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Some fairy pieces

	Archbishop (knight + bishop compound)
	Chancellor (knight + rook compound)
	Grasshopper (shown as an upside-down queen)
	Nightrider or unicorn (shown as an upside-down knight)

A fairy chess piece or unorthodox chess piece is a chess piece not used in conventional chess, but used in certain chess variants and some chess problems. These pieces vary in movement abilities and possible additional properties.

Due to distributed and uncoordinated nature of unorthodox chess development, often the same piece is referred to by different names or the same name is used for different pieces in various contexts (chess problems, various chess variants).

Contents 1 Classification 1.1 Movement type 1.1.1 Leapers 1.1.2 Riders 1.1.3 Hoppers 1.1.4 Locusts 1.1.5 Marine Piece 1.2 By game 1.2.1 Chinese pieces 1.3 By special attributes 1.3.1 Royal pieces 1.3.2 Xed pieces 2 Notations 2.1 Parlett's movement notation 2.1.1 Additions to Parlett's 2.2 Ralph Betza's "funny notation" 3 Notable examples 4 Notes 5 References 6 External links

[edit] Classification

A specialized solving program, WinChloe, recognizes more than 1200 different fairy pieces. Most (but not all) usual fairy chess pieces fall into one of three classes, although it should be noted that some are hybrid pieces (see the Chinese pieces, for example, which can move without capture as riders yet can only capture as hoppers). It is easy to create a new type of piece by simply combining the movement powers of two or more different pieces.

[edit] Movement type

[edit] Leapers

A (m,n)leaper is a piece that moves by a fixed vector between its start square and its arrival square. One of the coordinate of the vector 'start square - arrival square' must have an absolute value equal to m and the other one an absolute value equal to n. A leaper moves in the same way to capture or not to capture, the taken unit being on the arrival square. For instance, the knight is the (1,2)leaper. ^[1]

In shatranj, a forerunner to chess, the pieces later replaced by the bishop and queen were also leapers: the alfil was a (2,2)leaper (moving exactly two squares diagonally in any direction), and the fers a (1,1)leaper (moving exactly one square diagonally in any direction).^[2]

Some pieces can be described as combined leapers, i.e. as pieces having movement capabilities of multiple leapers. The king in orthodox chess is, as far as only its movement is concerned without taking into account check restrictions, example of a combination of (1,1)leaper and (1,0) leaper.

Leapers are not able to create pins, although they are often effective forking pieces. One additional property is that the check of a leaper can not be parried by interposing.

All orthodox chessmen belong to either leapers or riders although the Rook does 'hop' when it castles.

The Wazir is an orthogonal 1,0 leaper; the Fers is a diagonal 1,1 leaper; both used in Muslim versions of Chess. The King of standard Chess combines the two.
The Dababba is an orthogonal 2,0 leaper; the Alfil the 2,2 leaper; the Knight is a 1,2 leaper. The Alibaba combines the Dababba and Alfil; while the Squirrel can move to any square 2 units away.
The 'level-3' leapers would be the Threeleaper, a 3,0 leaper, the Tripper, a 3,3 leaper, the Camel, a 1,3 leaper and the Zebra, a 2,3 leaper.

Zero	Wazir	Dababba	Threeleaper
Wazir	Fers	Knight	Camel
Dababba	Knight	Alfil	Zebra
Threeleaper	Camel	Zebra	Tripper

A combined leaper is called an amphibian, if it has a larger range on the board than its components. The simplest amphibian is the Frog, a (1,1)-(0,3) leaper.

[edit] Riders

A rider is a piece that can move an unlimited distance in one direction, providing there are no pieces in the way.

There are three riders in orthodox chess: the rook can move an unlimited number of (1,0) cells and is therefore a (1,0) rider; the bishop is a (1,1) rider; and the queen is a (1,1) or (1,0) rider.

One of the most popular fairy chess riders is the nightrider, which can make an unlimited number of knight moves (that is, 2,1 cells) in any direction (though, like other riders, it cannot change direction half-way through its move).

Sliders are a noteworthy special case of riders which can only move between geometrically contiguous cells. All of the riders in orthodox chess are examples of sliders.

The names of riders are often obtained by taking the name of a leaper which moves a similar cell-size and adding the suffix rider. For example, the zebra is a (3,2) leaper, and the zebrarider is a (3,2) rider.

Riders can create both pins and skewers.

[edit] Hoppers

A hopper is a piece which moves by jumping over another piece (called a hurdle). The hurdle can usually be any piece of any color. Unless it can jump over a piece, it cannot move. Note that hoppers generally capture by taking the piece on the destination square, not by taking the hurdle (as is the case in checkers). An exception is the locust.

There are no hoppers in orthodox chess, although in xiangqi, the cannon captures as a hopper (when not capturing, it is a rider which can not capture - the so-called Chinese pieces (see below) share this characteristic).

