The Chess Variant Pages

This text was written by A. Missoum. The author will appreciate when the readers of this text send him a reasonable donation for his research efforts, to his address: 101 Eddy Street, Hull, Quebec, J8X-2W3, Canada. While this text is published on Hans Bodlaender's WWW pages, this does not mean any specific support by Hans Bodlaender for Missoum's proposal of a new notation for chess.

Matrix Chess Notation

A. Missoum

The game of Chess has its origin in the SHATRANJ game . The pieces were named RUKH (ROOK), FARAS (KNIGHT), FIL (BISHOP), FIRZAN (QUEEN), SHEIKH (KING), and BAIDAQ (PAWN). The two games have many similarities, except for the FIL and FIRZAN move, the castling, the Pawn prise en passant, and the optional two squares pawn move at the start of the game, see boards (1), (2). The ancient arab chess players introduced Algebraic, Numerical and Descriptive chess notations in order to record, replay and analyze played games. Some believe that the chess GrandMaster ABU BAKR MUHAMMAD AL SULI (8 th AD) may have invented these notations beside introducing original Openings (TABIATs), Middle (WASAT)), Endgames (MANSUBATS), and many importants chess problems related to mate in TWO, THREE, FOUR, OR FIVE moves. They advised the players to commit these notations to memory. The Arabic letters T, SH, R, M, K, W, Y were associated with the chessboard files a, b, c, d, e, f, g, h, and sometimes F, S, N for a, b, c, d were substituted. The Files were identified algebraically, the rank is named by its file letter and rank number. The descriptive notation (also called english notation) was as follows: KING PAWN (BAIDAQ AL SHEIKH), QUEEN PAWN (BAIDAQ AL FIRZAN), KNIGHT PAWN (BAIDAQ AL FARAS), ROOK PAWN (BAIDAQ AL RUKH), BISHOP PAWN (BAIDAQ AL FIL), KING BISHOP (FIL AL SHEIKH), QUEEN BISHOP (FIL AL FIRZAN), CONNECTED ROOKS (RUKH AL JAMIA), CONNECTED PAWNS (BAIDAQ AL JAMIA), see board (3). While this notation is more precise, it is somehow difficult to read. For this reason the algebraic chess notation was substituted and was internationally adopted and used for chess programming. This method of recording the chess game is also known as the Coordinate or Continental chess notation. Modern chess players adopted two main versions, Full in which both departure and arrival squares are named, and abbreviated, in which the departure square is named only when essential.

BOARD(1) SHATRANJ BOARD(2) CHESS


RU

FA

FI

FZ

SH

FI

FA

RU

888888

R

N

B

Q

K

B

N

R

BA

BA

BA

BA

BA

BA

BA

BA

888888

P

P

P

P

P

P

P

P









888


















888888


















888

888


















888









BA

BA

BA

BA

BA

BA

BA

BA

888

P

P

P

P

P

P

P

P

RU

FA

FI

FZ

SH

FI

FA

RU

888

R

N

B

Q

K

B

N

R

T S B M K W Y N A B C D E F G H

Remark: I will use the letters RU=RUKH (ROOK), FA= FARAS (KNIGHT), FI=FIL (BISHOP), FZ= FIRZAN (QUEEN), SH=SHEIKH (KING), BA=BAIDAQ (PAWN) for the Shatranj game, and R=ROOK, N=KNIGHT, B=BISHOP, Q=QUEEN, K=KING and P=PAWN for the chess game. In the Shatranj, two opponent FIL can never meet each others, and because of the FIRZAN and the FIL moves, the game may take longer than the actual chess. The important pieces in the Shatranj game are the RUKH (ROOK), FIL (BISHOP), FARAS (KNIGHT), while those of the chess are the QUEEN, the ROOK, the, KNIGHT, and the BISHOP. BOARD(3)


