This is a list of chess variants. Many thousands of variants exist. The 2007 catalogue The Encyclopedia of Chess Variants estimates that there are well over 2,000, and many more were considered too trivial for inclusion in the catalogue.[2]
The chess variants listed below are derived from chess by changing one or more of the many rules of the game. The rules can be grouped into categories, from the most innocuous (starting position) to the most dramatic (adding chance/randomness to the gameplay after the initial piece placement). If a variant changes rules from multiple categories, it belongs to the sub-section below corresponding to the later-listed category.
Starting position and armies
Piece types
Midgame rules and end-of-game rules
Board shape
Number of players
Use of hidden information or chance.
Names that represent a set of variants are annotated with "[multivariant]" after their name.
Variant starting position (rectangular board, standard piece types and rules)
Many variants employ standard chess rules and mechanics, but vary the number of pieces, or their starting positions. In most such variants, the pawns are placed on their usual squares, but the position of other pieces is either randomly determined or selected by the players. The motivation for these variants is usually to nullify established opening knowledge. The downside of these variants is that the initial position usually has less harmony and balance than the standard chess position.[3]
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Upside-down chess starting position (White sits at bottom)
Active chess [9x8]: Played on a 9×8 board, adding a queen with an extra pawn in front. Invented by G. Kuzmichov (1989), whose students tested the game, deciding that the optimal starting position was to place the second queen on the eighth or ninth files.[4]
Displacement chess [8x8, multivariant]: Some pieces in the initial position are exchanged but the rules remain exactly the same. Some examples of this may be that the king and queen are flipped, or the knight on the b-file is traded with the bishop on the f-file.
Double chess: Two full armies per side on a 12×16 board, the first to mate an enemy king wins. Pawns advance up to four steps on their first move. Capablanca found the game "remarkably interesting".[5] Invented by Julian Hayward (1916).
Endgame chess (or the Pawns Game, with unknown origins) [8x8]: Players start the game with only pawns and a king. Normal check, checkmate, en passant, and pawn promotion rules apply.[6]
Los Alamos chess (or anti-clerical chess) [6x6]: Played on a 6×6 board without bishops. This was the first chess-like game played by a computer program.
Upside-down chess [8x8]: The white and black pieces are switched so that White's pieces are on the 8th rank, with pawns on the 7th rank, one step away from promotion. The starting position looks like a standard chess starting position, but from the other player's perspective. As the pawns are blocked by pieces in the starting position, the game always starts with a knight move, and smothered mates are common.[7]
Casablanca chess: The starting position is chosen from a famous historic game; usually an interesting middlegame position. The position is verified to be approximately equal by a computer, and should have winning chances for both sides.[8] The first Casablanca chess tournament was played in May 2024, and won by Magnus Carlsen.[9][10]
Polgar reform chess [multivariant]: In his book Reform-Chess (1997), László Polgár proposed several variants played on board of size 5×8, 6×8, 8×6, or 9×6.[11] The initial piece setup is determined by players in the same way as in Benko's Pre-chess. There are special rules for castling depending on the board. Polgár recommended these variants to train creativity and to speed up the game.
Pre-chess: The game starts with white and black pawns set as usual, but the initial position of other pieces is selected by the players. White first places one of their pieces on their first rank, and then Black does the same. Players continue to alternate in this manner until all pieces have been placed, with the only restriction being that bishops must be on opposite-colour squares. The game then proceeds in the usual way. Proposed by Pal Benko in 1978.[12]
Chess960, one of the 960 possible starting positions
Fischer Random Chess (or Chess960): The placement of the pieces on the first rank is randomized; although there are rules such as the 2 starting Bishops have to be on different colour squares, and the King has to start between the 2 Rooks. The opponent's pieces mirror it. Invented by Bobby Fischer (1996).
These variants use standard chess pieces on a standard board, but players begin with non-standard numbers of pieces. For example, starting with multiple queens or fewer pawns. Many such games use unbalanced starting positions, with one player having more or fewer of particular pieces than the other player.
Dunsany's Chess (and the similar Horde chess): One side has standard chess pieces, and the other side has 32 pawns.
Handicap chess (or Chess with odds): Variations to equalise chances of players with different strength.
