(1) Special attention be given to the use of the Cannon, Vao and Leo in chess compositions.The Cannon (Pao), Vao and Leo (Chinese line pieces) are fairy chess pieces that move exactly like the orthodox Rook, Bishop and Queen respectively, but to capture must hop over one piece of either color. Instructional examples and composed problems are presented below to demonstrate their tactical potential. I have tried to make these problems entertaining in themselves. Four criticisms of orthodox (European) chess are discussed, and it is argued that a free placement version of chess could overcome these criticisms and eventually sustain more interest than orthodox chess.
(2) A new version of chess be developed which (i) allows some "free placement" of units, (ii) abandons castling
and double pawn moves, and (iii) incorporates the Cannon, Vao and Leo into the game.
CONTENTS:
1. The
Chinese Pieces: Cannon, Vao, Leo and Mao
2. Problems
and Endgame Studies with Chinese Line Pieces
3. Critique
of Orthodox Chess.
4. Free
Placement Chess.
5. Contact,
Links and References.
DIAGRAMS:
INSTRUCTIONAL
EXAMPLES: 1. The
Cannon, Vao, Leo and Mao 2. Triple
check
PROBLEMS
AND ENDGAME STUDIES:
3. Mate
in three 4. Mate
in three 5. White
draws 6. White
wins 7. Mate in
three 8. Helpmate
in two
9. Series
mate in four (2) 10. Mate
in three (3) 11. Mate
in two 12. Mate
in two 13. Mate
in three
FREE PLACEMENT CHESS:
A & B. Burmese
Pawn Placements.
The Cannon moves like an orthodox rook along a rank or file, but to capture must hop over one piece of either color (the "frame") and continue on the line beyond until encountering an opposing piece. This piece is then removed from the board and the Cannon occupies its square.
The Vao moves like a Bishop, but to capture must (like the Cannon) hop over a piece of either color.
The Leo combines the movement
and capturing of the Cannon and Vao, just as the orthodox Queen
combines the powers of the Rook and Bishop.
The Mao
moves to and captures on squares a Knight's move away, but
accomplishes this in two steps: (i) a one-step orthogonal move to an unoccupied
square, and (ii) a one-step move on an outward diagonal from that
square. Its move is not sufficiently distinct from that of the Knight
to justify their both being present in a game. Further, the unblockable
move of the orthodox Knight is to be preferred over the Mao, since it
distinguishes the Knight in a useful and pleasing way from line pieces.
The following
lists all possible moves and captures by the Chinese Pieces in Diagram
1.
White Cannon a1. Moves to a2 through a8. Captures on
c1.
White Vao b1. Moves to a2, d3. Captures on h7. It
can not move to c2 because this would put the white King in check.
Black Cannon c1. Moves to c2, c3, c4, d1. Captures
on a1.
Black Mao e1.
Moves to c2+, d3+. Captures on f3. It can not move to g2 because it is
blocked on f1.
Black Leo f1. Moves to e2, d3, c4+, b5, a6, f2, g1,
g2, h3. Captures on f7.
I have designed this example so that it is a simple
problem as well. In a "helpmate" Black cooperates with White to produce
a checkmate of the black King as soon as possible. So, from a game
perspective, Black makes the worst possible moves. The convention is
for Black to play first in a helpmate. So for this position, can you
"helpmate in one move"? This means Black makes a certain move that
allows White to checkmate on the next move.
The "Cannon" was introduced into Chinese Chess (Xiangqi) in the ninth century after artillery had been used in wars (Li, p. 222). The "Chariot" in Xiangqi moves and captures like an orthodox Rook, and the Cannon also moves like a Rook when "deployed." But to capture (fire), the Cannon must employ a "frame" (a piece of either color), and the action then extends on the line beyond the frame. The Mao (Horse) was also present in early versions of Xiangqi.
Apparently neither the Vao (called an "Arrow" by Fergus Duniho) nor the Leo were ever used in a chess variant, Asian or otherwise, until recently. The Chinese pieces were introduced into Western "Fairy Chess" problems by T. R. Dawson around 1914 (Dickins). In problem literature a Cannon is usually referred to as a "Pao," which is Dawson's rendering of the Chinese word for Cannon, and he made up the words "Vao" and "Leo." I prefer "Cannon" since the terms "Pao, Vao, Leo, Mao" are singsong and easy to confuse, and "Pao" starts with a "P" as does "Pawn."
