of material is usually imminent. Very large evaluations may indicate that checkmate is imminent. An evaluation function also implicitly encodes the value of the right to move, which can vary from a small fraction of a pawn to win or loss.

The output of a handcrafted evaluation function is typically an integer whose units are typically referred to as pawns. The term 'pawn' refers to the value when the player has one more pawn than the opponent in a position, as explained in Chess piece relative value. The integer 1 usually represents some fraction of a pawn, and commonly used in computer chess are centipawns, which are a hundredth of a pawn.

Historically in computer chess, the terms of an evaluation function are constructed (i.e. handcrafted) by the engine developer, as opposed to discovered through training neural networks. The general approach for constructing handcrafted evaluation functions is as a linear combination of various weighted terms determined to influence the value of a position. However, not all terms in a handcrafted evaluation function are linear, such as king safety and pawn structure. Each term may be considered to be composed of first order factors (those that depend only on the space and any piece on it), second order factors (the space in relation to other spaces), and nth-order factors (dependencies on history of the position).