Draughts

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Draughts
CheckersStandard.jpg
Starting position for English draughts on an 8×8 draughts board
Years activeat least 5,000
Genre(s) Board game
Abstract strategy game
Mind sport
Players2
Setup time<1 minute
Playing time30 minutes – 2 hours
Random chanceNone
Skill(s) required Strategy, tactics
Synonym(s)Checkers
Chequers

Draughts (British English) or checkers [note 1] (American English) is a group of strategy board games for two players which involve diagonal moves of uniform game pieces and mandatory captures by jumping over opponent pieces. Draughts developed from alquerque. [1] The name derives from the verb to draw or to move. [2]

Contents

The most popular forms are English draughts, also called American checkers, played on an 8×8 checkerboard; Russian draughts, also played on an 8×8, and international draughts, played on a 10×10 board. There are many other variants played on 8×8 boards. Canadian checkers and Singaporean/Malaysian checkers (also locally known as dum) are played on a 12×12 board.

English draughts was weakly solved in 2007 by the team of Canadian computer scientist Jonathan Schaeffer. From the standard starting position, both players can guarantee a draw with perfect play.

General rules

Draughts is played by two opponents, on opposite sides of the gameboard. One player has the dark pieces; the other has the light pieces. Players alternate turns. A player may not move an opponent's piece. A move consists of moving a piece diagonally to an adjacent unoccupied square. If the adjacent square contains an opponent's piece, and the square immediately beyond it is vacant, the piece may be captured (and removed from the game) by jumping over it.

Only the dark squares of the checkered board are used. A piece may move only diagonally into an unoccupied square. When presented, capturing is mandatory in most official rules, although some rule variations make capturing optional. [3] In almost all variants, the player without pieces remaining, or who cannot move due to being blocked, loses the game.

Men

Uncrowned pieces (men) move one step diagonally forwards, and capture an opponent's piece by moving two consecutive steps in the same line, jumping over the piece on the first step. Multiple enemy pieces can be captured in a single turn provided this is done by successive jumps made by a single piece; the jumps do not need to be in the same line and may "zigzag" (change diagonal direction). In English draughts men can jump only forwards; in international draughts and Russian draughts men can jump both forwards and backwards.

Kings

A game in international draughts, featuring a flying king Probleme Jeu de dames SR.gif
A game in international draughts, featuring a flying king

When a man reaches the kings row (also called crownhead, the farthest row forward), it becomes a king, and is marked by placing an additional piece on top of the first man (crowned), and acquires additional powers including the ability to move backwards and (in variants where they cannot already do so) capture backwards. Like men, a king can make successive jumps in a single turn provided that each jump captures an enemy man or king.

In international draughts, kings (also called flying kings) move any distance along unblocked diagonals, and may capture an opposing man any distance away by jumping to any of the unoccupied squares immediately beyond it. Because jumped pieces remain on the board until the turn is complete, it is possible to reach a position in a multi-jump move where the flying king is blocked from capturing further by a piece already jumped.

Flying kings are not used in English draughts; a king's only advantage over a man is the ability to move and capture backwards as well as forwards.

Naming

In most non-English languages (except those that acquired the game from English speakers), draughts is called dame, dames, damas, or a similar term that refers to ladies. The pieces are usually called men, stones, "peón" (pawn) or a similar term; men promoted to kings are called dames or ladies. In these languages, the queen in chess or in card games is usually called by the same term as the kings in draughts. A case in point includes the Greek terminology, in which draughts is called "ντάμα" (dama), which is also one term for the queen in chess.

National and regional variants

Russian Column draughts

Column draughts (Russian towers) is a kind of draughts, known in Russia since the beginning of the nineteenth century, in which the game is played according to the usual rules of draughts, but with the difference that the beaten draught is not removed from the playing field, and is captured under the beating figure (draught or tower).

The resulting towers move around the board as a whole, "obeying" the upper draught. When taking the tower, only the upper draught is removed from it. If on the top there is a draught of other color than removed as a result of fight, the tower becomes a tower of the rival. Rules of moves of draughts and kings correspond to the rules of Russian draughts.

