diagram. White's doubled pawns on the b-file are the best situation in the diagram, since advancing the pawns and exchanging can get them un-doubled and mobile. The doubled b-pawn is worth 0.75 points. If the black pawn on a6 were on c6, it would not be possible to dissolve the doubled pawn, and it would be worth only 0.5 points. The doubled pawn on f2 is worth about 0.5 points. The second white pawn on the h-file is worth only 0.33 points, and additional pawns on the file would be worth only 0.2 points. Changing valuations in the endgame As already noted when the standard values were first formulated, the relative strength of the pieces will change as a game progresses to the endgame. Pawns gain value as their path towards promotion becomes clear, and strategy begins to revolve around either defending or capturing them before they can promote. Knights lose value as their unique mobility becomes a detriment to crossing an empty board. Rooks and (to a lesser extent) bishops gain value as their lines of movement and attack are less obstructed. Queens slightly lose value as their high mobility becomes less proportionally useful when there are fewer pieces to attack and defend. Some examples follow. A queen versus two rooks In the middlegame, they are equal In the endgame, the two rooks are somewhat more powerful. With no other pieces on the board, two rooks are equal to a queen and a pawn A rook versus two minor pieces In the opening and middlegame, a rook and two pawns are weaker than two bishops; equal to or slightly weaker than a bishop and knight; and equal to two knights In the endgame, a rook and one pawn are equal to two knights; and equal to or slightly weaker than a bishop and knight. A rook and two pawns are equal to two bishops. Bishops are often more powerful than rooks in the opening. Rooks are usually more powerful than bishops in the middlegame, and rooks dominate the minor pieces in the endgame. As the tables in Berliner's system show, the values of pawns change dramatically in the endgame. In the opening and middlegame, pawns on the central files are more valuable. In the late middlegame and endgame the situation reverses, and pawns on the wings become more valuable due to their likelihood of becoming an outside passed pawn