Polygon

POLYGON Kosintsev I.G. (20.09.2009)

PREFACE Polygon is a class of a board abstract strategy for 2 and for 4 players with universal rules and with universal set of pieces as a result of a synthesis of classical, Japanese and China chesses, as an inevitable evolution to a more perfect, interesting and complex game. Polygon for 2 players includes three games with two basic variations (East and West): 1. Mini Polygon (similar to the classical chess or to Heian shogi 平安将棋 with 8x8 board). 2. Middle Polygon (similar to Grand chess with 10x10 board). 3. Great Polygon (similar to Chu shogi 中将棋 with 12x12 board). There is also X-Polygon (with 12x12 board) for 4 players. In agree with principals of honor and justice are removed the notion of check, checkmate, stalemate, drawn. This is very important for beginners and stimulates an attention of players and an uncompromised struggle.

BASIC RULES OF PLAY Article 1: The nature and objectives of the game The nature and objectives of the game Polygon

1. The game Polygon is played between two opponents who move their pieces alternately on a square board called `Polygon`. The player with the white pieces commences the game. A player is said to `have the move`, when move of his opponent has been ’made’. 2. The objective of each player is to capture the king of his opponent. The player who achieves this goal has won the game. The opponent whose king has been captured has lost the game. The nature and objectives of the game X-Polygon

1. The game X-Polygon is played between four opponents who move their pieces alternately on a square board called a `Polygon`. Four sets of different coloured pieces (of the blue king, of the red (pink) queen, of the green king and of the yellow queen) are needed to play this game. Players can only move their pieces on their turn at the same order (blue, red, green, yellow). The player with the blue pieces commences the game. A player is said to `have the move`, when move of his previous opponent has been ’made’. When on the board remain a marriage and an opposite pair of a king and a queen, the order of the movements is changed to such: marriage, king, marriage, queen and so on for all next moves. When on the board remain two marriages, the game is transferred to Polygon for two opponents (pairs). If two pairs are defined before a game the blue king play with the yellow queen and the green king play with red queen. 2. The objective of each player is to capture the pair of a king and a queen or marriage of his opponents, if he is not at alliance with one from them. Any two players (a king and a queen) achieved this goal first (solitude or at marriage) have won the game. When on the board remain a marriage and one king or a marriage and one queen (with or without other pieces), the marriage players won the game. When a marriage has captured another marriage, it won the game. The two opponents whose king and queen (marriage) have been captured or have been remained without possible pair have lost the game. 3. There is the rule of untouchables. When on the board remains a king without second one and with two queens (with or without other pieces) nobody can capture him. When on the board remains a queen without second one and with two kings with other pieces a king can only capture her. 4. When a king has captured or a queen has captured without marriage all pieces of this color are removing from the board and their turn is simply omit. In the case of a marriage is the color of pieces of the queen player changed to color of the king. Article 2: The initial position of the pieces on the Polygon 2.1. The board is composed of an 8x8 grid of 64 equal squares for Mini Polygon, of a 12x12 grid of 144 equal squares for Middle Polygon and for Mini X-Polygon, of a 16x16 grid of 256 equal squares for Great Polygon and for Middle X-Polygon, of a 20x20 grid of 400 equal squares for Great X-Polygon, alternately light and dark. The board is placed between the players in such a way that the near corner square to the right of the player is light. At X-Polygon is the near corner square of the queen’s player light.

a) for Mini Polygon (used at the classical chess) d t g k b p v f F

V

P

B

K

G

T

D

b) for Middle Polygon (used at Grand chess) n m d t g k b p v F F

V

P

B

K

G

T

D

M

N

c) for Great Polygon and for X-Polygon (used at Canadian checkers) r L n m d t g k b p v F F

V

P

B

K

G

T

D

M

N

L

R

2.2. The vertical columns of squares (A, O, E, I, F, V, P, B, K, G, T, D, M, N, L, R) are called `files`. The horizontal rows of squares (a, o, e, i, f, v, p, b, k, g, t, d, m, n, l, r) are called ranks`. A straight line of squares of the same color, touching corner to corner, is called a `diagonal`. 2.3. At the beginning of the game Polygon every player has 16 pieces of one color for Mini Polygon, correspondently 30 pieces of one color for Middle Polygon, 48 pieces of one color for Great Polygon. At the beginning of the game X-Polygon every player has 16 pieces of one color.