Peasants' Revolt: White has a king and eight pawns (the peasants) against Black's king, pawn, and four knights (the nobles). Black has the advantage. To narrow the contest, the game has also been played with three knights (on b8, c8, and g8) instead of four. By R. L. Frey (1947).[13][14]
Sixteen Pawns: White plays without their queen, but chooses where on the third and fourth ranks to place eight extra pawns. By Legall de Kermeur (18th century). Alexandre Deschapelles and Louis-Charles Mahé de La Bourdonnais later established that eight extra pawns favour White too much, and hence played the game with only five, six, or seven extra pawns for White instead.[15]
Weak!: White has the usual pieces, Black has one king, seven knights, and sixteen pawns. This game was played at a Columbia University chess club in the 1960s.[16]
Shako starting position. Cannons (shown as inverted rooks) are on a1, j1, a10, and j10. Elephants (shown as inverted bishops) are on a2, j2, a9, and j9.
Most of the pieces in these variants are borrowed from chess. The game goal and rules are also very similar to those in chess; however, these variants include one or more fairy pieces which move differently from chess pieces.
Baroque chess (or Ultima): Pieces on the first row move like queens, and pieces on the second row move like rooks. They are named after their unusual capturing methods. For example, leaper, immobilizer and coordinator.
Berolina chess: All pawns are replaced with Berolina pawns, that move diagonally and capture orthogonally.
Chess with different armies: Two sides use different sets of fairy pieces. There are several armies of approximately equal strength to choose from including the standard FIDE chess army.
Falcon-Hunter Chess: A falcon moves forward as a bishop; backward as a rook. The hunter moves forward as a rook; backward as a bishop. Players introduce the fairies as the game progresses. By Karl Schulz (1943).
Grasshopper chess [multivariant]: The pawns can promote to grasshopper, or grasshoppers are on the board in the initial position.
Pocket Mutation Chess: Player can put a piece temporarily into the pocket, optionally mutating it into another (including fairy) piece.
Spartan chess: Black (the Spartans) has an army headed by two kings, which otherwise consists exclusively of non-standard pieces, and battles the standard FIDE army (the Persians) of white.[17]
Super X Chess: Players can combine their own pieces by capturing them. King or queen can't combine. A combined piece has the ability to move as both pieces that got combined. Same kind of pieces can combine into new pieces. Pieces can't uncombine or combine again. By Miika Pihkala (2018).[18]
Torpedo chess: Pawns are replaced with torpedo pawns, which can move two squares forwards anywhere on the board as opposed to only on the first move. Pawns that move two squares can be captured en passant on the very next move. The rest of the pieces remain unchanged.[19]
Way of the Knight (WOTN): Invented by Ralph Betza, incorporating two elements from tabletop role-playing games. Begins with the standard starting position and pieces, however through capturing and advancing up the board pieces can earn "experience", and a sufficiently experienced piece is upgraded to a more powerful one. Upgrades include various fairy pieces, and involve player choices of "alignment".[20][21]
Variants with popular fairy pieces: Empress, Amazon, Princess
There are a number of variants which use the empress (rook + knight) and princess (bishop + knight) compound pieces. The empress is also called marshall or chancellor.[22] The princess is also called cardinal, archbishop, janus, paladin, or minister.[23] Another compound piece is the amazon (queen + knight). To adapt to the new pieces, the board is usually extended to 10×8 or 10×10 with additional pawns added.[24]
Almost Chess: Uses an 8×8 board, with the conventional starting position, but queens are replaced by chancellors (empresses). By Ralph Betza (1977). A related variant is Sort of Almost Chess (Ralph Betza, 1994), where one player has a queen and the other has a chancellor.
Capablanca Chess: A variant by the former world chess champion, José Raúl Capablanca. Played on a 10×8 board with chancellor (empress) and archbishop (princess).
Capablanca Random Chess: Generalises all possible variants of Capablanca Chess with random starting positions following a method similar to that used in Chess960. By Reinhard Scharnagl (2004).
Embassy Chess: Uses a 10×8 board with Marshall (Empress) and Cardinal (Princess). The starting position is borrowed from Grand Chess. By Kevin Hill (2005).
Gemini Chess:[25] Uses a 10×8 board with two Archbishops. From an idea of Dr Zied Haddad in 2016. The difference from Janus Chess is the initial setup where the archbishops are sandwiching the queen and king remaining in the center of the board.
Gothic chess: A commercial variant played on a 10×8 board with Chancellor (Empress) and Archbishop (Princess).
