and threatening to promote. When there is about fourteen points of material on both sides, the value of pawns on any file is about equal. After that, wing pawns become more valuable. C.J.S. Purdy gave a value of points in the opening and middlegame but 3 points in the endgame. Shortcomings of piece valuation systems There are shortcomings of giving each type of piece a single, static value. Two minor pieces plus two pawns are sometimes as good as a queen. Two rooks are sometimes better than a queen and pawn. Many of the systems have a 2-point difference between the rook and a , but most theorists put that difference at about points (see ). In some open positions, a rook plus a pair of bishops are stronger than two rooks plus a knight. Example 1 Positions in which a bishop and knight can be exchanged for a rook and pawn are fairly common (see diagram). In this position, White should not do that, e.g.: 1. Nxf7 Rxf7 2. Bxf7+ Kxf7 This seems like an even exchange (6 points for 6 points), but it is not, as two minor pieces are better than a rook and pawn in the middlegame. In most openings, two minor pieces are better than a rook and pawn and are usually at least as good as a rook and two pawns until the position is greatly simplified (i.e. late middlegame or endgame). Minor pieces get into play earlier than rooks, and they coordinate better, especially when there are many pieces and pawns on the board. On the other hand, rooks are usually blocked by pawns until later in the game. Pachman also notes that the is almost always better than a rook and pawn. Example 2 In this position, White has exchanged a queen and a pawn (10 points) for three minor pieces (9 points). White is better because three minor pieces are usually better than a queen because of their greater mobility, and Black's extra pawn is not important enough to change the situation. Three minor pieces are almost as strong as two rooks. Example 3 In this position, Black is ahead in material, but White is better. White's queenside is completely defended, and Black's additional queen has no target; additionally, White is much more active than Black and can gradually build up pressure on Black's weak kingside. See also Chess endgame has