Material

Royal Game, Woodcuts Art by Elke Rehder, Stefan Zweig The Royal Game IV↩︎

Material,
a term determined by the sum of piece values of each side. The material value is the most influential part of the evaluation. Usually it is the sum of a constant value for each piece present, measured in units of a fraction of a pawn, for instance the common centipawn scale, which allows positional features of the position, worth less than a single pawn, to be evaluated without requiring fractions but a fixed point score.

Contents

Basic Piece Values

Piece relative values concerning their relative strength in potential exchanges based on human experience and learning

Other Material Considerations

In chess, it is known that certain material features provide an advantage, such as the bishop pair (which might be worth as much as half a pawn). A program might increase the values of rooks when there are less pawns on the board or prefer knights when there are many pawns. Larry Kaufman performed statistical tests on a variety of different material configurations to approximate their values ¹ .

Other factors that affect material evaluation might be:

Bonus for the bishop pair (bishops complement each other, controlling squares of different color)
Penalty for the rook pair (Larry Kaufman called it "principle of redundancy")
Penalty for the knight pair (as two knights are less successful against the rook than any other pair of minor pieces)
decreasing the value of the rook pawns and increasing the value of the central pawns (though this can be done in the piece-square tables as well)
Trade down bonus that encourages the winning side to trade pieces but no pawns ²
Penalty for having no pawns, as it makes it more difficult to win the endgame
Bad trade penalty as proposed by Robert Hyatt, that is penalizing the material imbalances that are disadvantageous like having three pawns for a piece or a rook for two minors.
Elephantiasis effect as suggested by Harm Geert Muller (meaning that stronger pieces lose part of their value in presence of weaker pieces)

Insufficient Material

Using values like these blindly can lead to bad play. Most programs uses special code or tables to detect drawn or likely drawn material combinations. For example, KB vs K is a draw, as is KN vs K and KNN vs K. There is also a class of almost-certain draws, not mentioned in the FIDE rules because of the possibility of a checkmate (KN vs KN ³ , KB vs KN, KNN vs KB, KBN vs KB, KBN vs KR etc.) A general rule that, although not perfect, catches many likely draws is that if one side has no pawns left, it needs the equivalent of +4 pawns more material to win. For example, KRN vsv KR is usually a draw, where KRR vs KBN is usually a win for the rook side. For more details see draw evaluation and interior node recognizer.

Material Balance

The Material Balance is finally returned as the almost most dominating evaluation term, usually in Negamax from side to move's point of view, and in its pure form simply the difference of both sides material, MD:

md := material[side_2_move] - material[side_2_move ^ 1];

As mentioned, other material considerations, concerning insufficient material and material imbalances (e.g. rook versus two minor pieces, queen versus two rooks or three pieces, three pawns versus piece) should be taken into account - for instance to encourage exchanging pieces but no pawns if ahead, see the hashing approach of Chess 4.5.

Hashing and Tables

To save speed in the material evaluation, programs using rules often hash the material evaluation scores. With precomputed arrays of material values, this is not needed.