The set of pieces of any one color is presented at a following table:

Symbol Piece

Quantity of pieces of one color at the beginning of the game Polygon 8x8

10x10

12x12

X-Polygon 12x12

12x12

12x12

1

Grenadier

2

Soldier

8

12

12

12

12

7

3

Corporal

2

12

12

12

12

3

4

Sergeant

8

8

4

4

5

Adjutant

4

4

4

4

6

Lieutenant

2

2

2

2

7

Major

2

2

2

2

8

Colonel

2

2

2

2

9

Brigadier

2

2

2

2

10

General

2

2

2

2

11

Marshal

1

1

1

1

12

Bishop

2

2

13

Cardinal

2

2

14

Queen

15

King

16

Marriage

Sum

3

2 2 1

2 2 1

1 1

1

1

1

1

16

30

48

48

51

16

Symbols 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 (with the sign “-” for black pieces) can be any different pictures (pictograms).

2.4. The initial position of the pieces on the Polygon board is as follows: a) for Mini Polygon d

-8

-3

-6

-10 -15 -6

-3

-8

t

-2

-2

-2

-2

-2

-2

-2

-2

v

2

2

2

2

2

2

2

2

f

8

3

6

15

10

6

3

8

F

V

P

B

K

G

T

D

g k b p

b) for Middle Polygon n

-9

-8

-7

-6

-10 -15 -6

-7

-8

-9

m

-3

-3

-3

-3

-3

-3

-3

-3

-3

-3

d

-2

-2

-2

-2

-2

-2

-2

-2

-2

-2

p

2

2

2

2

2

2

2

2

2

2

v

3

3

3

3

3

3

3

3

3

3

F

9

8

7

6

15

10

6

7

8

9

F

V

P

B

K

G

T

D

M

N

t g k b

c) for Great Polygon (three variants) r

-9

-8

-7

-6

-10 -11 -15 -10 -6

-7

-8

-9

L

-4

-4

-4

-4

-5

-5

-5

-5

-4

-4

-4

-4

n

-3

-3

-3

-3

-3

-3

-3

-3

-3

-3

-3

-3

m

-2

-2

-2

-2

-2

-2

-2

-2

-2

-2

-2

-2

b

2

2

2

2

2

2

2

2

2

2

2

2

p

3

3

3

3

3

3

3

3

3

3

3

3

v

4

4

4

4

5

5

5

5

4

4

4

4

F

9

8

7

6

10

15

11

10

6

7

8

9

F

V

P

B

K

G

T

D

M

N

L

R

R

-9

-8

-7

-6

-10 -11 -15 -10 -6

-7

-8

-9

L

-4

-4

-5

-5

-12 -13 -13 -12 -5

-5

-4

-4

N

-3

-3

-3

-3

-3

-3

-3

-3

-3

-3

-3

-3

M

-2

-2

-2

-2

-2

-2

-2

-2

-2

-2

-2

-2

B

2

2

2

2

2

2

2

2

2

2

2

2

P

3

3

3

3

3

3

3

3

3

3

3

3

V

4

4

5

5

12

13

13

12

5

5

4

4

F

9

8

7

6

10

15

11

10

6

7

8

9

F

V

P

B

K

G

T

D

M

N

L

R

d t g k

D T G K

r

-9

-8

-7

-6

-10 -11 -15 -10 -6

-7

-8

-9

L

-4

-4

-5

-5

-12 -13 -13 -12 -5

-5

-4

-4

n

-3

-3

-3

-3

-3

-3

-3

-3

-3

-3

-3

-3

m

-2

-2

-2

-2

-2

-2

-2

-2

-2

-2

-2

-2

d

-1

-1

-1

t g k

1

1

1

b

2

2

2

2

2

2

2

2

2

2

2

2

p

3

3

3

3

3

3

3

3

3

3

3

3

v

4

4

5

5

12

13

13

12

5

5

4

4

F

9

8

7

6

10

15

11

10

6

7

8

9

F

V

P

B

K

G

T

D

M

N

L

R

d) for Mini X-Polygon r

1 4

8

3

2

2

6

8

15

l

8

1 0

3

2

2

6

1 0

8

n

6

6

3

2

2

3

3

3

m

2

2

2

2

2

2

2

2

b

2

2

2

2

2

2

2

2

p

3

3

3

2

2

3

6

6

v

8

1 0

6

2

2

3

1 0

8

f

1 5

8

6

2

2

3

8

14

F

V

P

B

M

N

L

R

d t g k

K

G

T

D

Article 3: The moves of the pieces 3.1. It is not permitted to move a piece to a square occupied by a piece of the same color. If a piece moves to a square occupied by a piece of the opponent the latter is captured and removed from the board (Polygon) as part of the same move. A piece is said to attack a piece of the opponent if the piece could make a capture on that square according to Articles from 3.2 to 3.12. Positions can’t be the same before and after one move. 3.2. There are two different ways of moving of the grenadier: a) The grenadier (1) may move to any unoccupied adjoining square (F) (“March”).

