# Value is a Relative Term

One of the most fundamental ideas taught to beginners is also the idea that is most maligned by those very same beginning players! What is this greatly maligned idea? The relative value of the pawns and pieces! As a chess instructor, I introduce this concept early on in my student’s chess education. While I make a point of defining the word “relative,” its definition is often lost not only on young beginners but adult beginners as well. Children will gleefully announce that they are winning because they have more of their opponent’s material (more “relative” points). Adults, on the other hand, know that the only way to win a game of chess is to checkmate the opposition’s King. However, they fall prey to subconsciously replacing the word “relative” with the word “absolute.” This means that they look at a pawn or piece’s value in absolute terms rather than in relative terms, Absolute pawn or piece value means that the unit by which we measure a pawn or piece’s worth is unchanging. This can lead to mechanical thinking which will can lead to loss. Let’s start our exploration of this subject by defining the matter at hand.

The relative value of the pawns and pieces is just that, a fluctuating approximate value. It’s a simple system that allows a player to assign a numerical value to the pawns and the pieces for book keeping purposes. The pawn is the base unit used in this system, with a relative value of one. Take a look at the table below (the King is considered priceless for obvious reasons so it’s not included):

Unit Value Number of Pawns
Pawn 1 1 Pawn
Knight 3 3 Pawns
Bishop 3 3 pawns
Rook 5 5 Pawns (or two pawns and a minor piece)
Queen 9 9 Pawns (three minor pieces or two minors and three pawns)

It’s no coincidence that that more powerful the piece, the higher it’s relative value. This system of valuation greatly helps the beginner when attacking and defending. If attacking, you wouldn’t trade a nine point Queen for a three point Knight unless checkmate was the outcome. It would be akin to walking up to someone and trading \$9.00 for \$3.00. Relative pawn and piece value serves as a guide for the chess novice, giving them a scale upon which to weigh the potential outcome of either side of an exchange. However, it has a dark side. That dark side is considering these values as absolute or written in stone!

Take the pawn, for example. The pawn has a relative value of one. Beginners tend to consider the pawn expendable since there are eight of them at the game’s start and they’re only worth one point each. What the beginner fails to understand is that this numerical value of “one” can greatly increase under certain circumstances. For example, a pawn one move away from being able to freely promote (not subject to capture) into a Queen would have to be worth more than one point. A pawn that delivers checkmate must be numerically greater than its counterparts elsewhere on the board. The same holds true for Knights and Bishops.

Both the Knight and Bishop have an approximate relative value of three points. Both these minor pieces have their own very different way of moving. The Knight is slow and, because of the way it moves, can take a greater number of moves to reach a position that’s just a square or two away. The Knight has that special ability to jump over other pieces which makes it very powerful in certain types of positions. The Bishop, on the other hand, can travel great distances in a single move. Its primary drawback is that it can only travel diagonally along either the light or dark squares. Therefore, each Bishop can only cover 32 of the 64 squares on the board (not all at once). Thus, we have two pieces that move in very different ways yet still share the same approximate value, three points each. The value of these two pieces can change depending on the type of game you’re playing. What do I mean by “type of game?”

Chess games can be either open, semi open, closed or semi closed games. To keep things simple, we’ll look at open and closed games, examining how the relative value of the Knight and Bishop fluctuate depending on the type of game being played. When I explain open and closed games to my beginning students, I keep it very simple: In an open game, there’s a lot of open space on the board, giving pieces the freedom to move around and control a lot of territory. With all that open space, the Bishop can control a larger number of squares than the Knight, having the ability to shoot across the board and capture unsuspecting pawns and pieces. The Bishop is much more powerful than the Knight in an open game since the Knight still has to go through a longer sequence of moves to get from one side of the board to the other. A closed game is one in which both side’s pawns and pieces are crammed into a position that shuts down any potential for immediate long distance attacks. The Bishop often becomes a “Bad Bishop” because it’s blocked in by its own pieces or opposition pieces. The Knight, on the other hand has the ability to jump over pawns and pieces that stand in the way of our friend the Bishop. Therefore, in a closed game, the Knight has a greater value than the Bishop. Many Chessamaticians (chess players that also love mathematics) assign a slightly higher relative value to the Bishop in an open game and the Knight in a closed game. In an open game you might consider the Bishop to be worth four points and the Knight three points. In a closed game, the Knight could be worth four points and the Bishop three.

Where beginners get into trouble early on is with mechanical thinking. The mechanical thinker will think of the relative value of the pieces as absolute. The mechanical thinker doesn’t consider that a pawn or piece’s value changes as the position on the board changes. To get my students to think “outside the box” and avoid mechanical thinking, I have them increase the relative value of their pawns and pieces based on the position. For example, when I start playing through a game during my lecture, I ask my students how many points the Rooks, Bishops and Queen are worth. They become very surprised when I announce that, on their starting squares (hemmed in by their own pawns) the Rooks, Bishops and Queen are worth nothing! How can that be? The answer is simple. These pieces are trapped on their starting squares and can do nothing until they have access to the board. Therefore, until they have access to the board, they have no immediate or relative value (Knights can enter the game immediately so their value is three points from the start). After white plays 1.e4, for example, the Queen and King-side Bishop have access to the board so their value is activated.

The point I’m trying to make with my students is that pawns and pieces only have a real value when those pawns and pieces are actively participating in the game. A Rook sitting on its starting square isn’t active and, while it might have a relative value of five points, that assignment of value is pointless unless the Rook partakes in the game. When you start looking at pawn and piece value in relationship to position and activity, you start playing better chess. Here’s a game to play through. Here’s your homework: Play through this game and see if the pawns and pieces for both sides increase and decrease as the game plays through based on what you now know about relative value. Enjoy!

Hugh Patterson

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