Geometry and Chess

Chess is a game that relies on geometry, namely lines. The chessboard itself is composed of sixty-four alternating light and dark squares. The board can be further divided into lines, more specifically, ranks, files and diagonals. It is imperative that the beginner become intimately acquainted with these three types of lines in order to play chess well. The beginner often neglects the importance geometry plays regarding the game itself. We’ll start this introduction to the lines found on the chessboard by briefly describing each of the three, starting with the ranks.

Ranks, numbering one through eight, run to the left and right on the chessboard. The first rank starts at the bottom of the board and is where the White pieces start the game. The second rank is directly above the first and is occupied by White’s pawns. The ranks continue sequentially, with the Black pawns occupying the seventh rank and the Black’s pieces occupying the eighth rank. The board is cut in half between the fourth and fifth ranks (Whit’s side being ranks 1 through 4 and Black’s side being ranks 5 through 8). If you’re using a tournament board or mat, you’ll see the rank’s numbers printed on the left and right sides of the board.

Files run up and down the board forming columns and like the ranks, are composed of eight squares each. The files are designated by the letters “a” through “h.” The letters on a typical tournament board are found on the top and bottom edges of the board. Thus ranks run left to right and files run up and down on the chessboard. The “a” file is on the left side of the board and the “h” file is on the right side of the board.

Lastly, we have the diagonal, a line beginners often have trouble with. Simply put, a diagonal is a line of identically colored squares that are grouped together at an angle. An example of a diagonal are the eight squares of identical color that start at the a1 square and end at the h8 square. Just follow the squares; a1, b2, c3, d4, e5, f6, g7 and h8. If you’re new to the game, become accustom to each grouping of identically colored squares that makes up each of the board’s 26 diagonals.

As your chess career develops and you further study the game, you’ll come across the words “open” and “closed” in tandem with the word “line” or “lines.” Let’s take a closer look, starting with an open line:

In the simplest terms, a line (either a rank, file or diagonal) is open if there’s no pawn or piece occupying that line. In the above example, the e file is open. This brings us to an important concept the beginner must embrace, control of the open rank, file or diagonal.

If a rank, file or diagonal is open and you have the ability to take control of it, you absolutely should. In our example, the e file is completely open. The Rook on a1 is not yet activated. Remember, all you material (especially your pieces) needs to be activated early on. Therefore, activating or moving a piece to a square that allows that piece to participate in the game is crucial for victory. Thus, moving the a1 Rook to the open e file gives that Rook something important to do. What’s so important about controlling an open rank, file or diagonal? Controlling, in this case the open e file, means that the opposition (Black) has to think twice about moving any of his or her material onto that file for fear of losing that material. In our example, White, temporarily owns the e file. This brings us to a brief discussion regarding just who can control an open rank, file or diagonal as well as the terms “open” and “closed” games.

Ranks and files are eight squares in length while diagonals run from two to eight squares in length (depending on the diagonal). Note we designate diagonals by their starting and ending squares. The dark squared diagonal starting on a1 and ending on h8 is referred to as the a1-h8 diagonal (eight squares in length) while the diagonal starting on the a7 square and ending on the b8 square is referred to as the a7-b8 diagonal (two squares in length).

Again, it’s important to know just who can control these two to eight square angled lines on the board (diagonals), as well as the ranks and files. Enter our long distance attackers! For diagonals, we have the Bishop and Queen. For the ranks and files it’s the Rooks and Queen. These three pieces are the only material that can control open or semi open lines. It’s all about the long distance attackers. Whats even better about the long distance attacker is that they can control squares on the opposition’s side of the board from the safety of their own side of the board! Short distance fighters, the pawn, Knight and King, don’t have this awesome super power! So, the Rook or Queen can control ranks and files while the Bishop or Queen can control the diagonals. Notice the Queen can control all three, ranks, files and diagonals. No wonder she’s so powerful! Now to the concept of open and closed games.