F

F

F

F

1

F

F

F

F

b) The grenadier (1) may remove from the board (Polygon) itself and all pieces at all adjoining squares(X).

X

X

X

X

1

X

X

X

X

3.3. There are two different ways of moving of the soldier: a) The soldier (2) may move to the unoccupied second square (F) along the file, the rank or a diagonal on which it stands (“March”).

F

F

F

F

2

F

F

F

F

b) The soldier (2) may move to any adjoining square (X).

X

X

X

X

2

X

X

X

X

c) When a soldier (2) reaches the edge of the board furthest from the starting position of pieces of this color it must be exchanged as part of the same move for a new general (10) of the same color. This exchange of a soldier for general is called `promotion` and the effect of the new piece is immediate. This rule acts at X-Polygon only for pieces of the marriage. If a soldier is already at furthest from both starting position edge of the board at moment when the king captures a queen it is also promoted immediately.

3.3. The corporal (3) may move to one of the sixteen squares (X), not near then a second square along the file and the rank and not far then a second square along the file or the rank.

X

X

X

X

X

X

X

3

X

X X

X

X X

X

X

X

3.4. The sergeant (4), adjutant (5) may move to first, second and third square (X) along the file, the rank or a diagonal on which it stands.

X

X X

X

X

X X

X

X

X

X

X

X

X

4 5

X

X

X

X

X X

X

X

X X

3.5. The lieutenant (6), major (7) may move to any square (X) along a diagonal on which it stands. X

X X

X X

X X

X 6 7

X

X

X

X

X

X

X

X

3.6. The colonel (8), brigadier (9) may move to any square (X) along the file or the rank on which it stands. X X X X X

X

X

X

8 9 X X X X

X

X

X

X

3.7. The general (10), marshal (11) may move to any square (X) along the file, the rank or a diagonal on which it stands. X

X X

X X

X

X

X

X

X

X

X

X

X

X

X

10 11

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

3.8. There are two different ways of moving of bishop and cardinal: a) The bishop (12), cardinal (13) may move to first, second and third unoccupied square (F) along the file, the rank or a diagonal on which it stands (“March”).

F

F F

F

F

F F

F

F

F

F

F

F

F

12 13

F

F

F

F

F F

F

F

F F

b) The bishop (12), cardinal (13) may capture (remove from the board) the opponent piece arranged at first, second and third square (X) along the file, the rank or a diagonal without the motion

X

X X

X

X

X

X

X

X

X

X

X

12 13

X

X

X

X

X

X

X

X

X

X

X

X

3.9. When making these moves the soldier, sergeant, lieutenant, colonel, general and bishop cannot move (X) over any intervening pieces (Z) but the adjutant, major, brigadier, marshal and cardinal may move (M) over one intervening piece (Z). Z Z

Z Z

Z

Z M M

X X

X

X

X

X

X

Z

O

Z

X

X

X

X Z M

M

M

M

Z M M

This rule for East variation is changed at West variation so: the adjutant, major, brigadier, marshal and cardinal can move also as a corporal instead the possibility to move over one intervening piece, i.e., the adjutant (5) moves as both a sergeant (4) and a corporal (3), the major (7) moves as both a lieutenant (6) and a corporal (3), the brigadier (9) moves as both a colonel (8) and a corporal (3), the marshal (11) moves as both a general (10) and a corporal (3), the cardinal (12) moves as both a bishop (13) and a corporal (3).