Flying kings; men can capture backwards

International draughts / American Pool checkers family
National variantBoard sizePieces per sideDouble-corner or light square on player's near-right?First moveCapture constraintsNotes
International draughts (or Polish draughts)10×1020YesWhiteA sequence must capture the maximum possible number of pieces.Pieces promote only when ending their move on the final rank, not when passing through it. It is mainly played in the Netherlands, Suriname, France, Belgium, some eastern European countries, some parts of Africa, some parts of the former USSR, and other European countries.
Ghanaian draughts (or damii)10×1020No [4] WhiteAny sequence may be chosen, as long as all possible captures are made. Overlooking a king's capture opportunity leads to forfeiture of the king.Played in Ghana. Having only a single piece remaining (man or king) loses the game.
Frisian draughts  [ nl ]10×1020YesWhiteA sequence of capture must give the maximum "value" to the capture, and a king (called a wolf) has a value of less than two men but more than one man. If a sequence with a capturing wolf and a sequence with a capturing man have the same value, the wolf must capture. The main difference with the other games is that the captures can be made diagonally, but also straight forwards and sideways.Played primarily in Friesland (Dutch province) historically, but in the last decade spreading rapidly over Europe (e.g. the Netherlands, Belgium, Italy, Czech Republic, Ukraine and Russia) and Africa, as a result of a number of recent international tournaments and the availability of an iOS and Android app "Frisian Draughts".
Canadian checkers 12×1230YesWhiteA sequence must capture the maximum possible number of pieces.International rules on a 12×12 board. Played mainly in Canada.
Brazilian draughts (or derecha)8×812YesWhiteA sequence must capture the maximum possible number of pieces.Played in Brazil. The rules come from international draughts, but board size and number of pieces come from English draughts.

In the Philippines, it is known as derecha and is played on a mirrored board, often replaced by a crossed lined board (only diagonals are represented).

Pool checkers 8×812YesBlackAny sequence may be chosen, as long as all possible captures are made.Also called Spanish Pool checkers. It is mainly played in the southeastern United States; traditional among African American players. A man reaching the kings row is promoted only if he does not have additional backwards jumps (as in international draughts).[ permanent dead link ]

In an ending with three kings versus one king, the player with three kings must win in thirteen moves or the game is a draw.

Jamaican draughts/checkers 8×812YesBlackAny sequence may be chosen, as long as all possible captures are made.Similar to Pool checkers with the exception of the main diagonal on the right instead of the left. A man reaching the kings row is promoted only if he does not have additional backwards jumps (as in international draughts).

In an ending with three kings versus one king, the player with three kings must win in thirteen moves or the game is a draw.

Russian draughts 8×812YesWhiteAny sequence may be chosen, as long as all possible captures are made.Also called shashki or Russian shashki checkers. It is mainly played in the former USSR and in Israel. Rules are similar to international draughts, except:
  • a man that enters the kings row during a jump and can continue to jump backwards, jumps backwards as a king, not as a man;
  • choosing a sequence that captures the maximum possible number of pieces is not required.

There is also a 10×8 board variant (with two additional columns labelled i and k) and the give-away variant Poddavki . There are official championships for shashki and its variants.

Mozambican draughts/checkers 8×812NoWhiteA sequence must capture the maximum possible number of pieces. Although, a king has the weight of two pieces, this means with two captures, one of a king and one of piece you must choose the king; two captures, one of a king and one of two pieces, you can choose; two captures with one of a king and one of three pieces you choose the three pieces; two captures, one of two kings and one of three pieces, you choose the kings...Also called "Dama" or "Damas". It is played along all of the region of Mozambique. In an ending with three kings versus one king, the player with three kings must win in twelve moves or the game is a draw.

