Notes on Material Imbalances

The chess piece values calculated from Kaufman's Material Imbalances are the latest in a long line of approximations. The history of their evolution is documented in The Value of the Chess Pieces by Edward Winter.

In the 19th century, Staunton, and later Steinitz, presented a curious set of values which seem too complicated for practical play.

In Staunton's Handbook, page 34, it is stated that some scientists have calculated the approximate mathematical value, to be as follows: Taking the pawn as the unit, the Knight is worth 3.05; the Bishop 3.50; the Rook 5.48; and the Queen 9.94.

On this basis, which in the main is in accordance with our own experience and observations, we shall proceed to indicate, in connection with the above approximate valuation, some of the most important general principles of regulating the actions of the men which we believe are now mostly accepted by the strongest masters of the day, and the knowledge of which very often enables the player to dispense with analysis, or at any rate greatly assists his calculations. • Relative Value of Pieces and Principles of Play, 'From The Modern Chess Instructor by Wilhelm Steinitz'

This was eventually simplified to the 1/3/5/9(10) system that all players learn as beginners. Skipping ahead to Kaufman's ground breaking essay, a book which predated it by a year or two was 'Secrets Of Modern Chess Strategy' by John Watson (Gambit 1998), a winner of several 'Book of the Year' awards. He underscored the evolution of thought on the value of pieces by spending one chapter in the first half of the book ('Traditional'),

Part 1: The Refinement of Traditional Theory
6: Minor-Piece Issues

and five chapters in the second half ('Modern'),

Part 2: New Ideas and the Modern Revolution
4: The Modern Bishop
5: The Contemporary Knight
6: Bishops versus Knights 1: One-on-One
7: Bishops versus Knights 2: Minor-Piece Pairs
8: The Exchange Sacrifice

Introducing the subject, he wrote,

The relative value of minor pieces stands at the core of modern chess. Time and again, superiority in the middlegame is decided by who has the better minor pieces. (p.66)

Watson also referenced another resource, 'Bishop versus Knight - The Verdict' by Steve Mayer (Batsford 1997). Kaufman noted two other essays on the subject,

• Timoshchenko, G. (1993). 'Bishop or Knight?', ICCA Journal, Vol. 16, No. 4
• Sturman, M. (1996). 'Beware the Bishop Pair' ICCA Journal, Vol. 19, No. 2

The most comprehensive treatment of imbalances to date is 'Rethinking the Chess Pieces' by Andrew Soltis (Batsford 2005), which pulls together much of the historical matter. I'll come back to this book in a future post.