3.10. There are two different ways of moving the queen: The queen (14) may move to any unoccupied adjoining square (F).

F

F

F

F

14

F

F

F

F

b) The queen (14) may move to the unoccupied square (F) along the file or the rank on which it stands over row of intervening pieces (S) of the same color (“Jumping”).

F S F

S

14

S

S

F

S S S F 3.11. There are two different ways of moving the king, by: a) The king (15) may move to any adjoining square (X).

X

X

X

X

15

X

X

X

X

b) When a king (15) captures a queen the latter is removed from the board (Polygon) and the king must be exchanged as part of the same move for a new piece “marriage” (16) of the same color. This exchange of the king is called `marriage` and the effect of the new piece is immediate.

c) The king (15) may move to the unoccupied square (F) along the file or the rank on which it stands over row of intervening pieces (S) of the same color (“Jumping”).

F S F

S

15

S

S

F

S S S F

3.12. The marriage (16) may move to any adjoining square (X).

X

X

X

X

16

X

X

X

X

Article 4: The completion of the game The completion of the game Polygon. 1. The game is won by the player who has captured the king of the opponent. This immediately ends the game. 2. The game is won by the player whose opponent declares he resigns. This immediately ends the game. 3. The game is won by the player with the black pieces when on game board only two pieces (kings) remain and neither player can capture the king of the opponent with next move. The game is said to end in a `primitive position`. This immediately ends the game. 4. The game is won by the player with the black pieces if any identical position has appeared on the game board at least three times. 5. The game is won by the player with the black pieces if each player has made at least the last 30 consecutive moves without any capture. The completion of the game X-Polygon. 1. The game is won by the players who has captured pare of a king and a queen (marriage) of his opponents. This immediately ends the game. 2. When on the board remain a marriage and one king or a marriage and one queen (with or without other pieces), the marriage players won the game. 3. The game is won by players whose opponents declare their resign. This immediately ends the game. 4. The game is won by the players with the green pieces when on game board only two pieces (marriage) remain and neither player can capture the marriage of the opponent with next move. The game is said to end in a `primitive position`. This immediately ends the game. 5. The game is won by the alliance of the player with the green pieces if any identical position has appeared on the game board at least three times. 6. The game is won by the alliance of the player with the green pieces if each player has made at least the last 30 consecutive moves without any capture.

Article 5: Coordinate Polygon notation Algebraic notation is the most widely used method for recording the moves of a board game. One of its variants, "long algebraic notation", is the official standard used in all recognized international competition involving human players. Every move is signed by own formulas for every player: Piece (number) - get piece square (file, rank) – put piece square (file, rank). Here is an example of the simple games in that notation

a) for Mini Polygon Move

Player 1 (white pieces)

Player 2 (black pieces)

2 KvKb 2 KbBk 10 KfKd

2 KtKk 2 KkBk

1 2 3 Result

1-0

The final position:

d

-8

-3

-6

-10 10

-6

-3

-8

t

-2

-2

-2

-2

-2

-2

-2

g k

-2

b p v

2

2

2

2

2

2

2

f

8

3

6

15

6

3

8

F

V

P

B

G

T

D

K

b) for Middle Polygon: Move

Player 1 (white pieces)

Player 2 (black pieces)

2 GpGk 2 GkKg 3 GvDb 10 GfGn

2 GdGg 2 GgKg 3 GmDt

1 2 3 4 Result

1-0

The final position: n

-9

-8

-7

-6

-10 -15 -6

-7

-8

-9

m

-3

-3

-3

-3

-3

-3

-3

-3

-3

-3

d

-2

-2

-2

-2

-2

-2

-2

-2

-2

-2

p

2

2

2

2

2

2

2

2

2

2

v

3

3

3

3

3

3

3

3

3

3

f

9

8

7

6

15

10

6

7

8

9

F

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t g k b

c) for Great Polygon: Move

Player 1 (white pieces)

Player 2 (black pieces)