Grand Chess: Uses a 10×10 board with marshall (empress) and cardinal (princess). Invented by Christian Freeling (1984).
Janus Chess: Uses a 10×8 board with two januses (princesses). By Werner Schöndorf (1978).
Maharajah and the Sepoys: Black has a complete army, and White only one piece: the maharajah (a royal amazon).
Modern Chess: Played on a 9×9 board, with an extra pawn and a prime minister (princess). By Gabriel Vicente Maura (1968).
Musketeer chess:[26] A commercial variant, inspired from Seirawan Chess. This variant introduces 10 fairy pieces: archbishop, chancellor, hawk (different rules from Seirawan Chess), elephant (different rules from Seirawan Chess), leopard, cannon (different from Xiangqi), unicorn, fortress, spider, and amazon (also called dragon in this game). Players have a choice of 2 pieces among the 10 possible and method used to introduce them during the game.
2000 A.D.: Played on a 10×10 board, features the empress, capricorn, gorgon, chimaera, dragon, minotaur, unicorn, and fury fairy chess pieces. By V. R. Parton.
Bear chess[28][29][30] — 10x10 chess variant, proposed by Mikhail Sosnovsky in 1985 in Kalinin.[31][32] Board 10x10; extra pieces are Bears, which leap as N or two squares as R or B; baseline (a1-j1/a10-j10) RNBBeQKBeBNR. Pawns can move up to three squares initially (e.p. permitted). In castling, K moves to c/h files.
Chessers: There are multiple variants that combine the rules of chess and checkers, including a 1925 variant by Frank Maus,[33] and a 1960 proprietary variant by Phillips Publishers, Inc.[34]
Decimal Chess [multivariant]: Played on a 10×10 board, usually add extra pieces. Some decimal chesses use only standard pieces, but others such as Decimal Falcon-Hunter Chess use fairy pieces. One such variant is Decimal Rettah chess, which adds a king, queen and two pawns. Invented by V. R. Parton.
Dragonchess: Three 8x12 boards with some standard chess pieces and many other pieces, some of which move between the levels. Created by Gary Gygax.[36]
Duell: Dice are used instead of pieces. Played on a 9×8 board.
Etchessera: Played on a regular chessboard but where players build their own chess army from a collection of 17 different pieces.[37]
Gess: Chess with variable pieces, played on a Go board.
Prince & Princess: The chess variant that uses the criterion of succession, where the king or queen are replaced in favor of the prince or the princess, created by Antonio Maravi Oyague.[39]
Proteus: A chess variant using dice to represent normal chess pieces, created by Steve Jackson Games.[40]
Shako: Played on a 10×10 board. New pieces are the cannon from xiangqi (Chinese chess) and an elephant moving as a fers+alfil of old shatranj (ancestors of queen and bishop), so diagonally one or two squares with jumps allowed. By Jean Louis-Cazaux (1997).[41]
Stratomic: Adds nuclear missiles to the standard chess array on a 10×10 board. When launched they irradiate any 3×3 area (friendly pieces included) except kings. By Robert Montay-Marsais (1972).
Wildebeest Chess: Uses an 11×10 board, each player has two camels and a wildebeest (camel + knight). Pawns move one, two, or three squares initially. By R. Wayne Schmittberger (1987).
Wolf Chess: On an 8×10 board, with fairy pieces wolf (empress), fox (princess), nightrider, sergeant (almost a Berolina pawn), and elephant (amazon). By Arno von Wilpert (1943).
In these variants one or both players can move more than once per turn. The board and the pieces in these variants are the same as in standard chess.
Avalanche chess: Each move consists of a standard chess move followed by a move of one of the opponent's pawns.
Double-Move Chess: Similar to Marseillais chess, but with no en passant, check, or checkmate. The objective is to capture the king. By Fred Galvin (1957).[42]
Double-Take Chess: Each player, once per game, can make two moves during one of their turns. These two moves cannot be used to place the opponent's king in checkmate.[43]
Kung-fu chess: A variant without turns. Any player can move any of their pieces at any given moment.
Marseillais chess (or Two-move chess): After the first turn of the game by White being a single move, each player moves twice per turn.