1QR

2QR


1QN

8QN


1QB

8QB


1Q

8Q


1K

8K


1KB

8KB


1KN

8KN


1KR

8KR


2QR

7QR


2QN

7QN


2QB

7QB


2Q

7Q


2K

7K


2KB

7KB


2KN

7KN


2KR

7KR


3QR

6QR


3QN

6QN


3QB

6QB


3Q

6Q


3K

6K


3KB

6KB


3KN

6KN


3KR

6KR


4QR

5QR


4QN

5QN


4QB

5QB


4Q

5Q


4K

5K


4KB

5KB


4KN

5KN


4KR

5KR


5KR

4QR


5QN

4QN


5QB

4QB


5Q

4Q


5K

4K


5KB

4KB


5KN

4KN


5KR

4KR


6QR

3QR


6QN

3QN


6QB

3QB


6Q

3Q


6K

3K


6KB

3KB


6KN

3KN


6KR

3KR


7QR

2QR


7QN

2QN


7QB

2QB


7Q

2Q


7K

2K


7KB

2KB


7KN

2KN


7KR

2KR


8QR

1QR


8QN

1QN


8QB

1QB


8Q

1Q


8K

1K


8KB

1KB


8KN

1KN


8KR

1KR

BOARD(4) NUMERICAL NOTATION


57

58

59

60

61

62

63

64

49

50

51

52

53

54

55

56

41

42

43

44

45

46

47

48

33

34

35

36

37

38

39

40

25

26

27

28

29

30

31

32

17

18

19

20

21

22

23

24

9

10

11

12

13

14

15

16

1

2

3

4

5

6

7

8

.This notation was used by the arabs to describe the FIL, FARAS, RUKH and FIRZAN tours

The Arabs also devised the following notation related to tactic and strategy position see Board(5).


1:0

0:2

1:1

0:1

1:0

0:2

1:1

0:1

1:1

1:0

0:1

2:0

1:1

1:0

1:1

2:0

1:1

0:1

1:0

0:2

1:1

0:1

1:0

0:2

0:1

2:0

1:1

1:0

0:1

2:0

1:1

1:0

1:0

0:2

1:1

0:1

1:0

0:2

1:1

0:1

1:1

1:0

0:1

2:0

1:1

1:0

0:1

2:0

1:1

0:1

1:0

0:2

1:1

0:1

1:0

0:2

0:1

2:0

1:1

1:0

0:1

2:0

1:1

1:0

For example, the squares 2:0 in d7 indicates that white could attack twice this square, while the squares 0:1 in c3 mean that black could attack this square once. This notation can be viewedas the pieces view of the board (that is the pieces are watching the square of the board in order to occupy them) and or the board view of the pieces (that is the squares of the chessboard are watching the pieces coming to attack, or occupy them.).

Lets mention that in an ancient arab manuscript, the invention of the Shatranj (Chess) is described as follows:

# The inventor of chess made the board to represent a field of battle upon which two armies are drawn up for contest, and the six figures, Sheikh, Firzan, Fil, Faras, Rukh and Baidaq represent the six classes upon which war was turns and which are essential to it. Of these the first is the King who rules, the second the vizier who advise, the third the commander of the army who arranges, the fourth the cavalry, the fifth the fortress (Husun) and the sixth is the infantry. He represented the King by the Sheikh, the Vizier by the firzan, the commander of the army by the Rukh, the cavalry by the Faras, the fortress by the Fil, and the infantry by the Baidaqs. This is the classification of the chessmen (ALAT AL SHATRANJ. The following was his intention in the arrangement . He puts the Sheikh in the centre because the King ought to be in the heart of the army. He put the Firzan next to him because the strongest places in the battle array ought to be where King and Vizier are. He put the Faras between Fil and Rukh because cavalry ought to be at the defense of the fortresses. He put the rukh next to the Faras because the commander ought to be in command of the right and the left wings. He puts the Baidaq in a line front of these because the infantry is placed in the van of the battle. This was his intention in the arrangement of the chessmen. His intention in the arrangement of the pieces in the game was to be to a struggle and attack. He gave the Baidaq a move of one square in a straight line. Because it is not right for the foot-soldier to quit his position in battle, nor to advance except step by step. He made it take obliquely because the injury he inflicts on his enemy in the battle happens unexpectedly. He appointed that he should become a Firzan when he reached the end of the board, because a man who advances and penetrates to the enemys camp, and preserves himself from capture or overthrow, deserves the viziership in war. He gave the Faras a far reaching move, because the horsemen, being mounted, can transport himself to a distance, and can fall back to his camp when he is threatened. He made his moveas oblique one in moving forwards and backwards and in capturing, because the horsemen of necessity attacks his enemy, lance in hand, and takes him by swift and sudden movements. He gave the rukh the move in the four cardinal directions as far as the end of the lines confronting him, which is the most extended move of the pieces, because in war it is the commander of the right and the left wings who haras and burden to their utmost the enemy weaks points which are opposite to them. He made the Sheikhs move a single square in every direction, because the King is not one who should move swiftly. He is free to move at choice either forwards or backwards. The rule for the Firzan is the same, except that his liberty of move is less than the Sheikh s. When he takes, he takes according to his ward...#

(see A.J.R. MURRAY, History Of Chess )

This text gives a precise parallelism between Shatranj (Chess) and the war where cavalry, elephants, commanders, Fortresses, King and Infantry were involved.