Flying kings; men cannot capture backwards

Spanish draughts family
National variantBoard sizePieces per sideDouble-corner or light square on player's near-right?First moveCapture constraintsNotes
Spanish draughts 8×812Light square is on right, but double corner is on left, as play is on the light squares. (Play on the dark squares with dark square on right is Portuguese draughts.)WhiteA sequence must capture the maximum possible number of pieces, and the maximum possible number of kings from all such sequences.Also called Spanish checkers. It is mainly played in Portugal, some parts of South America, and some Northern African countries.
Malaysian/Singaporean checkers 12×1230YesNot fixedCaptures are mandatory. Failing to capture results in forfeiture of that piece (huffing).Mainly played in Malaysia, Singapore, and the region nearby. Also known locally as "Black–White Chess". Sometimes it is played on an 8×8 board when a 12×12 board is unavailable; a 10×10 board is rare in this region.
Czech draughts 8×812YesWhiteIf there are sequences of captures with either a man or a king, the king must be chosen. After that, any sequence may be chosen, as long as all possible captures are made.This variant is from the family of the Spanish game.
Hungarian Highlander (Slovak) draughts 8×88WhiteAll pieces are long-range. Jumping is mandatory after first move of the rook. Any sequence may be chosen, as long as all possible captures are made.The uppermost symbol of the cube determines its value, which is decreased after being jumped. Having only one piece remaining loses the game.
Argentinian draughts 8×8

10x10

12

15

NoWhiteA sequence must capture the maximum possible number of pieces, and the maximum possible number of kings from all such sequences. If both sequences capture the same number of pieces and one is with a king, the king must do.The rules are similar to the Spanish game, but the king, when it captures, must stop after the captured piece, and may begin a new capture movement from there.

With this rule, there is no draw with two pieces versus one.

Thai draughts 8×88YesBlackAny sequence may be chosen, as long as all possible captures are made.During a capturing move, pieces are removed immediately after capture. Kings stop on the square directly behind the piece captured and must continue capturing from there, if possible, even in the direction where they have come from.
German draughts (or Dame)8×812YesBlackAny sequence may be chosen, as long as all possible captures are made.Kings stop on the square directly behind the piece captured and must continue capturing from there as long as possible.
Turkish draughts 8×816N/AWhiteA sequence must capture the maximum possible number of pieces.Also known as Dama. All 64 squares are used, dark and light. Men move straight forwards or sideways, instead of diagonally. When a man reaches the last row, it is promoted to a flying king (Dama), which moves like a rook (or a queen in the Armenian variant). The pieces start on the second and third rows.

It is played in Turkey, Kuwait, Israel, Lebanon, Syria, Jordan, Greece, and several other locations in the Middle East, as well as in the same locations as Russian checkers. There are several variants in these countries, with the Armenian variant (called tama) allowing also forward-diagonal movement of men.

Myanmar draughts 8×812WhiteA sequence must capture the maximum possible number of pieces.Players agree before starting the game between "Must Capture" or "Free Capture". In the "Must Capture" type of game, a man that fails to capture is forfeited (huffed). In the "Free Capture" game, capturing is optional.
Tanzanian draughts 8×812YesNot fixedAny sequence may be chosen, as long as all possible captures are made.Captures are mandatory. When either a king or a man can capture, there is no priority.

No flying kings; men cannot capture backwards

English draughts / American straight checkers family
National variantBoard sizePieces per sideDouble-corner or light square on player's near-right?First moveCapture constraintsNotes
English draughts 8×812YesBlackAny sequence may be chosen, as long as all possible captures are made.Also called "straight checkers" or American checkers, since it is also played in the United States.
Italian draughts 8×812NoWhiteMen cannot jump kings. A sequence must capture the maximum possible number of pieces. If more than one sequence qualifies, the capture must be done with a king instead of a man. If more than one sequence qualifies, the one that captures a greater number of kings must be chosen. If there are still more sequences, the one that captures a king first must be chosen.It is mainly played in Italy and some North African countries.
Gothic checkers (or Altdeutsches Damespiel or Altdeutsche Dame)8×816N/AWhiteCaptures are mandatory.All 64 squares are used, dark and light. Men move one cell diagonally forward and capture in any of the five cells directly forward, diagonally forward, or sideways, but not backward. Men promote on the last row. Kings may move and attack in any of the eight directions. There is also a variant with flying kings.

