IntroductionThe purpose consisted in creation of such initial position (opening setup) in Chess games with extra pieces (for example, Archbishop and Chancellor) where following conditions were satisfied: 1. Protection of pawns should be symmetrical on a vertical and on a horizontal lines of the board, 2. Each pawn must be covered, 3. Three consistently located squares have to be differently filled, 4. All rules of Classical Chess would remain without changes, 5.Using in the game a new piece (distinct from pieces in Classical Chess) which can diversifies combinational motives, 6.Proceeding from the fact, that for greater boards with a lot of pieces it is not desirable to increase density of power lines, for this reason the following condition was satisfied: the number of free squares of a board is more than number of pieces.
As in many Chess games it is not reached. For example - Capablanca Chess, Bird Chess, Carrera Chess and so on.
Setup - Third row (8th row for the Black): P - Pawns; second row (9th row for the Black): R - Rook, N - Knight, B - Bishop, U - Unicorn (an imaginary creature usually depicted as a white horse with one horn growing from its forehead). This name is taken from David Paulowichs "Unicorn chess" and will well coordinate with another Western names of the Symchess pieces, because the name "Camel" from Tamerlane Chess does not approach to these Western names, Q - Queen, K - King (White King is located on a dark square), U - Unicorn, B - Bishop, N - Knight, R - Rook; first row : A - Archbishop(d1), C - Chancellor(g1). The Black pieces are "mirror image" to the White pieces.
p p p p p p p p p p / R N B U Q K U B N R / . . . A(d1) . . C(g1) . . .
As is known a King is the most important piece of a Chess game. Considering special propensity of ancient people to the well-known number 0.618 (golden section) , it is clear why a King is always located on one square in the right from the middle of a board. As 0.6/1 (width of a board) = 0.6. Obviously this number approximately is equal to the 0.618. It is natural, that we have not changed this "ancient tradition".
PiecesPieces - P, R, B, N, A, C, Q and K - wellknown pieces. The Unicorn (U) has a kind of stretched Knights move: it jumps one diagonally and two stright, so e.g. from a1 to b4 or d2, from d2 to g1, g3, e5, c5, a3 and a1, and so on. As a Knight, U is not obstructed by pieces standing on passed squares. U - has moved like the Camel from Tamerlane Chess. It is only piece which is very dangerous for all pieces on Symchess set, because A, C, Q, N, B and R could not moves like U. For example, "Unicorn Fork" - in empty board U(g2) may attack any pieces A, C, Q, N, B, R and K which located on squares f5, h5, j3, j1, d1 or d3. On the contrary, in this position opponent`s pieces could not attack U. It is looks like "Knight Fork" against Q, R, B, and K. The Unicorns has properties of the Bishops that can moves on white or black squares only. The Chancellor - has the combined moves of a Rook and a Knight. The Archbishop - has the combined moves of a Bishop and a Knight.
RulesThe game follows the Standart Chess rules without exceptions. Castling like Capablanca Chess in the second ( 9th row for the black ) row and the Pawns may be promoted to Archbishop, Chancellor and Unicorn also.
Figure 1. Symchess general view ("Mirror image" symmetry)
Notes"The perfect symmetry is required to completely minimize the starting advantage of White" - Derek Nall.
All Pawns are protected from a3 to j3 like this: 2 1 1 4 3 3 4 1 1 2 and it is a symmetrical setup like Classical Chess (1 1 1 4 4 1 1 1). Arrangement of the Unicorns - closer to the center is more effective so they from the very beginning of game influence the central fields e5 and f5. Also they can quickly pass to defense by translation on a1 and j1. Presence of a free horizontal in rear of the King raises resources of defense, that enables retreat of the King at powerful attacks by the adversary. It is an abstract wargame, with no random chance. Initial position of the game it is well balanced (the power lines of pieces are symmetric also does not differ from Classical Chess). The square board has advantage above rectangular one (for example, 10x8; 14x8 and so on), because the square board has the sentral symmetry to an average point of board but rectangular has not and also the rectangular board sharply reduces influence of pieces in comparison with a square board. In Figure 2 shows an evaluation the total influence of all pieces on each square of an empty board.
...the nature of the ground is the fundamental factor in aiding the army to set up its victory - Sun Tzu "Art of War"
Figure 2. Total Influence
Figure 2 clearly illustrates that the center is the most powerful place to locate pieces. The four corners are the safest places to locate the King since they are the least accessible squres on the board. The influence of pieces on a square board is symmetric. On strength U is little bit weaker than a Knight. Because, N influence on the all board more than U. Approximately U = 0.9N.