Now after this breve historical introduction, I will introduce my Matrix Chess Notation and show its advantages over the classical algebraic chess notation

MATRIX CHESS NOTATION

Lets recall that a n x k matrix is simply a rectangular board of n columns and k rows written:

C11 C12 C13 ... C1n

C21 C22 C23 ... C2n

(C)= (Cij) 1 I N

1 J K C31 C32 C33 ... C3n

.......................................

.......................................

Ck1 Ck2 Ck3 ... Ckn

The Cij are called the components of the matrix, and they can be numbers, functions, matrices, block of matrices or else.

Example 2 5 6 7

3 4 9 1

6 2 8 4

is a 4x3 rectangular matrix and its components are numbers.

In our case, we will consider the following rectangular (or square) matrix types:

1 2 3 ... ... n-2 n-1 n


WB11

WB12

WB13

......

.....

WB1n-2

WB1n-1

WBn

WB21

WB22

WB23

....

....

WB2n-2

WB2n-1

WB2n












WBij





















WBk-11

WBk-12

WBk-13



WBk-1n-2

WB k-1n-1

WBk-1n

WB k 1

WB k 2

WB k 3



WB k n-2

Wb k n-1

Wbk n

where WBij is the ij th move of white, resp black, and W, B stand for white, resp black pieces of the chess. Now, for purely practical reasons, we will write the components WBij, 1 i n, 1 j k of the chess matrix as follows:

M S

WBij

G U

which means that at the ij th move, white moves from the squares G to M, resp black moves from the squares U to G, where G, M, U, S can be any of the chess board squares

ai, bi, ci, di, ei, fi, gi, hi, i=1,2,3,4,5,6,7,8, and W, B are anyone of the pieces K=King, Q=Queen, R=Rook, N=Knight, B=Bishop, P=Pawn

Example: f3 f8 signifies that white Knight moves from the squares g1 to f3

NB resp Black Bishop moves from squares c8 to f8

g1 c8

We will adopt the following rules:

RULE1 If at a ij th move, white, resp black have the same denomination, we will simply consider the symbol of one of the two pieces

Example: a7 d3 Means that white Rook moves from squares a1 to a7

R resp black Rook moves from sqaures d7 to d3

a1 d7

RULE2 The pawn move is simply represented by the column letter he occupies

Example: 4 5 Means that white pawn moves from squares c2 to c4

cd and black pawn moves from squares d7 to d5

2 7

5 6 Means that white pawn moves from e4 to e4, and

e Black pawn moves from e5 to e6

4 5

RULE3 If at the ij th move, White, or black, or both make a piece (pawn) capture, it will be put at the upper corner of the matrix component

Example: Pa6 Bf3 means that White Rook captures a black pawn at a6, resp

RN Black Knight captures a white Bishop at f3

d1 g1

If both side capture a pawn or a piece we will write that piece (pawn) in between the arrival squares of white and blackof the corresponding matrix component.

Example: a6 P f3 Means that white rook captures a black Pawn at a6

RN resp., black Knight captures a white Pawn at f3

d1 g1

RULE 4 We will use the following chess symbolism

! Good move, !! Excellent move, Bad move, ?? Blunder

o Kings side castling, O Queens side castling, # mate, + Check, ++ double check, 1/0 White win, 0/1 black win, 1/2 1/2 draw. !? Move of doubtful value, Ad Ad libidum, Ep en passant

Remark : in the matrix chess notation we dont use the signs x for capture, and O-O for small castling, O-O-O for the great castling.

RULE 5 We will use the following abbreviations (optional) for the well known chess openings on top of the four or five components of the matrix chess notation.

