By WIM Alexey Root
Would you want to trade $9 for $3? How about giving up $9 to get $5 back? If your answer to those questions is "no" in real life, then it should be "no" in chess too. In chess, each piece and pawn has a point value. That value should be considered when you trade one "chessman" for another.
We will discuss how those values are determined. This article will focus on the bishop, the rook, and the queen, and the knight, pawn, and king article is next.
The average mobility of a chessman on an empty board determines its point value. Mobility means the number of squares that a chessman can move to legally. The higher the average mobility, the higher the point value of the chessman. Mathematical calculations of mobility are in the first comment to this blog posting. The comment was by a 12-year-old boy, which shows that you can be good at math (and at chess) when you are young.
A bishop has a point value of 3 because it is more mobile than a pawn but less mobile than a rook (5 points) or a queen (9 points). Let's think about why a bishop is less mobile. A bishop will never cover more than 32 squares on the board, because it always travels on just one color of square. In the corner, on an empty board, the bishop may move up to 7 squares. In the center, the bishop may move to 13 squares. Count for yourself in the diagram below.
The bishop on h1 can move to g2, f3, e4, d5, c6, b7, or a8. The bishop on e5 can move to f6, g7, h8, d6, c7, b8, d4, c3, b2, a1, f4, g3, or h2. Bishops are more powerful in the center.
But it's not just center placement that matters to bishops. Bishops also like open diagonals to move on, or they are less mobile. In the next diagram, which would you rather have, white's bishop on e5 or black's bishop on f8?
If you answered white's bishop on e5, you are correct. Black's bishop on f8 is a bad bishop, hemmed in by its own pawns. The f8-bishop has almost no value in this position. Let's switch gears and look at white's rook on g1. Compare white's rook to black's rook on h8. The black rook can move to g8. It can also move to h7, but then it would be taken by white's pawn on g6. It has almost no mobility and is a worthless piece for black. In contrast, the white rook on g1 can move to many squares and is very valuable to white.
Generally speaking, the typical value of a rook is 5 points (5 pawns). But, as you saw in the previous diagram, some rooks are better than others! One interesting fact about the rook is that, on an empty board, it can always move to 14 squares. The rook is the only piece that is just as mobile along the corner or edge of an empty board as in the middle. Try it and see!
Since a queen can move like a rook or like a bishop on any given move, you might expect that her point value would be that of a bishop (3) plus that of a rook (5). But she is worth 9 points. Why would that be? Remember that a bishop can only move to 32 squares. The queen, in contrast, can cover all 64 squares on a board. Her mobility and the fact she has combination powers (bishop and rook) make her more valuable. She is truly a superwoman.
In this article, we learned the values of three of the pieces.
A bishop is worth 3 points (3 pawns).
A rook is worth 5 points (5 pawns).
A queen is worth 9 points (9 pawns).
But we also learned that these point values are based on the average mobility of these chessmen on an empty chessboard. In real life, boards are not empty. There may be pawns blocking the open lines (diagonals and files) on which bishops, rooks, and queens love to move. So if your bishop, rook, or queen is blocked in particular game, you may want to trade it off. A non-mobile piece is worth less than its normal value. Just like a dollar is not worth a dollar if there is inflation, but that's a story for your economics class!