Monster chess (or Super King): White has the king and four pawns (c2-f2) against the entire black army but may make two successive moves per turn. There is no check. Players win by capturing the king. In a variant, White's pieces begin one row forward of their usual starting position, and the White's pawns may not begin with a double step. Another variant denies Black promotion rights (pawns reaching the last rank remain as pawns). White may always promote.
Multimove Chess (i, j): A class of chess variants where white gets i moves per turn and black gets j moves per turn. Check is not enforced, and victory is by capturing the enemy king. The games are described and analysed logically in a 2015 journal article. The authors weakly solved the game for all (i, j) pairs except for (1, 1) (functionally, regular chess) and (2, 2).[44]
Progressive chess (or Scottish chess): White moves once, then Black moves twice, then White moves three times, and so on.
Swarm chess: During each turn, each piece that a player can move must be moved.[45]
Absorption chess (also called cannibal chess, power absorption chess, or seizer's chess): Pieces gain the abilities of the pieces they capture.[46][47]
ASEAN chess: Pawns start on the 3rd ranks. Queens can only move 1 square diagonally and Bishops only 1 square diagonally or 1 square directly forward.[48]
Atomic chess: Capture on any square results in an "atomic explosion" which kills (i.e. removes from the game) all pieces in the eight surrounding squares, except for pawns.
Beirut Chess: Players secretly equip one of their men with a "bomb", which can be detonated at any time, wiping out all pieces on surrounding squares. Win by checkmating the opponent, or blowing up their king. By Jim Winslow (1992).
Benedict chess: Instead of capturing by displacement, players may convert an enemy piece they attack to their own color.[49]
Chad: Kings are limited to 3×3 "castles" on a 12×12 board dominated by eight rooks per side which can promote to queens. By Christian Freeling (1979).
Checkers chess: Pieces can only move forward until they have reached the far rank.[50]
Chessplus: Commercial variant. Up to two of any friendly piece save the King may occupy the same single square. Either piece may choose to carry the other with it if or when it moves.[51]
Circe chess: Captured pieces are reborn on their starting squares.
Congo: Kings (lions) are limited to 3×3 "castles" on a 7×7 board. By Demian Freeling (1982).
Cubic Chess: Piece cubes display the six piece types; a player can promote any pawn by rotating its cube to match a captured piece type. By Vladimír Pribylinec (1977).
Dragonfly: Played on a 7×7 or hex board, no queens, captured non-pawn pieces never die (à la Chessgi) and can be dropped on any open square. By Christian Freeling.
Dynamo Chess: Capturing is replaced by pushing or pulling enemy pieces off the board. By Hans Klüver and Peter Kahl (1968). A close variant of Push Chess (by Fred Galvin, 1967).[52]
Einstein chess: Pieces transform into more or less powerful pieces when they move.[53]
Gravity chess: After every turn, all pieces other than pawns fall towards the higher ranks of the board, until they either reach the eighth rank, or another piece or pawn in the way.[54][55]
Grid chess: The board is overlaid with a grid of lines. For a move to be legal, it must cross at least one of these lines.
Guard chess (or Icelandic chess): Allows captures only when a piece is completely unprotected by friendly pieces. Checkmate occurs when the piece forcing the mate is protected and therefore cannot be captured.[56]
Haft Schrödinger Chess: Every piece starts in a quantum superposition initially able to be any piece until the waveform is collapsed by observation. As in chess, Haft Schrödinger Chess does not have hidden information, whereas Schrödinger's Chess is regarded as a game of hidden information.[57][58]
Hierarchical chess: Pieces must be moved in the order: pawn, knight, bishop, rook, queen, king. A player who has the corresponding piece but cannot move it loses.[59]
Hostage chess: Captured pieces are held in the capturer's "prison", and can be released by the opponent and dropped into play (like shogi) via a "hostage exchange". By John Leslie (1997).
Jedi Knight chess: Knights may move three steps diagonally or horizontally or both, depending on the rules accepted.[60]
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Jump Chess example checkmate
Jump chess: The rook, bishop and queen may move from one side of any piece (friend or foe) to the other side in their normal direction of movement. No change for the King and Knight. Jump move is exactly two squares, and can be used to give check or to capture. Jump moves are notated using '^'. In the starting position, 1.R^a3 and 1.B^a3 are both legal. By former Pentamind[61] champion Alain Dekker (2004).[62]
Kamikaze chess (or Hara-Kiri chess): When capturing, the capturing piece is removed from play also. This means a king cannot defend itself by capturing an attacker. A capture is not allowed if it exposes one's own king to discovered check. Idea from B. G. Laws (1928).[63] The king is royal and removing a check takes precedence over capturing. The king must be lost last; moving into check is permitted after all other pieces have been captured.