Symchess has following advantages above Classical Chess:
1. The quantity of various types of positions increases, for example: for Classical Chess maximum quantity of positions is 13 in a degree 64; for Symchess - 19 in a degree 100, 2. The large square board (10x10) and new pieces A, C, U allow to receive new and interesting Chess endings, for example: A vs C; U vs N and so on, 3. Presence of last empty horizontal line (the line 1 for White; the line 10 for Black) increases resources of defense, 4. In Classical Chess a King has "one line of pawns" for defense, but in Symchess a King has "extra line of pieces " for defense in addition,
It is necessary to note, that the given arrangement of pieces has universal character. Because, changing moves of an Unicorn it is possible to receive various symmetric variants of a game*.
If to look more closely to opening setup of many Chess games, it is possible to notice undistinguished but exclusively important distinction. Concerning an average horizontal line the Black pieces are "mirror image" to the white pieces (or a line symmetry). The "mirror image" does left by right, upwards by a bottom and so on. For this reason, White King is located on a dark square against Black King which is located on a light square. Thus a Black Army automatically become "a mirror double" to a White Army. It is impossible to put an equal-sign between them. They are strongly differ by the nature. The central symmetry stand above in comparison with linear symmetry and also is more aesthetic. For example, well-known East game Go has the central symmetry. Or the ancient (and modern) Tamerlan Chess has the central and mirror symmetry simultaneously. And it is not vain, old East proverb says: "Common people play renju, Chess is game of heroes (generals), Go is reserved for Gods".
A figure is called centrally symmetric with respect to a single point if, on a reversal with respect to it, it covers itself.
For the maximal equalizing of a game, and reduction of advantage of the first move to a minimum "line symmetry" or "mirror symmetry" of opening setup must be changed to a "revolving symmetry" or "central symmetry".*
Figure 3. Symchess opening setup (Central symmetry)
The start position for both Army is absolutely symmetrical, from the point of view of mathematics. All double pieces are located on the squares of same color. The midpoint of central symmetry is located between squares e5, f5 and e6, f6. The Basic condition of Chess games: "contenders should have equal opportunities before game", it is the basic axiom. Reciprocal symmetric moves for Black are not possible. For example 1.f3-f5 e8-e6, 2. f5-e6 .... Symmetry is broken. In a Classical Chess this axiom is not carried out and for this reason playing with White pieces have enormous advantage, because opening setup has a mirror symmetry and reciprocal symmetric moves for Black lead them to fast defeat. In Figure 4 are shown another variant of opening setup. This variant has been offered by Sam Trenholme.
Pawns protection: 2 1 1 2 5 5 2 1 1 2
In view of principle of 'exception of two identical pieces in one number from three squares' is possible to offer 2 more variants of initial position in Symchess.(In view of preservation of the order R,N,B,Q,K,B,N,R).
0 0 0 0 0 0 0 0 0 0 / U R N B Q K B N R U / . . . A(d1) . . C(g1) . . . (I variant)
0 0 0 0 0 0 0 0 0 0 / R N U B Q K B U N R / . . A(c1) . . . . C(h1) . . (II variant)
First of them can be rejected from aesthetic reasons (normal castling impossible). The second has lack. Total of protection of pawns - it is minimal(2x4+2x3+6x1=20). Opening setup from Symchess and Sam Trenholmes` variant for Symchess are the optimal because, the total sum of protection of pawns is maximal (=22) and also all pawns are protected symmetrically.
A P P E N D I X
Below, graphic representations of used pieces are shown:
- Queen; - King; - Bishop; - Knight; - Unicorn; - Chancellor; - Archbishop; - Rook; - Pawn; - Fil.
For the best strategic and tactical planning of a game, it is possible to take advantage of following power dependences between pieces:
Q = R + B > C = R + N > A = B + N > R > B > F = N > U = 2-2.5P
It is the shortest "fool mat" in Symchess found by David Paulowich. 1. g5 - f7 2. Kg3? - Qg7 3. Qf2?? - Qxg5 checkmat!
* - for example, Symchess with The Fils. Pawns protection: 1 1 1 3 3 3 3 1 1 1
Figure 5, Symchess with the Fils.
The Fil (F) move like King or leaps two squares diagonally and orthogonally. In this case Fil = Rook. Complicated version of Symchess are shown in Figure 6.
Figure 6, Super Version of Symchess
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By Namik Zade.
Web page created: 2006-03-20. Web page last updated: 2006-03-20