stronger than two rooks (ten points) or a queen (nine points). Chess-variant theorist Betza identified the 'leveling effect', which causes reduction of the value of stronger pieces in the presence of opponent weaker pieces, due to the latter interdicting access to part of the board for the former in order to prevent the value difference from evaporating by 1-for-1 trading. This explains why trading rooks in the presence of a queen-vs-3-minors imbalance favors the queen player, as the rooks hinder the queen, but not so much the minors. The evaluation of the pieces depends on many parameters. Edward Lasker said, "It is difficult to compare the relative value of different pieces, as so much depends on the peculiarities of the position...". Nevertheless, he said that the bishop and knight () are equal, the rook is worth a minor piece plus one or two pawns, and the queen is worth three minor pieces or two rooks. Larry Kaufman suggests the following values in the middlegame: The is worth a half a pawn more than the individual values of its constituent bishops combined. The position of the pieces also makes a significant difference, e.g. pawns near the edges are worth less than those near the centre, pawns close to promotion are worth far more, pieces controlling the centre are worth more than average, trapped pieces (such as ) are worth less, etc. Alternative valuations Although the 1-3-3-5-9 system of point totals is the most commonly given, many other systems of valuing pieces have been proposed. Several systems have the bishop as usually being slightly more powerful than a knight. Note: Where a value for the king is given, this is used when considering piece development, its power in the endgame, etc. Hans Berliner's system World Correspondence Chess Champion Hans Berliner gives the following valuations, based on experience and computer experiments: There are adjustments for the and of a pawn and adjustments for the pieces depending on how or the position is. Bishops, rooks, and queens gain up to 10 percent more value in open positions and lose up to 20 percent in closed positions. Knights gain up to 50 percent in closed positions and lose up to 30 percent in the corners and edges of the board. The value of a may be at least 10 percent higher than that of a . There are different types of doubled pawns; see the