Sport

Starting position for international draughts which is played on a 10x10 board International draughts.jpg
Starting position for international draughts which is played on a 10×10 board

The World Championship in English draughts began in 1840. The winners in men's have been from the United Kingdom, United States, Barbados, and most recently Italy (3-Move division). The women's championship in English draughts started in 1993. The women's winners have been from Ireland, Turkmenistan, and Ukraine.

The World Championship in international draughts began in 1885 in France, and since 1948 has been organized by the World Draughts Federation (FMJD, Fédération Mondiale du Jeu de Dames). It occurs every two years. In even years following the tournament, the World Title match takes place. The men's championship has had winners from the Netherlands, Canada, the Soviet Union, Senegal, Latvia, and Russia. The first Women's World Championship was held in 1973. The World Junior Championship has been played since 1971. European Championships have been held since 1965 (men's) and 2000 (women's).

Other official World Championships began as follows: Brazilian draughts, in 1985; Russian draughts, in 1993; Turkish draughts, in 2014.

Invented variants

Games sometimes confused with draughts variants

History

Ancient games

A similar game has been played for millennia. [2] A board resembling a draughts board was found in Ur dating from 3000 BC. [5] In the British Museum are specimens of ancient Egyptian checkerboards, found with their pieces in burial chambers, and the game was played by Queen Hatasu. [2] [6] Plato mentioned a game, πεττεία or petteia , as being of Egyptian origin, [6] and Homer also mentions it. [6] The method of capture was placing two pieces on either side of the opponent's piece. It was said to have been played during the Trojan War. [7] [8] The Romans played a derivation of petteia called latrunculi , or the game of the Little Soldiers. The pieces, and sporadically the game itself, were called calculi (pebbles). [6] [9]

Alquerque

Alquerque board and setup Alquerque board at starting position 2.svg
Alquerque board and setup

An Arabic game called Quirkat or al-qirq, with similar play to modern draughts, was played on a 5×5 board. It is mentioned in the 10th-century work Kitab al-Aghani. [5] Al qirq was also the name for the game that is now called nine men's morris. [10] Al qirq was brought to Spain by the Moors, [11] where it became known as Alquerque , the Spanish derivation of the Arabic name. The rules are given in the 13th-century book Libro de los juegos . [5] In about 1100, probably in the south of France, the game of Alquerque was adapted using backgammon pieces on a chessboard. [12] Each piece was called a "fers", the same name as the chess queen, as the move of the two pieces was the same at the time. [13]

Crowning

Men in medieval clothing playing draughts 1145-Playing-at-Draughts-q75-1517x1525.jpg
Men in medieval clothing playing draughts

The rule of crowning was used by the 13th century, as it is mentioned in the Philip Mouskat's Chronique in 1243 [5] when the game was known as Fierges, the name used for the chess queen (derived from the Persian ferz, meaning royal counsellor or vizier). The pieces became known as "dames" when that name was also adopted for the chess queen. [13] The rule forcing players to take whenever possible was introduced in France in around 1535, at which point the game became known as Jeu forcé, identical to modern English draughts. [5] [12] The game without forced capture became known as Le jeu plaisant de dames, the precursor of international draughts.

The 18th-century English author Samuel Johnson wrote a foreword to a 1756 book about draughts by William Payne, the earliest book in English about the game. [6]

Computer draughts

English draughts (American 8×8 checkers) has been the arena for several notable advances in game artificial intelligence. In the 1950s, Arthur Samuel created one of the first board game-playing programs of any kind. More recently, in 2007 scientists at the University of Alberta [14] developed their "Chinook" program to the point where it is unbeatable. A brute force approach that took hundreds of computers working nearly two decades was used to solve the game, [15] showing that a game of draughts will always end in a draw if neither player makes a mistake. [16] [17] The solution is for the draughts variation called go-as-you-please (GAYP) checkers and not for the variation called three-move restriction checkers. As of December 2007, this makes English draughts the most complex game ever solved.

Computational complexity

Generalized Checkers is played on an N × N board.