Knight relay chess: Pieces defended by a friendly knight can move as a knight.
Legan chess: Played as if the board would be rotated 45°, initial position and pawn movements are adjusted accordingly.
Madrasi chess (or Weird chess): A piece which is attacked by the same type of piece of the opposite color is paralysed.
Monochromatic chess: All pieces must stay on the same color square as they initially begin.
No Castling Chess: standard rules except that castling is not allowed, which means king safety is reduced. Proposed in 2019 by Vladimir Kramnik with the aim of reducing draws and uninteresting games, and tested on Alpha Zero.[1]
Patrol chess: Captures and checks are only possible if the capturing or checking piece is guarded by a friendly piece.
PlunderChess: The capturing piece is allowed to temporarily take the moving abilities of the piece taken.
Pocket Knight Chess (or Tombola Chess): Players have an extra knight they keep at the side of the board. Once during the game, a player may place the knight on any empty square for their move. Play then proceeds as normal.[64][65]
Portal Chess [multivariant]: Any of a number of games that involve pieces or squares for teleportation around the board(s).
Refusal chess (or Outlaw chess, Rejection chess): A played move can be refused by the opponent, forcing the first player to change to another move, which must be accepted.[66]
Replacement chess (or Bhagavathi Chess, Canadian Chess, Madhouse Chess, or Repeating Chess): Captured pieces are not removed from the board but relocated by the captor to any vacant square.[67]
Rifle chess (or Shooting chess, Sniper chess): When capturing, the capturing piece remains unmoved on its original square, instead of occupying the square of the piece captured.[68]
Sovereign Chess: This variant is played on a 16×16 board. In addition to the standard black and white pieces, the board is also encircled by 80 other coloured pieces (10 colours of 8 pieces each). Coloured squares near the center of the board correspond to the coloured pieces around the board, and when a player's piece occupies a coloured square, that player gains control of the matching coloured pieces. If a piece on a coloured square is moved or captured, control of the matching pieces is lost (transferred to the other player in case of capture). Players may also switch the color of their initial army through "regime change". By Mark Bates.[69][70]
Anti-king chess. The anti-king is shown as an inverted king.
Anti-King chess: Features an anti-king. The anti-king moves in the same way as a king. This piece is in check when not attacked. If a player's anti-king is in check and unable to move to a square attacked by the opponent, the player loses (checkmate). The anti-king cannot capture enemy pieces, but can capture friendly pieces. A king may not attack the opponent's anti-king. The anti-king may not check its own king. (That is, a position when a king and an anti-king are on adjacent squares is possible, does not mean any check and does not help the anti-king to avoid check if any other piece does not attack him.) Other rules are the same as in standard chess, including check and checkmate to the regular king. By Peter Aronson (2002).[71][72]
Apocalypse: On a 5×5 board, each side has two knights and five pawns, win by eliminating all enemy pawns. Prepared moves are executed simultaneously. By C. S. Elliott (1976).
Colour Chess: Played on a multicoloured board of six colours, with the order of turns taken as in Marseillais chess but with rules indicating which colour each piece may move to. The game is won by capturing the opponent's king (rather than checkmate) and kings may remain in check. Similar variants include Sequence Colour Chess, and Swarm Colour Chess.[73][74] By Tom Norfolk (2017).[75]
Duck Chess: In addition to the usual pieces, the two players have joint control of a small rubber duck which acts as a "blocker" (i.e. nothing can move onto or through it), and which must be moved to a new square after every turn. The goal is to successfully capture the opponent's king. A stalemated player wins.[76]
Extinction chess: To win, a player must capture all of any one type of pieces of the opponent (for example, all the knights an opponent has, or all their pawns, etc.).
Hexapawn: Played on a rectangular board of variable size with only pawns. The goal of each player is to advance one of their pawns to the opposite end of the board or to prevent the other player from moving.
Jesön Mor: Nine knights per side on a 9×9 board. The first to occupy square e5, and then leave it, wins the game. From Mongolia.