The most popular hopper in fairy chess is the grasshopper, which moves along the same lines as an orthodox queen, except that it must hop over some other piece and land on the square immediately beyond it.

[edit] Locusts

A locust is any piece which captures by hopping over its victim (as in checkers). It is sometimes considered a type of hopper.

[edit] Marine Piece

A marine piece is a combination piece consisting of a rider (for ordinary moves) and a locust (for captures) in the same directions. Marine pieces have names alluding to the sea and its myths, e.g., nereïde (marine bishop), triton (marine rook), mermaid (marine queen), or poseidon (marine king).

[edit] By game

Some classes of pieces come from a certain game; often these have a common set of characteristics.

[edit] Chinese pieces

Chinese pieces are pieces derived from units found in xiangqi, the Chinese form of chess. The most common Chinese pieces are the leo, pao and vao (each of which are derived from the Chinese cannon) and the mao (derived from the horse). Those derived from the cannon are distinguished by moving as a leaper when capturing, but otherwise moving as a rider. Less frequently encountered Chinese pieces include the moa, nao and rao.

[edit] By special attributes

[edit] Royal pieces

A royal piece is one which must not be allowed to be captured. If a royal piece is threatened with capture and cannot avoid capture next move, then the game is lost (this is checkmate). In orthodox chess, each side has one royal piece, the king. In fairy chess any other orthodox piece or fairy piece may instead be designated royal, there may be more than one royal piece, or there may be no royal pieces at all (in which case the aim of the game must be something other than to deliver checkmate, such as capturing all of the opponent's pieces).

[edit] Xed pieces

Name	Notes
Crowned pieces	Any piece which, in addition to its normal powers, can move like a King.
Knighted piece	Any piece which, in addition to its normal powers, can move like a knight. For example, an amazon is a knighted queen.

[edit] Notations

[edit] Parlett's movement notation

In his book The Oxford History of Board Games^[3] David Parlett used a notation to describe fairy piece movements. The move is specified by an expression of the form m={expression}, where m stands for "move", and the expression is composed from the following elements:

• Distance (numbers, n)
  • 1 - a distance of one (i.e. to adjacent square)
  • 2 - a distance of two
  • n - any distance in the given direction
• Direction (punctuation, X)
  • * - orthogonally or diagonally (all eight possible directions)
  • + - orthogonally (four possible directions)
  • > - orthogonally forwards
  • < - orthogonally backwards
  • <> - orthogonally forwards and backwards
  • = - orthogonally sideways (used here instead of Parlett's divide symbol.)
  • >= - orthogonally forwards or sideways
  • <= - orthogonally backwards or sideways
  • X - diagonally (four possible directions)
  • X> - diagonally forwards
  • X< - diagonally backwards
• Grouping
  • / - two orthogonal moves separated by a slash denote a hippogonal move (i.e. jumping like knights)

[edit] Additions to Parlett's

The following can be added to Parlett's to make it more complete:

• Conditions under which the move may occur (lowercase alphanumeric, except n)
  • (default) - May occur at any point in the game
  • i - May only be made on the initial move (eg. pawn's 2 moves forward)
  • c - May only be made on a capture (eg. pawn's diagonal capture)
  • o - May not be used for a capture (eg. pawn's forward move)
• Move type
  • (default) - Captures by landing on the piece; blocked by intermediate pieces
  • ~ - Leaper (leaps)
  • ^ - Locust (captures by leaping; implies leaper)
• Grouping (punctuation)
  • / - two orthogonal moves separated by a slash denote a hippogonal move (i.e. jumping like knights); this is in Parlett's, but is repeated here for completeness
  • , (comma) - separates move options; only one of the comma-delimited options may be chosen per move
  • () - grouping operator; see nightrider
  • - - range operator
• Other:
  • & - See text for details

The format (not including grouping) is: <conditions> <move type> <distance> <direction> <other>

On this basis, the traditional chess moves are:

• King: 1*
• Queen: n*
• Bishop: nX
• Rook: n+
• Pawn: o1>, c1X>, oi2>
• Knight: ~1/2

[edit] Ralph Betza's "funny notation"

Ralph Betza created a classification scheme for fairy chess pieces (including standard chess pieces) in terms of the moves of basic pieces with modifiers.^[4]

For example, the FIDE Rook, which can be described as a Wazir-rider, can be notated WW, with shorthand R. The FIDE Bishop can be notated as a Fers-rider, or FF. Finally, a FIDE pawn can be notated fmWfcF (or fcFfmW), meaning it is a piece that moves forward like a Wazir, and captures forward like a Fers (and has no other moves). This is setting aside the initial two-square move and promotion.