AL = ALEKHINE, BE = BENONI, BI = BIDONI, EN = ENGLISH, GN = GRUNFELD, EI = EAST INDIAN, WI = WEST INDIAN, KG = KING GAMBIT, QG= QUEEN GAMBIT, EV = EVANS GAMBIT, SG = SCOTISH GAMBIT, IT = ITALIAN, 2N = TWO KNIGHTS, 3N = THREE KNIGHTS, 4N = FOUR KNIGHTS, NE = NETHERLAND, SL = SLAVIC, RU = RUSSIAN, PE =PETROFF, NI = NIMZOVITCH, MO= MORRA GAMBIT , PI = PIRC, PH = PHILIDOR, BG = BOUGOLIAGOV, TC = TCHIGORINE, CK = CARO KAHN, VI= VIENNESE, BR = BERLIN, OR=ORTHODOX, SK = SCANDINAVIAN, RU = RUIZ LOPEZ, PA=PAULSEN, CH= SCHEVENINGE, SI= SICILIAN, DR= DRAGON, SA= SEAMISCH, LE= LETTON, FR= FRENCH, MG=MARSHALL GAMBIT, BR= BAIRD, RA= RAUSER, FA= FALKBEER, PO= PONZIANI, etc...

Now, lets consider an arbitrary chess game and apply it the algebraic and matrix chess notations. I have chosen the following short and concise chess game commented by the French chess GrandMaster and world champion ANDRE FRANCOIS PHILIDOR (1847). The algebraic notation of this game is the following

1 e4 e5 2. Bc4 c6 3. D4 e x d4 4. Qxd4 d6 5.f4 Be6 6.Bd3 d5
7. e5 c5 8. Qf2 Nc6 9. c3 g6 10 h3 h5 11 g3 Nh6 12. Nf3 Be7

13. a4 Nf5 14.Kf1 h4 15. G4 Ng3+ 16 Kg2 Nxb1 17.Kxh1 Qd7
18. Qg1 a5 19. Be3 b6 20. Na3 0-0-0 21 Ba6+ Kc7 22 Nc2 Ra8
23 Bf5 Qd8 24 b4 Qf8 25 bxc5 cxc5 26 Nd2 c4 27 Nf3 f6
28 Bb6+ Kb7 29 Bxc6 Kxc6 30 Ncd4+ Kd7 31 f5 Bg8 32 e6+ Ke8

33 Nb5 Bd6 34 Qd4 Black Resign

Philidor commented this game as follows: 3.d4 you must push this pawn twice to prevent the opponent from advancing his pawns to the center. And play d7-d5, thus attacking your bishop and gaining adavantage. If he plays d7-d5 this will totally change the game.

5...Be6 he plays this bishop to advance his queens pawn and leave space for his king bishop and may capture it. 8.... Nc6 If instead of developing this piece, he will continue to adavance his pawns, he will lose the game. In this situation, you have four pawns against his three pawns on the kings side, and three pawns against his four pawns on the queen side. The player who first will separate the pawns oh his oppoent where they are in majority will win the game.

11. g3 this move is essential because by playing h4, black will cut the communication between your pawns on the king side.

Remark : Usually, the comments follows the moves. But I preferes to write them at the bottom of the algebraic chess notation.

Now, Philidor chess game can be written in Matrix Chess Notation as follows:

-------------PH -----------------------

1 2 3 4 5 6 7


4 5

e

2 7


c4 6

Bc

f1 7


4 Pd4

de

2 5


* 6

Qd

d1 7


4 e6

fB

2 c8


d3 5

Bd

c4 6


5 5

ec

4 6


Board of

pieces

position


f2 c6

QN

d4 b8


3 6

cg

2 7


3 5

h

2 7


3 h6

gN

2 g8


f3 e7

NB

g1 f8


4 f5

aN

2 h6


f1 4

Kh

e1 5


Board of

pieces

position


4 g3

gN+

3 f5


g2 Rh1

KN

f1 g3


Nh1 d7

KQ

g2 d8


g1 5

Qa

f8 7


e3 6

Bb

c1 7


a3

NO

b1


a6 c7

+BK

d3 c8


Board of

pieces position


c2 a8

NR

a3 d8


b5 d8

BQ

a6 d7


4 f8

bQ

2 d8


Pc5

b

4 5


d2 4

Nc

f3 5


f3 6

Nf

d2 7


b6 b7

+BK

e3 C7


Board of

pieces position


N c6 B

+BK

b5 b7


d4 d7

+NK

c2 c6


5 g8

fB

4 e6


6 e8

+eK

5 d7


b5 d6

NB

d4 e7


d4

Q.

f1 1/0



Board of pieces

position

COMMENTS: 3d4 This prevent your opponent from posting the pawn at the center and with d5 he will attack your bishop. 5...Bc6 will oppose your King bishop and later captures it or he will push his King pawn and leaves space for his King bishop. 8... Nc6 If he continues to push forwards his pawns, he4 will lose the game. 10... h5 He pushes this pawn in order to prevent yours from advancing, etc...
Now what are the advantages of this matrix Chess notation over the classical algebraic chess notation. There are many.