There are four designations here; open, semi open, closed and semi closed games. It’s important for beginners to understand the four types of games, especially the difference between open and closed games. What’s so important about knowing these four types of games? Within a single game of chess, the position can switch from one type to another within a few moves, so knowing what each of these positions means will help the player to know what to do in a given situation. Each type of game or position requires a different type of strategical or positional thinking. Let’s start by looking at the two most basic types, open and closed games.

In an open game, the board is just that, wide open. This translates to there being a great deal of space (open or empty squares) for the pieces to not only move to but control. Thus, long distance pieces, such as the Bishop, Rook and Queen rule the board. Open games mean open space or squares devoid of pawns and pieces. In an open game you have room to attack from a distance. You also, due to long distance pieces ruling the board, have greater opportunity for tactical plays.

Closed games can be thought of as the opposite of open games. Rather than having open space where your Bishop, Rook and Queen can control the position, the board is shut down or locked up with pawns and pieces. Think of a closed game as being stuck in holiday traffic, a state of gridlock in which only a flying car would solve your problem. Long distance attackers become nearly worthless when there’s no room to move. We call “room to move” mobility is chess and a closed game or position gives our Bishop, Rook and Queen little in the way of mobility. Pieces loose their power when they lack mobility. Fortunately, we have the pawn and Knight to help us out when things are tight or closed.

I just mentioned how great a flying car would be when stuck in traffic. You could simply push a button and your car would rise above the traffic and your problem would be solved. In chess there’s a piece that can do just that and we call him the Knight! Let’s take a closer look at our best friend in a closed game or position.

The Knight is the only piece that moves and captures in a non-linear way. While its “L” shaped movement is difficult for the beginner to learn and master, it is well worth the effort to master it because the Knight has a power no other piece has, the ability to jump over other pieces (and pawns). This ability to jump over traffic on the chessboard makes it a dangerous weapon in closed games. You can see how this would be a great advantage when there’s gridlock on the board!

The pawn is another great weapon in closed games because of its low relative value. No piece is willing to stand by and let the lowly pawn capture it. Considering the pieces range in value from three to nine points, it’s no wonder that our one point friend can push away the the most power pieces! Of course, you need to make sure your little one point friend has some protection when he stands up to a piece. Pawns are a great weapon for closed games.

As for semi open and semi closed games, as beginners you can think about them in terms of positions that share the characteristics of true open and closed games. In these types of positions, use the piece that best suits the position at hand. You can use a closed game piece to open the board up a bit and then bring in your long distance pieces to attack or control lines. I’ll be going into greater detail about piece use in semi open and closed games in future articles.

For now remember, just as a mechanic or carpenter would tell you, you need the right tool for a specific job. Thus, in chess, you need the right tool to control the ranks, files and diagonals in open games and the right tool for those tight positions in closed games. I have a special wrench designed for tight places where a regular wrench wouldn’t fit in my tool kit. Don’t try and use a Rook to fix a tight position. That’s what you have the Knight for. Here’s a game to enjoy until next week. Things get a bit tight in this game but one player’s brought the right wrench, I mean piece, for the job. Enjoy.

Hugh Patterson

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About Hugh Patterson

Prior to teaching chess, Hugh Patterson was a professional guitarist for nearly three decades, playing in a number of well known San Francisco bands including KGB, The Offs, No Alternative, The Swinging Possums and The Watchmen. After recording a number of albums and CDs he retired from music to teach chess. He currently teaches ten chess classes a week through Academic Chess. He also created and runs a chess program for at-risk teenagers incarcerated in juvenile correctional facilities. In addition to writing a weekly column for The Chess Improver, Hugh also writes a weekly blog for the United States Chess League team, The Seattle Sluggers. He teaches chess privately as well, giving instruction to many well known musicians who are only now discovering the joys of chess. Hugh is an Correspondence Chess player with the ICCF (International Correspondence Chess Federation). He studied chemistry in college but has worked in fields ranging from Investment Banking and commodities trading to Plastics design and fabrication. However, Hugh prefers chess to all else (except Mrs. Patterson and his beloved dog and cat).