If new pieces are to be added to orthodox chess,
the Chinese line pieces (Cannon, Vao, Leo) are a logical choice. In
earlier experiments I thought the "Lion" was preferable. This piece
both moves and captures as the Leo captures. The Lion proved to be a
terror in the opening but a tethered lamb in an endgame. By contrast
the Leo is always a mobile piece, though much weaker than an orthodox
Queen. The "Grasshopper" moves and captures like the Lion except only
to the one square immediately beyond the frame piece. Thus it is a much
weaker piece than even the Lion. It has been very popular in fairy
chess problems, usually appearing in considerable numbers. This may be
due more to fashion than function, but in any case it is too immobile
to add much interest as a game piece. The "Nightrider" may make
repeated Knight moves along a single direction. It too has been very
popular in problems, but children have enough trouble learning how a
Knight moves to ask them to master the Nightrider. Few other powerful
fairy pieces seem suitable for use in a "near-orthodox" game, perhaps
with the exception of the "Aldarider" (moves like a Queen except that
it hops over every other square, occupied or not). Surely the Chinese
line pieces are leading candidates to be added to orthodox chess, and
to learn one is to learn all three. They do not capture as they move,
but this is not a total breach of orthodoxy since the trait is shared
by the Pawn.
The Chinese line pieces (CVL = Cannon, Vao, Leo) have the following characteristics:
With both a Cannon and
orthodox Pawns on the board the oddity of a triple check (on three
different lines) becomes possible. With an en passant capture the
Cannon can check on the rank of the capturing pawn. In Diagram 2
Black's last move can be deduced ("retrograde analysis"). It could not
have been with the King. The only possibility would be Kc6 - b6, but on
c6 there is a double check by the Pawn on b5 and Vao on h1 that White
could not have produced with one move. Likewise Black could not have
played Pawn c6 - c5 since there would have been an impossible double
check by the Bishop on d4 and Cannon on d6. Thus the position must have
arisen by White checking with the Bishop on d4 and Black replying c7 -
c5. White can now play b5 x c6, en passant, which produces a triple
check and mate. With free placement we will argue that double pawn
moves (and hence en passant capture) should be abandoned. A. Legal Initial PositionsFor all the compositions below one can proceed as if they were just orthodox positions with Chinese pieces added. Thus any Pawns present on the second rank can move two squares forward (Option #1). Allowing Pawns to appear on the first or last rank would be a useful convention for composing. A case can be made that promotion to a dummy Pawn should be allowed in orthodox chess. This would be a slight simplification of the rules, and would probably not effect the outcome of
(1) Each side has one King and any number of Pawns, Rooks, Knights, Bishops, Queens, Cannons, Vaos, or Leos, as long as all the pieces fit on the board.
(2) All positions are allowed unless they imply a check has been ignored. Thus Pawns may be on the first or last rank. Multiple Pawns can be lined up on a single file without implying a capture. It is not required that the initial position be derivable from some standard position by a sequence of legal moves.
B. Legal Moves
(1) All the moves of orthodox chess and Chinese line pieces are allowed except for double Pawns moves (and hence en passant capture) and castling.
(2) A Pawn can "promote" to an immobile unpromotable Pawn.
C. Options
(1) Orthodox Pawns are stipulated.
(2) The only fairy pieces that are present are Cannons.
(3) The board is 10x10.
I have used Alybadix,
a chess problem solving program designed by Ilkka Blom, to check direct
mate, helpmate and series problems below. "Fairybadix" is the component
of Alybadix that accommodates fairy pieces (over 220) and fairy
conditions. The Windows interface for Alybadix (APwin, developed by P.
H. Wiereyn) was used to produce the diagrams. The endgame studies were
not checked by computer - please report any errors. Links to the
solution of each problem appear next to the diagrams. The diagram is
repeated on its solution page. You may use any of the text and
diagrams. Please retain credits.
Diagram 3 presents a "direct mate" problem: The
moves alternate with White playing first. White must find the move on
his first turn (the "key") that results in a checkmate in the
stipulated number of moves, regardless of the defenses chosen by black.
So for this problem White must checkmate on his third move. An
additional, unintended first move by White which also solves the
problem is called a "cook." With the availability of problem solving
computer programs, direct mate problems are rarely unsound now. A
common way to designate that a diagram represents a direct mate in n
moves is by the symbol "#n".
SOLUTION
Another direct mate in three moves.