2 TbKg 3 TpDk 5 TvTk 5 TkTd 11 TfTr

2 TmKt 3 TnDd 5 TlTd 2 GmTd

1 2 3 4 5 Result

1-0

r

-9

-8

-7

-6

-10 -11 11

-10 -6

-7

-8

-9

L

-4

-4

-4

-4

-5

-5

-5

-4

-4

-4

-4

n

-3

-3

-3

-3

-3

-3

-3

-3

-3

-3

-3

m

-2

-2

-2

-2

-2

-2

-2

-2

-2

-2

d

-2

t

-2

g

2

k

-3

3

b

2

2

2

2

2

2

2

2

2

2

2

p

3

3

3

3

3

3

3

3

3

3

3

v

4

4

4

4

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5

5

4

4

4

4

F

9

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d) for X-Polygon Move 1 2 3 4 5 Result

Player 1 (blue pieces)

Player 2 (red pieces)

Player 3 (green pieces)

Player 4 (yellow pieces)

2 BbGb 3 PpKb 3 VpBk 2 BpKp 10VvRr

2 BmGm 3 PnPd 10 VlGt 10 GtBk

2 MmTm 3 NnDm 10 LlDd 10 DdDg

2 MbDb 3 NpDp 2 DbDg 10 LvFr

1-0-0-1

The final position: 1 0

2

6

l

2

6

n

2

r

2

m

3

8

10 8

3

3

2

2

2

2

2

2

6

6

d t

1 0

g k b

2

p

3

v

8

f

1 5 F

2

2

3

2

2

3

2

6

2

2

3

8

6

2

2

3

8

14

V

P

B

M

N

L

R

K

G

T

D

8

Coordinate notation is similar to algebraic notation except that no abbreviation or symbol is used to show which piece is moving. It can do this without ambiguity because it always includes the square from which the piece moves as well as its destination. It has proved hard for humans to write and read, but is used internally by some game-related computer software

Positions are usually signed, using the list of formulas for every piece, and shown as diagrams (images). Article 6: The Polygon qualification system Polygon League (PL) is an international organization that connects all Polygon players around the world and acts as the governing body of international Polygon competition. PL is split into four divisions: Mini, Middle, Great and X divisions correspondently to Mini, Middle, Great Polygon and X-Polygon. The unique personal number of player at one division define own qualification (strength) of player which depend directly from results of official (rating) games. The less number mean the greater strength. Champion has the number one. A more subtle issue is related to pairing. 1. Challenger always plays at Polygon by white pieces, acceptor by black. At X-Polygon plays always men-challenger by blue pieces, women-challenger by red pieces, men-acceptor by green pieces, women-acceptor by yellow pieces. 2. Any player can challenge another player only one class higher or same class. 3. If and only if the player with low number loses a game, players exchange own personal numbers. 4. If a player don’t play N weeks (repose) own number are increased on 2 power N-1 every week with adequate reduces numbers other players. 5. One player has not the right to play successive more then twelve official (rating) games with one opponent. All players are divided on fourteen classes as can you see at next table. The number of players at one class K is basis B in power K, where B can be 2,3,4,5 and so on. B is 4 for our case and can increase with growing number of registered players. Nobody can be a member of two classes at once. Class of player Champion 1 2 3 4 5 6 7 8 9 10 11 12 Beginner

Title King or Queen Cardinal Bishop Marshal General Brigadier Colonel Major Lieutenant Adjutant Sergeant Corporal Soldier Grenadier

Numbers of players 1 2-5 6-21 22-85 86-341 342-1365 1366-5461 5462-21845 21846-87381 87382-349525 349526-1398101 1398102-5592405 5592406-22369621 22369622 and so on

Quantity of players 1 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 other

This game is recommended for study at school as part of mathematics. That will increase inevitably the intellectual level of a society. External links: 1. Chess. http://en.wikipedia.org/wiki/Chess 2. FIDE Laws of Chess. http://www.fide.com/component/handbook/?id=124&view=article 3. FIDE. http://en.wikipedia.org/wiki/FIDE 4. Shogi Variant. http://en.wikipedia.org/wiki/Shogi_variant 5. Shogi Vault. Comprehensive Guide to Advanced Shogi. http://www.shogi.sakura.ne.jp/ 6. Shogi Variants. http://trout.customer.netspace.net.au/ 7. Xiangqi. http://en.wikipedia.org/wiki/Xiangqi 8. Elo rating system. http://en.wikipedia.org/wiki/Elo_rating_system