[edit] Notable examples

Name	Parlett	Found in	Notes
Alfil	~2X	Shatranj
Amazon	n*, ~1/2		Combines the powers of the queen and the knight. Also called superqueen. Note, that in the variant Knightmare chess, an amazon is a queen that moves as either a bishop or a knight.
Andernach grasshopper		Andernach chess	A grasshopper that changes the colour of the hurdle it leaps over. Also known as a chopper.
Archbishop			See "Cardinal"
Assassin		Stealth Chess
Balloon		Four Dimensional Chess	A bishop-like piece used in four-dimensional chess, i.e. it changes all coordinates simultaneously while moving.
Berolina pawn	o1X>, c1>, io2X>		Moves one square diagonally forward (except on its first move, when it may move two), but captures by moving one square straight forward. Compare with pawn.
Bishop	nX	Orthodox Chess
Camel	~1/3
Cannon			See "pao"
Cardinal	nX, ~1/2		Combines the powers of Bishop and Knight. Also called a Princess, Archbishop or Janus.
Chancellor			See "Empress"
Checker	cn(^2X>), o1X> King: cn(^2X), o1X		Multiple captures in one turn, or without capturing can move forward one diagonal space, but cannot move backward until after it has finished a turn on the far rank of the board. (cf. Draughts, Checkers)
Chopper			See "Andernach grasshopper"
Colonel	n>, n=, 2/1> 1*		Moves as forwards and sideways rook, the forwards moves of a knight, or a king found in Chess with different armies.
Dabbaba	~2+	Tamerlane Chess	Old historic piece, also known as war machine or machine.
Dummy			A piece with no moves at all. It may be captured, gain temporarily moving ability by relay, or pushed or pulled around by other pieces if there are pushing or pulling pieces on the board. Different from zero.
Elephant	2X	Xiangqi (Chinese)	A (2,2) leaper, but it cannot jump over an intervening piece, like the ma. In Chinese Chess, the elephant is restricted to its half of the board.
Empress	n+, ~1/2		Combines the powers of the Rook and Knight. Also called a Chancellor or Marshal.
Fers	1X	Shatranj	Move one square in any direction diagonally.
Giraffe	~1/4
Grasshopper			A hopper which moves along the same lines as a queen and lands on the square immediately beyond that of the hurdle. One of the most popular fairy pieces. In diagrams, the grasshopper is usually represented by an inverted queen.
Janus		Janus chess	See "Cardinal"
King	1*	Orthodox Chess	Move one square in any direction. Royal in orthodox chess. A non-royal piece which moves in this way is sometimes called a man.
Khohn	1X, 1>	Makruk	Move one square in any direction diagonally or one square straight forward. It has the same moves as the Silver General in Shogi.
Knight	~1/2	Orthodox Chess
Kraken	~n/m		Leap to any square on the board, including the one it is currently on (leaping to the current square has the effect of passing a move). Compare with universal leaper.
Leeloo		Quintessential Chess	Combines the powers of Quintessence and Rook
Leo	on*, c^&	Chinese	Combines the powers of the pao and vao; it moves like a queen when not capturing (that is, a (1,0) or (1,1) rider), but captures by leaping over an intervening piece and taking the piece on the leo's destination square (the captured piece can be any number of squares beyond the hurdle).
Lion	~n*		A hopper which moves along the same lines as a queen and which can land on a square any distance beyond the hurdle.
Maharaja			A royal amazon which is the only piece on its side.
Mao		Chinese	Moves like a knight except that it does not leap. It first moves one square orthogonally in any direction, and then continues in the same general direction one square diagonally. The square it is on after its orthogonal move must be vacant. For example, if a white mao is on b2 and there is a white pawn on b3, the mao cannot move to a4 or c4; if the pawn is on c3, however, it can move to both those squares (because the first part of the move is orthogonal, not diagonal).
Marshal			See "Empress"
Moa		Chinese	as the mao, but the first step is diagonal and the second orthogonal, not the other way round.
Murray Lion	~0/2, ~2/2, c1*		Can move and capture as an Alfil or Dabbabah, and capture only as a king. This piece stems from a misinterpretation of the Lion of Chu Shogi but has become popular in fairy chess problems and chess variants. It is named after the chess historian Harold James Ruthven Murray who brought it up.
Nao		Chinese	A Chinese nightrider - moves as a normal nightrider (that is, a (2,1) rider) when not capturing, but which captures by leaping over an intervening piece and taking the piece on the nao's destination square (the captured piece can be any number of knight-moves beyond the hurdle).
Nightrider	n(1/2) (in same direction)		A rider which moves any number of 2,1 cells (i.e., knight moves) in the same direction. A nightrider on b2 on an empty board, therefore, can move to a4, c4, d6, e8, d3, f4, h5 and d1. A pawn of the opposing colour on d6 could be captured, but the nightrider could not move any further in that direction (i.e. it couldn't move on to e8). A pawn on b3, for example, would have no effect. On diagrams, the nightrider is usually represented by an inverted knight. One of the most popular fairy pieces. See diagram below.