It is PSPACE-hard to determine whether a specified player has a winning strategy. And if a polynomial bound is placed on the number of moves that are allowed in between jumps (which is a reasonable generalization of the drawing rule in standard Checkers), then the problem is in PSPACE, thus it is PSPACE-complete. [18] However, without this bound, Checkers is EXPTIME-complete. [19]

However, other problems have only polynomial complexity: [18]

See also

Notes

  1. When this word is used in the UK, it is usually spelt chequers (as in Chinese chequers); see further at American and British spelling differences.

Related Research Articles

Chinese checkers abstract strategy game

Sternhalma, commonly known as Chinese Checkers or Chinese Chequers, is a strategy board game of German origin which can be played by two, three, four, or six people, playing individually or with partners. The game is a modern and simplified variation of the game Halma.

International draughts strategy board game

International draughts is a strategy board game for two players, one of the variants of draughts. The gameboard comprises 10×10 squares in alternating dark and light colours, of which only the 50 dark squares are used. Each player has 20 pieces, light for one player and dark for the other, at opposite sides of the board. In conventional diagrams, the board is displayed with the light pieces at the bottom; in this orientation, the lower-left corner square must be dark.

American Pool checkers, also called "American Pool", is a variant of draughts, mainly played in the mid-Atlantic and southeastern United States and in Puerto Rico.

Fox games are a category of board games for two players, where one player is the fox and tries to eat the geese/sheep, and the opposing player directs the geese/sheep and attempts to trap the fox, or reach a destination on the board. In another variant, Fox and Hounds, the fox merely tries to evade the hounds. There are several versions known: in Britain, France, Italy, Germany, Netherlands, Sápmi (riebantablu), Sweden (Rävspel), Iceland (Refskák), Slovakia, Russia and Nepal (Bagh-Chal).

English draughts board game draughts

English draughts or checkers, also called American checkers or straight checkers, is a form of the strategy board game draughts. It is played on an 8×8 chequered board with 12 pieces per side. The pieces move and capture diagonally forward, until they reach the opposite end of the board, when they are crowned and can thereafter move and capture both backward and forward.

Lasca board game

Lasca is a draughts variant, invented by the second World Chess Champion Emanuel Lasker (1868–1941). Lasca is derived from English draughts and a Russian draughts game Bashni (Towers).

Turkish draughts Variant of draughts played in the Mediterranean and Middle East

Turkish draughts is a variant of draughts (checkers) played in Turkey, Greece, Egypt, Kuwait, Lebanon, Syria, Jordan and several other locations around the Mediterranean Sea.

Russian draughts variant of draughts played in the former USSR, Eastern Europe, and Israel

Russian draughts is a variant of draughts (checkers) played in Russia and some parts of the former USSR, as well as parts of Eastern Europe and Israel.

Armenian draughts is a variant of draughts played in Armenia. Its rules are quite similar to Turkish draughts. Armenian draughts, however, allows diagonal movement, too.

Cheskers game on cell board

Cheskers is a variant of checkers and chess invented by Solomon Golomb in 1948.

Czech draughts is a board game played in the territory formerly occupied by the Czechoslovak Republic. It is governed by the Czech Draughts Federation.

Italian draughts

Italian draughts is a variant of the draughts family played mainly in Italy and Northern Africa. It is a two-handed game played on a board consisting of sixty-four squares, thirty-two white and thirty-two black. There are twenty-four pieces: twelve white and twelve black. The board is placed so that the rightmost square on both sides of the board is black.

Philosophy shogi checkers (哲学飛将碁) is a board game similar to English draughts, invented by Inoue Enryō, Japanese philosopher, and described by his student in 1890. It has same board size with shogi and game ends with capturing the opponent's king, similar to shogi and Western chess.

Hexdame

Hexdame is a strategy board game for two players invented by Christian Freeling in 1979. The game is a literal adaptation of the game international draughts to a hexagonal gameboard.

Dameo

Dameo is a strategy board game for two players invented by Christian Freeling in 2000. It is a variant of the game draughts and is played on an 8×8 checkered gameboard.

Brazilian draughts

Brazilian draughts is a variant of the strategy board game draughts. Brazilian Checkers follows the same rules and conventions as International draughts, the only differences are the smaller gameboard, and fewer checkers per player.