The usual specifications for an endgame study are
for white to win or to draw, but not in a fixed number of moves. To
"win" means White obtains a clear material advantage, perhaps
checkmates in some lines, or arrives at a position known in the
literature to be a win. The specification to draw means that there are
sufficient exchanges that neither side can force a win, perhaps White
or Black is stalemated in some lines, or a position can be forced to
recur. The use of fairy pieces in endgame studies is much less frequent
than their use in direct mate and helpmate problems.
SOLUTION
Diagram 6 illustrates the use of a
Chinese piece, here the white Vao on c2, to modify an existing
composition. The pawns here are orthodox (option 1 above). Thus the
black pawn on h7 can move to h5. The original study by Holzhausen and
Sohege appears on the solution link.
In memory of Kate Wolf.
SOLUTION
Many published problems with fairy pieces are
"helpmates," in which Black and White cooperate to achieve a mating
move by White. It is conventional for Black to move first, and for
Black moves to be listed first in transcribing a solution. Thus in
Diagram 8, Black moves first, the players alternate moving, and White's
second move is a checkmate. Since there is no variational play in a
helpmate, it has become conventional in two move helpmates for there to
be two or more thematically related solutions.
SOLUTION
In a "series mate" only white makes moves, without any checking until
the final move which must be a checkmate. Here Problem 1 is the
diagram. For Problem 2 replace the Cannon with a Rook. The mating
position in Problem 2 is more elegant and may have been anticipated.
SOLUTION
SOLUTIONOrthodox chess is vulnerable to criticism on the following points.
The rise of chess playing computer programs makes "memorization" a serious threat to orthodox chess as a game of wits. In the humiliating 1997 match victory of "Deep Blue" over then world champion Gary Kasparov, the huge opening repertoire of the computer was decisive (Chess Life, p. 45). Granted the best tactical chess players often excel at opening theory, and innovation in the opening demands a high order of creativity. But such praise can not apply to Deep Blue, which won the sixth and final game of the match by the automated retrieval of an opening variation. Does it speak well of chess that this capability is such an important factor in determining who wins?
Computers will Dominate.
A recent
tabulation lists 15 chess programs having a rating of over
2600. Shredder 7.04 was highest at 2726. There are only about 100
players in the world with a rating of over 2600. So already
the typical club player has virtually no chance against many chess
playing programs. One source
claims that the top 200 players in the world are holding their own
against the robots in the last three years. Perhaps, but just another
doubling of chip speed could reverse that. Computer domination of
competitive chess is already a fact. And think of the temptation to
cheat in human tournaments by using a concealed or remote computer.
There are too many draws at high levels of
play.
Whatever game is being played, it is difficult to prevent the
combatants from prematurely agreeing to a draw. But even without
connivance, chess at the highest levels is subject to excessive draws.
In the 23 world championship matches from 1951 to 2000 the draws
numbered 321 out of 492 games (link),
or 62 percent. In the 1986 match between Karpov and Kasparov 40 of the
48 games were drawn.
Certain rules are unnecessary.
It is reasonable to judge that one set of rules is more "simple" than
another if it employs fewer words. Another criterion, more important
but more difficult to measure, would be how easy it is to learn a set
of rules. It is appealing to play a game under the simplest possible
rules that enable typical play.
The most arbitrary and difficult to learn rules of
orthodox chess describe (1) the initial placement of the pieces, (2)
castling, (3) en passant capture. Of course an adult masters these
rules after a few hours of study and playing. But they are not so easy
for children, who if unsupervised may play for years and still place a
Queen on the wrong color, or not know about en passant capture. All
three of these rules are unnecessary if free placement is implemented.
Orthodox chess, with its fixed initial position, is unlikely to be independently invented, as by an extraterrestrial civilization. By contrast, the Asian game Weiqi (Go) has such simple rules that there may be many alien civilizations that play the same game. Further support for this conjecture derives from the Weiqi symbolism of flood control (Li, p. 140).
Over the years there have been many suggestions to allow shuffling the positions of the major pieces in orthodox chess behind the line of Pawns on the second rank. One such proposal, involving randomization, was made by former world chess champion Bobby Fischer (Chess Life, p. 531). In this proposal castling is awkwardly maintained, as if it were an essential feature of chess. But if we allow all the pieces, including Pawns, to be placed freely within some "home territory" (such as the first three ranks), we at once make castling unnecessary since the King can be placed in a secured location on the side of the board. Free placement also removes the motivation for permitting a double first move by Pawns since they can start out on the third (or fourth) rank. Pawns might also be placed on the first rank for defensive purposes.
