If we're going to have chess matches over the internet, it behooves us to agree on a standard notation. Therefore, I will present to you here a primer for the most commonly used notation, "algebraic".
The Board
Looking at the board from white's position, the columns (or "files") are named A through H. The leftmost column then is A, and the rightmost is H. The rows (or "ranks") of the board are numbered 1 through 8, starting at the "bottom" (when looked at from white's perspective) and going to the top.
Therefore, from white's perspective, the lower-leftest square on the board is called "a1", and the upper-rightest square is called "h8".
Conversely, when looked at from black's perspective, black's lower-leftest square is "h8", and the upper-rightest square is "a1".
The Moves
The basic form of a move is, first name the type of piece being moved, and then the square to which the piece is moving. Pieces are denoted with the following codes:
King: "K"
Queen: "Q"
Rook: "R"
Bishop: "B"
Knight: "N"
Pawn: (nothing)
Ergo, moving a knight to the square f6 (a common early game move for black) is written: "Nf6". Moving a pawn requires only the destination square. Therefore, Debaser's first move in our match is written simply "e4".
If a capture takes place, an "x" is placed in between the piece and the destination square. For instance, a Queen taking a piece on the upper-left hand corner of the board would be written "Qxa1". If a pawn makes a capture, the pawn's originating column is noted, followed by the normal capture notation. Hence, if a black pawn on b6 captures a piece on c5, it is written "bxc5".
Other Stuff
A check is signified by a "+" after the move. Moving a bishop to check the other's king might be written "Be4+".
Checkmate is signified similarly by "#".
Kingside castling is written "O-O". Queenside castling is written "O-O-O".
If a pawn promotes, the promoted piece type is written after the normal move. For instance, a white pawn reaching the d8 square and becoming a Queen would be written "d8Q".
There are a few other idiosyncrasies, but we'll deal with them as they occur.
Sample Game
Here is a full, famous game from history, to demonstrate this notation in a real-world example. Bonus points to anyone who can properly identify this game. HINT: It's VERY VERY famous (among chess nerds).
1. e4 e5
2. f4 exf4
3. Bc4 Qh4+
4. Kf1 b5
5. Bxb5 Nf6
6. Nf3 Qh6
7. d3 Nh5
8. Nh4 Qg5
9. Nf5 c6
10. g4 Nf6
11. Rg1 cxb5
12. h4 Qg6
13. h5 Qg5
14. Qf3 Ng8
15. Bxf4 Qf6
16. Nc3 Bc5
17. Nd5 Qxb2
18. Bd6 Bxg1
19. e5 Qxa1+
20. Ke2 Na6
21. Nxg7+ Kd8
22. Qf6+ Nxf6
23. Be7#
Guide to Algebraic Chess Notation.
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