1) The matrix chess notation is more visual than the algebraic chess notation. It is simply written as a board which directly shows the respective pieces moves of white and black.

The pieces (pawns) capture is directly seen at the upper corner of each matrix component. Hence one can have a quick idea about the material balance between white and black. For example, at the end of the first row of the matrix chess notation of Philidor game, we see that both white and black captured one pawn. So, after seven moves, there is a material balance between white and black

2) At the end of each row of the matrix is set a chess board with piece positions of white and black.(see the above matrix chess notation). This gives a direct view of the positional fighting aspect between white and black, without the need of puting the pieces on the chessboard. One can therefore analyze the played chess game from the pieces position at the end of each row (or group of seven moves ) of the matrix chess notation. Also, at any ij th move of white, resp black the player can exactly figure out the piece position of his pieces and tghose of his opponent on the chessboard. For example, at the 11 th move, it suffices to consider the board of pieces position at the end of the first row and add it the 8th, 9th, 10th and 11 th move of white resp black.

3) At the top of the left of the first row of the matrix are put the chess opening and defense types So, the player have a first idea about the opening and defense types used by white and black.

4) The reader can point any one of the matrix chess component and exactly knows the ij th move of white and black. For eample, the intersection of the fourth column and the third row of the matrix chess is the 14 + 4 = 18 th move of white, resp black.

5) The chess comments are put at the bottom of the matrix, and this will clearly distinguish between the moves and the comments. On the other hands, In the algebraic chess notation, the mixing of the moves and the comments create some confusion for the ordinary chess player.

6) Reading the algebraic chess notation is like reading a page of a roman or a book. The player has to go through all the line step by step in order to understand the game. Sometimes someone has to go more times over a same line to follow the game. This constitutes a handicap for the ordinary chess player.

7) The matrix chess notation gives a direct view of the frequency of the pieces and pawns move

Thus we directly see from the matrix chess notation, that in Philidor chess game, white used 13 times the pawn, 7 times the Bishops, 7 times the Knights, 3 times the Queen and 3 times the King, while Black used 14 times the Pawn, 4 times the Bishops, 5 times the Knights, 1 time the Rook, 2 times the Queen and 5 times the King. So, the chess battle between white and black was mainly a pawn battle as pointed by Philidor The Pawns are the soul of the game. .. Nevertheless, it must be understood that Philidor meant that the chess plan must be built for the sole promotions of the pawns, and not that the pawns are better than the pieces.

8) From the matrix chess notation, we can directly extract the matrices of pieces, or the squares used by white, resp black. This will give a more understanding of the game. Thus in Philidor game, the matrices of pieces and squares used of white are:

Pe4 Bc4 Pd4 Qd4 Pf4 Bd3 Pe5

Qf2 Pc3 Ph3 Pg3 Nf3 Pa4 Kf1

Pg4 Kg2 Kh1 Qg1 Be3 Na3 Ba6 MATRIX of pieces used

Nc2 Bf5 Pb4 Pc5 Nd2 Nf3 Bb6

Bc6 Nd4 Pf5 Pe6 Nb5 Qd4

This matrix gives an idea of the pieces view of the board ( ie the pieces watching to occopy the squares of the chess board)

e4 c4 d4 d4 f4 d3 e5

f2 c3 h3 g3 f3 a4 f1 Matrix of the square

g4 g2 h1 g1 e3 a3 a6 Used

c2 f5 b4 c5 d2 f3 b6

c6 d4 f5 e6 b5 d4 .

This matrix gives the board view of the pieces by white (i.e. the squares of the board are watching the pieces coming to occupy them, or attacking them). So, from the matrix of the pieces used, we see that white started by ocuppying e4, then opened a line for the queen by c4, then move to d4 to control the center, then start a right flank move, etc. So, a precise analysis of the game could be focused on the matrix of pieces move and the matrix of the squares used by white and black.