Pao		Chinese	Moves like a rook when not capturing (that is, a (1,0) rider), but captures by leaping over an intervening piece and taking the piece on the pao's destination square (the captured piece can be any number of squares beyond the hurdle). Found in xiangqi (in which context it is normally known in English as a cannon).
Pawn	o1>, c1X>, io2>	Orthodox Chess	Moves one square straight forward (except on its first move, when it may move two squares), but captures one square forward diagonally. Compare with Berolina pawn.
Pentere		Quinquereme Chess	Combines the powers of Queen and Quintessence
Princess			See "Cardinal"
Quang trung rook			Moves as rook but when capturing must move on square away from captured piece in the same direction.
Queen	n*	Orthodox Chess	Combines the powers of the bishop and rook.
Quintessence			A nightrider who takes 90-degree turns in a zig-zag manner on each step. First described in 2002 by Jörg Knappen and found in several chess variants since then.
Rao		Chinese	A Chinese rose - moves as a normal rose when not capturing, but captures by leaping over an intervening piece and taking the piece on the rao's destination square. The captured piece can be any distance beyond the hurdle.
RennCavalier		Renniasance Chess	Moves in the same move one square diagonally and any number of squares othogonally or any number of squares orthogonally and one diagonally. t has two paths to the same target square and must make at least a blockable knight's move. Called Cavalier in RennChess, but the name Cavalier is used for other pieces as well. Renniasance Chess was invented by 1980 by Eric V. Greenwood.
RennDuke		Renniasance Chess	Moves in the same move one square orthogonally and then any number of squares diagonally or any number of squares diagonally and then one straight. It has two paths to the same target square and must make at least a blockable knight's move. Called Duke in RennChess, but the name Duke is used for other pieces as well.
Rook	n+	Orthodox Chess
Rose			Moves as a nightrider, except that rather than moving in a straight line, it moves along pseudo-circular ones. A rose standing on e1 on an empty board, for instance, can move to any of the squares on the large circle c2, b4, c6, e7, g6, h4 and g2; as well as c2 and a1; or d3 and b4; or d3, e5 and g6; or f3, e5, c6 and a5; or f3 and h4. As with the nightrider, an opposite-coloured piece on any one of these squares can be captured, but prevents the rose from progressing any further along that line. See diagram below.
Spy	2>, 2=, (1/1)>	Chess Empire	The spy can move two spaces forwards or sideways, or can move like a knight one forward and then one horizontally or vice versa. It can leap over pieces and can only move two spaces; thus, it is "trapped" on its own color like a bishop.
Squirrel	~0/2, ~1/2, ~2/2	Fairy Chess Problems	Jumps to any field in a distance of 2. It was discovered independently several times and is also known as Centurion or Castle.
Superpawn	on>, cnX>	Fairy Chess Problems	Moves without capture any number of fields forward, captures diagonally forwards like a bishop. Promotes on the 8th rank. Cannot capture en passant nor be captured en passant. May be placed in the first rank. Invented by Werner Speckmann in 1967.[5]
Superqueen			See "Amazon"
Universal leaper			Leap to any square on the board apart from the one it is on. Compare with kraken.
Unicorn			A name usually given to a B+N piece. In Raumschach it is a triagonal rider, moves through the vertices of the cubes. See diagram below.
Vao		Chinese	Moves like a bishop when not capturing (that is, a (1,1) rider), but captures by leaping over an intervening piece and taking the piece on the vao's destination square (the captured piece can be any number of squares beyond the hurdle).
Wazir	1+		Move one square orthogonally in any direction.
Zebra	~2/3
Zero	~0/0		A piece which can make a zero move, i. e., jump and land on its starting square without any side effects. This gives the player the option to pass a move. Sometimes used as a component to more complex pieces.
Zurafa		Tamerlane Chess	Starts with a (1,4) leap (like the modern Giraffe) and may continue moving outwards as a rook.

Nightrider makes any number of knight moves in the same direction.

Rose. Moves as Nightrider, but along pseudo-circular lines. (two possible paths depicted.) Of course it may move clockwise or counter-clockwise.

E D C B A The unicorn, represented here by an up-side-down knight, moves through the vertices of cubes, triagonally. A unicorn from its starting position can only reach 30 cubes. The white unicorn's destination squares are marked with a circle, black's with an X. It is important to remember that the boards are stacked, with board E on top.

[edit] Notes

[edit] References

[edit] External links

• Piececlopedia - an extensive list of fairy chess pieces, their history and movement diagrams
• Who is Who on Eight by Eight Compiled by Ivan A Derzhanski, shows also piece values
• Jerome Grimbert's List of Fairy Chess Pieces (french)
• Fairy chess pieces and fairy problem conditions (in german)

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