In recent years variants have been proposed that permit some freedom of placement. In "Free Programme Chess" the units are placed in turn anywhere in one's half of the board. The Kings are placed first. Pawns may be placed freely but can not be doubled or placed on the first rank. They retain the double move from the second rank. Bishops must be placed on opposite colors (Pritchard, p. 20). A master level tournament was held using these rules in Tbilisi, Georgia in 1995. Some free placement chess variants can be found on The Chess Variant Pages (for example, the variant called "Free Placement"). We suspect that the best game will result from free placement with restrictions. Just deciding what home territory should be is not easy. Murray (p. 454) claimed that early experiments "in which the pieces were rearranged so as to be more nearly in contact at the commencement of play," did not survive because with the advent of a much more powerful Queen and Bishop the forces were too close together. But if so, the forces can simply be moved apart one or more spaces, alternately employing straight pawn lines or an asymmetric Burmese arrangement (Diagrams A or B above).
If one thinks the war analogy of chess is useful,
free placement is more realistic and better training than starting play
in one fixed arrangement as in orthodox chess. Recent wars involve
considerable positioning of forces and supplies long before hostilities
commence. And once they do, battle lines no longer conform to
traditional arrangements of foot soldiers, cavalry, elephants,
artillery, commanders, etc. as in centuries past.
Free placement provides the opportunity to introduce new pieces in the palette of Western chess. It has been proposed that the Chinese line pieces are the best choice. With an increased force it is reasonable to expand the playing field, thus the use of a 10 x10 board would probably make the best game if, say, two Cannons, two Vaos and a Leo were added to each player's orthodox pieces. Murray stated that "enlarged games of chess have rarely shown any vitality," because they were too taxing to be recreational (p. 454). But a larger board may decrease complications that arise in a cluttered position. And the 12 x 8 "Courier Game" was popular from 1200 to after 1650, about the duration of orthodox chess so far.
Free Placement ameliorates each of the four problems with orthodox chess listed above. With thousands of viable starting positions the possibility of defeating an opponent by using a previously analyzed opening is greatly lessened. The placement phase should also make matters much more difficult for computer programs. Ultimately the computers would excel in this strategic effort also, but to do so will require a different and more interesting programming method than the current brute force evaluation of all possible moves. And during play, the use of a 10x10 board and additional pieces will increase the number of possible moves. If the number on each turn were increased by just 50%, after 12 "plies" (six moves) the number of variations to test increases by over 100 times. That should slow down the silicon competitors. There should be fewer draws also. An agreement to draw can be prohibited during placement, and the greater freedom of arrangement and loss of familiar guideposts should engender aggressive schemes and blunders. Also the penetrating power of the Chinese line pieces should make blocked positions more difficult to maintain. For example, the sacrifice of a Vao for two Pawns should be a frequent consideration since the Vao is a less valuable piece than either a Knight or Bishop. Finally, free placement can eliminate the most arbitrary rules of orthodox chess: the initial position, castling, double pawn moves and en passant capture. If we also allow promotion to a Pawn, only then will all the following simple descriptions apply to chess.
(1) The empty board is homogeneous. Only the edge of the board, and for Pawns their direction of movement, effect the power of a piece. With free placement and in the course of a game, any piece may occupy any square.Elimination of en passant capture and castling excludes many problems that involve deducing what the last move was. But castling is an absurd option in the context of free placement of the major pieces. Determining the last move could still be a problem.
(2) Only one piece moves at a time.
(3) A capturing piece always occupies the square of the piece captured.
(4) All positions are non-historical. The possible moves and captures in a position are determined solely by the location of the pieces on the board and who has the move, regardless of the particular sequence of moves that could have produced the position.
Comments, corrections or suggestions are welcomed.
Email: Daniel
W. VanArsdale
Alybadix.
http://alybadix.bl.ee/
Chess Life,
Special Summer Issue 1997, Vol. 52, No. 7.
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Dodgson's "Frogs Manuscript"
Decoded
Duniho, Fergus. Eurasian
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Li, David H. The
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Murray, H. J. R. A
History of Chess. Oxford University Press, Oxbow Books
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Employ the
Dead - Sam Loyd - Dummy Promotion
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