9) Another flexibility of the matrix chess notation is that the chess game can be seen as a game of vectors move (group of moves) instead of single moves as for the algebraic chess notation.Thus Philidor chess game can be viewed as a game of seven successive vectors moves (rows move) of white, resp black So, one can analyze Philidor game in terms of group of moves . This will add more extension of the tactic, strategy, pieces position, and the plan of the game.Thus, Philidor chess game can be seen as a game of five successive vector moves instead of 34 successive single moves: The vectors move of white can be designated by the vectors

V1 = (Pe4 Bc4 Pd4 Qd4 Pf4 Bd3 Pe5 )

V2 = (Qf2 Pc3 Ph3 Pg3 Nf3 Pa4 Kf1 )

V3 = (Pg4 Kg2 Kh1 Qg1 Be3 Na3 Ba6 )

V4 = ( Nc2 Bf5 Pb4 Pc5 Nd2 Nf3 Bb6 )

V5 = ( Bc6 Nd4 Pf5 Pe6 Nb5 Qd4 )

10) We can also partition the matrix chess notation into a matrix of matrices, or a matrix of vectors. For example, Philidor chess game cab be viewed as a matrix of four matrices of moves:

or else

A B


4 5

e

2 7


c4 6

Bc

f1 7


4 Pd4

de

2 5


* 6

Qd

d1 7


4 e6

fB

2 c8


d3 5

Bd

c4 6


5 5

ec

4 6



f2 c6

QN

d4 b8


3 6

cg M!

2 7


3 5

h

2 7


3 h6

gN

2 g8


f3 e7

NB M2

g1 f8


4 f5

aN

2 h6


f1 4

Kh

e1 5



4 g3

gN+

3 f5


g2 Rh1

KN

f1 g3


Nh1 d7

KQ

g2 d8


g1 5

Qa

f8 7


e3 6

Bb

c1 7


a3

NO

b1


a6 c7

+BK

d3 c8



c2 a8

NR

a3 d8


b5 d8

BQ N3

a6 d7


4 f8

bQ

2 d8


Pc5

b

4 5


d2 4

Nc M4

f3 5


f3 6

Nf

d2 7


b6 b7

+BK

e3 C7



N c6 B

+BK

b5 b7


d4 d7

+NK

c2 c6


5 g8

fB

4 e6


6 e8

+eK

5 d7


b5 d6

NB

d4 e7


d4

Q.

f1 1/0



C D

11) Because of the geometric properties (reflection, translations, rotations) of matrices, one can also apply them to the matrix chess notation .Thus one can apply reflections of the matrix about its diagonals, or me dian lines and read the matrix chess notation differently Thus, a reflection of the matrix chess notation about its line diagonal AD gives the new matrix notation:




d4

Q

f1 1/0


b5 d6

NB

d4 e7


6 e8

+eK

5 d7


5 g8

fB

4 e6


d4 d7

+NK

c2 c6


N c6 B

+BK

b5 b7



b6 b7

+BK

e3 C7


f3 6

Nf

d2 7


d2 4

Nc

f3 5


Pc4 Pc5 b

4 5


4 f8

bQ

2 d8


b5 d8

BQ

a6 d7


c2 a8

NR

a3 d8



a6 c7

BK

d3 c8


a3

NO

b1


e3 6

Bb

c1 7


g1 5 Qa

f8 7


Nh1 d7

KQ

g2 D8


g2 Rh1

KN

f1 g3


4 g3

QN

3 f5



f1 4

Kh

e1 5


4 f8

aN

2 h6


f3 e7

NB

g1 f8


3 h6

gN

2 g8


3 5

h

2 7


3 6

Og

2 7


f2 c6

QN

d4 b8



5 5

ec

4 6


d3 5

Bd

c4 6


4 e6

fB

2 c8


Pd4 6

Qd

d1 7


4 Pd4

de

2 5


c4 6

Bc

f1 7


4 5

e

2 7


This is simply the backward play of Philidor chess game. Reading backward the chess game gives more understanding of the game .

12) From the matrix chess notation one can read the chess game row by row, column by column, from bottom to top, or top to bottom, left to right or right to left.

