Explain Chess Engine Evaluation Function

Evaluation assigns a numeric score to a chess position from White's perspective (positive = White better). It runs at leaf nodes and during quiescence search. A good eval guides alpha-beta cutoffs; a bad eval makes even deep search play nonsense. Today's top engines use NNUE (Efficiently Updatable Neural Networks); learning engines still benefit from understanding classical material + PST + tapered design.

Approaches

Classical vs NNUE

Hand-crafted eval

Sum explicit terms: material, piece-square tables (PST), pawn structure, mobility, king safety. Weights tuned by humans or automated tuning (Texel tuning).

NNUE eval

Sparse neural net on piece features → hidden layer → output cp. Incrementally updated when pieces move. Trained on millions of positions. Stockfish default since 2020.

Classical stack

What Gets Summed?

Material

+900 Q

Piece-square tables

±30 cp

Pawn structure

±20 cp

Mobility

±15 cp

King safety

±40 cp

100Pawn value (cp)

320Minor piece (typical)

64Squares per PST

256Phase scale (0–256)

Tapered eval

Middlegame vs Endgame Blend

Game phase interpolates MG and EG PST values

Opening/MG (phase 256)TransitionEndgame (phase 0)

Knights worth more in closed middlegames; rooks worth more when files open. Phase = f(non-pawn material) — fewer pieces → lower phase → more endgame weights.

phase = gamePhase();  // 0 = EG, 256 = MG
score = (mgScore * phase + egScore * (256 - phase)) / 256;

Components

Key Eval Terms

♟

Material & PST

Base piece values plus per-square bonuses from lookup tables (separate MG/EG arrays). A knight on e5 scores higher than on a1.

♙

Pawn structure

Doubled, isolated, backward, passed pawns — each has a penalty or bonus. Passed pawns especially ramp up toward promotion.

♞

Mobility & space

Count legal moves or attacked squares per piece type. More active pieces → higher score. Cheap bitboard-based approximation.

🧠

NNUE (modern default)

Feature = (piece type, square, king bucket). Accumulator updated incrementally on make/unmake. Single forward pass → cp. Replaces most hand terms in Stockfish.

Term	Classical	NNUE
Material	Explicit sum	Learned implicitly
Piece placement	PST tables	Feature weights
King safety	Pawn shield, attack units	Learned from data
Update cost	O(pieces) sum	O(1) accumulator delta

Build order for a hobby engine

Start with material only — verify search plays legal chess
Add MG/EG PSTs and tapered phase — immediate strength jump
Add pawn terms and mobility when basics work
Consider NNUE only after move gen + search + TT are solid
Eval is called millions of times — keep it fast

Eval feeds search

Leaf scores drive alpha-beta, quiescence stand pat, and futility pruning.

Search Algorithm Quiescence Search Engine Anatomy

Related: Search Algorithm · Quiescence Search · All Blogs