King of the Hill: In addition to checkmate, a legal move that moves one's own king to one of the center squares (d4, d5, e4, e5) wins. This is analogous to Sannin shogi's rule that allows a player to win by legally moving their king to the center.[77]
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Knightmate starting position
Knightmate (or Mate The Knight): The goal is to checkmate the opponent's knight (initially on e-file). The kings on b- and g-files can be captured as other pieces. Pawns can promote to kings but not to knights. By Bruce Zimov (1972).[78]
Losing chess (or Antichess, Giveaway chess, Suicide chess, Killer chess, Take-all chess, Take-me chess, Reverse chess): Capturing moves are mandatory and the objective is to lose all one's pieces. There is no check; the king is captured like an ordinary piece.
Racing Kings: Players race kings to the 8th rank. Captures, but no checks or checkmate.[79]
Three-check chess: Takes the "three strikes, you're out" rule from baseball and applies it to chess; standard rules of chess apply,[80] but a player can alternatively win by putting their opponent in check three times.[81][82][83] In The Encyclopedia of Chess Variants, David Pritchard notes it being of probable Soviet origin, and that Anatoly Karpov was an "invincible" player in his youth.[81][84]
Baskerville's hexagonal chess: Earliest attempt at a strict hexagonal analog to chess. 83 cell hex board with four corners. Same as Gliński's Hexagonal Chess, but no special pawn moves or hex diagonal king moves. Opposing bishops occupy differently colored spaces, thus preventing them from attacking each other. By H. D. Baskerville (1929).
Brusky's hexagonal chess: Chess on an irregular board of 84 hex cells. Same as Gliński's Hexagonal Chess, but with ten pawns instead of nine, linear startup, two forward move directions for pawns, pawns capture forward diagonally, and castling. By Yakov Brusky (1966).
De Vasa's hexagonal chess: Chess on a rhombus-shaped board of 81 hex cells. Same as Gliński's Hexagonal Chess, but linear startup, two forward move directions for pawns, pawns capture forward diagonally to the side, and castling. Invented by Helge E. de Vasa (1953).
Gliński's hexagonal chess: The most popular version of chess for the hex board. Includes three bishops, nine pawns, 91 hex cells. Invented by Władysław Gliński (1936).
McCooey's hexagonal chess: Chess on the same hexagonal board as Gliński's Hexagonal Chess, but using a different starting array, seven pawns instead of nine, and pawns capture forward diagonally. By Richard Honeycutt and David McCooey (1978–1979).
Polgar Superstar Chess: Hexagonal variant played on a special star-shaped board. Invented by László Polgár (2002).[87][88]
Shafran's hexagonal chess: Chess on an irregular hex board of 70 cells. Same as Gliński's Hexagonal Chess, but differs by starting position, pawn first-move options, pawns capturing forward diagonally, and castling. Invented by Grigorevich Shafran (1939).
Strozewski's hexagonal chess: Chess on a square-shaped board of 81 hex cells. King and Knight move as if cells were squares. Invented by Casimir S. Strozewski (1976).
Troy: A variant inspired by the Trojan War played on a 91-cell hexagonal board. Pieces are named after characters from the myth.[89]
Tri-Chess: A variation of Triangular Chess. The rook and bishop are increased to six directions; the queen, to twelve. By George Dekle Sr.
Triangular Chess: Board comprises 96 triangles. The rook and bishop have three directions; the queen, six. Three extra pawns and a unicorn. By George Dekle Sr.
Balbo's Game: A novel-shaped board with 70 squares. Full armies for each player, minus one pawn. No castling. By G. Balbo (1974).
Chessence: Nine pieces per player move according to their relative positions to each other on a 6×9 board with missing squares and kings immobile in the corners. By Jim Winslow (1989).
Circular chess: Played on a circular board consisting of four rings, each of sixteen squares.
Cross chess: Cross-shaped cells, board geometry like hex chess but moves akin to normal chess (e.g. bishops have four directions, not six; queens eight, not twelve). Extra rook, knight, and pawn per side. By George Dekle Sr.
Cylinder chess: Played on a cylinder board with a- and h-files "connected". Thus a player can use them as if the a-file were next to the h-file (and vice versa).
Infinite chess: Numerous players and mathematicians have conceived of chess variations played on an unbounded chessboard.[85] In one example, when using "Converse's rules," the pieces and their relative starting positions are unchanged—only the board is infinitely large.