13) Since each component of the matrix chess notation is simply the addition of a ij th move of white and black to the previous i-1, j-1 th moves, then the matrix chess notation can be viewed as a matrix of positions for white, resp black

P11 P12 P13 P14 ... P1 n-2 P1 n-1 P1n

P21 P22 P23 P24 ... P2 n-2 P2 n-1 P2n

P31 P32 P33 P34 ... P3 n-2 P2 n-1 P3n

................................................................................

................................................................................

Pk1 Pk2 Pk3 Pk4 Pk n-2 Pk n-1 Pkn

Where each Pij 1 i n, 1 j k Is the ij th position of white respectively black pieces. One can therefore write computer programs which when one clicks on a ij th component of the matrix chess notation, this will automatically gives the associated ij th pieces position of white, resp black . Thus Philidor chess game can be seen as the matrix of positions:

P12 P12 P13 P14 P15

P21 P22 P23 P24 P25

P31 P32 P33 P34 P35

P41 P42 P43 P44 P45

P51 P52 P53 P54 P55

So, one can switch on and off from chess matrix components to pieces position on the chessboard and vice versa. We can write computer programs to switch from the matrix of pieces moves to the matrix of squares used by white and black. Also, Now, each board position Pij of the matrix of positions can be seen as a vector V= (CP, IP, SP, DP, GB, BB, GN, BN, SK, UK, CS, UC, OL, OD, SP, TE, DV, CR, PN, QC, etc...) where CP =Connected pawns, IP= Isolated pawns, DP = Doubled pawns, GB = Good bishop BB= Bad bishop, GN= Good Knight, BN = Bad Knight, SK= King secure, UK= King unsecure CS= Castling, UC= Uncastling, OL= Open line, OD=Open diagonal, SP=Space of manoeuvring UP= Not manoeuvring space, TE= Tempo, DV= Piece development, CR = Connected rooks, Posting Knight, Queen centralization, etc then the matrix of pieces position on the chessboard can be converted into a matrix of matrix blocks where each position Pij is itself a matrix block. This will add more understanding and interpretation of the played chess game.

Lets mention that modern approach on tactic and strategy ( STEINIZ ) consider:

Motivated attack based on a number of favorable characteristics which they justify it.

More freedom of manoeuvring, Center occupation or control, vulnerable position of the opponent King, Weak points (squares, lines and diagonals), Better pawn structures, majority of pawns on wing sides, good bishops and Knights, Bad bishop and Knights, Connected Rooks, Centralization, posting pawns, matrial adavantage, overprotection, blocus, prophylaxis,..

Principle of accumulation, an attack is motivated only and only if the position is superior to the opponent, and when it become imparative to convert the plus values into effect. If both sides have balanced positions, wait and multiply the plus values to provocate the balance rupture into an advantage.

The reader could practice applying the matrix chess notation to this following game

1 e4 c6 2 d4 d5 3 exd5 c x d5 4 Bd3 Nc6 5 c3 Nf6 6 Bf4 Bg4 7 f3 Bh5 8 Ne2 e6
9 Nd2 Bd6 10 Bg3 Qc7 11 Nb3 Bg6 12 Rc1 Bxd3 13 Qxd3 0-0 14 Bxd6 Q x d6
15 0-0 Rfe8 16 Ng3 g6 17 Rce1 Rac8 18 Re2 Nb8 19 a4 Nfd7 20 a5 Qa6

21 Qxa6 bxa6 22 Ra1 Rc7 23 Nc1 Rec8 24 Nd3 Rb7 25 Ra3 Nc6 26 Nf1 Rb5
27 b4 Nd8 28 Ne3 Rbb8 29 Kf2 Nb7 30 Nc5 Ndxc5 31 bxc5 Nd8 32 f4 Nc6 33 Ng4 Rb1
34 Ne5 Nxe5 35 f x e5 Kf8 36 Ke3 Rcb8 37 Rf2 Ke7+ 38 Rc2 Kd7 39 Raa2 Ra8

40 Kd3 Rd1+ 41 Rd2 Rc1 42 Rac2 Rcb1 43 Rf2 Ke7 44 c6 Rb8 45 c4 Rb3 +
46 Rc3 d x c4 47 Kxc4 Rb4 48 Kd3 Re8 49 Ke3 Rb5 50 Ra2 Rf8 51 g4 Kd8
52 c7+ Kc8 53 Rf2 Rxa5 54 Rc6 Ra3+ 55 Ke4 Kd7 56 Rxf7+ Kxc6 57 Rxf8 Kxc7
58 Rf7+ Kd8 59 Rxh7 g7 60 Rg7 Ra2 61 Rxg5 Rxh2 62 Rg8+ Kc7 63 Rg6 a
64 Rxc6 Kb7 65 Rf6 Rg2 66 e6 Rxg4+ 67 Ka5 Kc7 68 Rf7+ Kd8 69 Rxa7 Rh4 70 Kc5 Black resign

