# Three questions on GM Larry Kaufman's article about the average relative value of the chess pieces [closed]

I have three questions related to this article written by GM Larry Kaufman: https://www.chess.com/article/view/the-evaluation-of-material-imbalances-by-im-larry-kaufman

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Question n°1: Kaufman rounded all his results to the nearest quarter... But what are the exact results Kaufman obtained?

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Question n°2:

The average value of either knight or unpaired bishop came out about 3.14 pawns. This value is a bit depressed by the inclusion of endings with no other pieces, as in such endings the bishop is worth only about 2½ pawns and the knight even less, partly because the minor piece side cannot win if its last pawn is exchanged. As long as there are other pieces on the board (so minimum mating material is not a major issue), the minor piece is worth about 3¼ pawns.

He calculated the average values of the minor pieces and got 3.14 pawns. Then he calculated the average values of the minor pieces but by excluding some endings and got 3.25 pawns. And then he disregarded the true average values of the minor pieces, and instead he prefered to take the average values of the minor pieces with excluding some endings... Why? Being unable to win because of insufficent material is a part of the game, so I think it should be taken into account into the average values of the minor pieces.

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Question n°3:

There is some differences between the best values for humans and the best values for computers... [...] For human players:

• Knight = 3.5
• Bishop (unpaired) = 3.5
• Rook = 5.25
• Two Bishops = 7.5
• Queen = 10

What is he talking about? Firstly the values he had previously calculated were calculated using games made by humans only, not computers. Secondly his new values "for human players" are too inflated (if we compare them to other approximations of the pieces made by other people). So I see no reason to say that the previous values were actually for computers (a statement which seems to be simply false), and to therefore inflate all of them by +0.25.

• Your three separate questions should be three separate questions. Commented Jul 12, 2014 at 6:22
• The results he got are interesting but of no real value. The relative "value" of pieces has been known for a long time. The effect of board position is to make digits to the right of the decimal point meaningless. Sometimes, values to the left of the decimal point become fluid too! Commented Jul 12, 2014 at 12:03