SULTAN KHAN (1905-1966). He was born in the PUNJAB (India) and he learned chess at the age of nine. In 1929 we won the all championship of India. Then in London he won the British championship. Then he started to defeat many leading Chess GrandMasters. He came second after Tartakover and third after Capablanca in the Hasting tournament (1931). Later he left Europe to India where he remained for the rest of his life. Capablanca called Sultan Khan a genius. Here follows a chess game between Sultan Khan and Flohr (Caro-Kahn defence).

Now we can rewrite this game in matrix chess notation as follows:

14) Another advantage of the matrix chess notation is that we can also apply it to the chess descriptive notation as follows: Consider the following Capablanca-Fine chess game: written in descriptive chess notation

1P-Q4 N-KB3 2 P-QB4 P-K3 3N-QB3 P-Q4 4.B-N5 QN-Q2 5.P-K3 B-K2 6.N-B3 P-B4 7.PxQP BpxP 8.QxP PxP 9B-N5 O-O 10.KBxN BxB 11.BxN BxB 12QxQP Q-B1 13.N-Q4 R-Q1 14.O-O B-B3 15.Q-QB5 B-K1 16.Qx Q QrxQ 17.KR-Q1 P-KN3 18.N/4-K2 K-B1 19.RxR RxR 20R-Q1 RxR ch 21 NxR K-K2 22 N/1-B3 B-N2 23 N-Q4 K-Q3 24 K-B1 K-B4 25N/4-K2 K-B5 26 K-K1 K-Q6 27 K-Q1 BxN1! 28 NxB B-B3 29 N-K2 B-R sch! 30 P-N3 B-B3 31 P-KR4 P-B3 32 N-B4ch K-B6 33 K-B1 P-KN4! 34 PxP PxP 35 N-K6 BxP 36 NxP P-KR4! 37 K-Q1 P-R5 38 K-K2 P-R6 39 P-B3 P-R7 40 N-K4ch P-R7 41 N-B2 P-R8/q 42 NxQ K-B6 44 P-K4 K-Q5 45 P-R3 P-R4 46 P-R4 P-N3 47 K-N3 K-K8 48 P-K5 BxP black resigns

This game can be written in matrix chess notation as follows:

1 2 3 4 5 6 7 8


Q4 B3

PN


B4 K3

P


B3 Q4

NP

Q


N5 Q2

BQ

Q


K3 K2

PB


B3 B4

NP


P

(PB)

Q P


P

(QP)


N5

Bo


N B

(B)


N B

(B)


P B1

x Q

Q


Q4 Q1

NR


B3

oB


B5 K1

QB

Q


Q

(Q)

R


Q1 N3

RP

K K


K B1

NK

4


R

(R)


Q1 R

Rx


R K2

xNK


B3 N2

NB


Q4 Q3

NK


B1 B4

K


K2 B5

NK

4


K1 Q6

K


Q1 N

KBx


B B3

xNB


K2 R5

NB+


N3 B3

PB


R4 B3

P

K


B4 B6

+ NK


B1 N4

KP!

K


P

(P)


K6 P

Nbx


P R4

xNP!

K


Q1 R5

KP


K2 R6

KP


B3 R7

P


K4 N5

+NP


B2 Q

NP

R8


Q N

(NB)


B2 B6

K


K4 Q5

PK


R3 R4

P


R4 N3

P


N3 K8

K


K5 P

PBx

In conclusion : The matrix chess notation possesses many advantages over the classical algebraic chess notation.


Written and copyright by A. Missoum. The author appreciates some reasonable donations for his research efforts to send to his address: 101 Eddy Street, Hull, Quebec, J8X-2W3, Canada.
Converted to html by Hans Bodlaender. Apologies for the less than perfect format: this was a wordperfect file, read into Word, then converted from Word format to html, and then edited, both in html-code and by using Netscape Gold.
WWW page created: January 26, 1997.