Poddavki

Poddavki is a draughts game based on the rules of Russian draughts, main difference from other draughts games is that a player wins if he doesn't have any legal moves on his turn. The game is possible because capturing is mandatory. Played in Russia and some parts of the former USSR.

Bashni variation of checkers

Bashni, also known as column draughts, multi-level checkers, and rarer Chinese checkers, is a variation of draughts, known in Russia since the XIX century. The game is played according to the basic rules of Russian draughts, with the main difference being that draughts being jumped over are not removed from the playing field but are instead placed under the jumping piece . The resulting towers move across the board as one piece, obeying the status of the upper draught. When a tower is jumped over, only the upper draught is removed from it. If, as a result of the combat, the top draught changes colour, ownership of the tower passes on to the opposing player. Based on Bashni, but according to the basic rules of English draughts, world chess champion Emanuel Lasker developed the draughts game "Laska" and, in 1911, published its description. Lasker described towers that can only be "double-layered": i.e. there can be no alternation of colors. He also showed that during the game the number of game pieces either remains constant or decreases. Column draughts are a subject of interest for the mathematical Sciences: combinatorics, theory of paired zero-sum games, etc.

Tanzanian draughts

Tanzanian draughts is a variant of draughts (checkers) board game played usually in Tanzania. This is the strategy game that is played by two people using pieces on board. The game is very similar to Czech draughts but in this type the player can capture using king or men, there is no priority for that. Apart from that they are completely similar in any way. The game is also somehow similar American checkers and Shashki in case of starting position however rules of playing Tanzanian checkers differ. Like many other kinds of draughts, there is possibility that either player can win the game or draw can be offered but this is based on the negotiations of players or supporters of the game.

Malaysian/Singaporean checkers

Malaysian checkers or Singaporean checkers, is a variant of the board game of draughts played primarily in Malaysia and Singapore, especially among the elder men. Similar to the Canadian checkers, it is played on a 12x12 checkered board. The game can also be played on a 8x8 board if a 12x12 board is unavailable. However, it is distinct from Checkers and Canadian Checkers in terms of its additional rules. Popular alternative names used locally for this game include Dum and Dam.

References

Citations

  1. Masters, James. "Draughts, Checkers - Online Guide". www.tradgames.org.uk.
  2. 1 2 3 Strutt, Joseph (1801). The sports and pastimes of the people of England. London. p. 255.
  3. As is standard in modern Variants; see more at The Online Guide to Traditional Games
  4. Salm and Falola, Culture and Customs of Ghana, p. 160
  5. 1 2 3 4 5 Oxland, Kevin (2004). Gameplay and design (Illustrated ed.). Pearson Education. p. 333. ISBN   978-0-321-20467-7.
  6. 1 2 3 4 5 "Lure of checkers". The Ellensburgh Capital. 17 February 1916. p. 1. Retrieved 16 April 2009.
  7. "Petteia". 9 December 2006. Archived from the original on 9 December 2006.
  8. Austin, Roland G. (September 1940). "Greek Board Games". Antiquity. University of Liverpool, England. 14: 257–271. Archived from the original on 8 April 2009. Retrieved 16 April 2009.
  9. Peck, Harry Thurston (1898). "Latruncŭli". Harpers Dictionary of Classical Antiquities. New York: Harper and Brothers. Retrieved 23 November 2006.
  10. Berger, F (2004). "From circle and square to the image of the world: a possible interpretation or some petroglyphs of merels boards" (PDF). Rock Art Research. 21 (1): 11–25. Archived from the original (PDF) on 21 November 2004.
  11. Bell, R. C. (1979). Board and Table Games from Many Civilizations. I. New York City: Dover Publications. pp. 47–48. ISBN   0-486-23855-5.
  12. 1 2 Bell, Robert Charles (1981). Board and Table Game Antiques (Illustrated ed.). Osprey Publishing. p. 33. ISBN   0-85263-538-9.
  13. 1 2 Murray, H. J. R. (1913). A History of Chess. Benjamin Press (originally published by Oxford University Press). ISBN   0-936317-01-9. OCLC   13472872.
  14. Chinook - World Man-Machine Checkers Champion Archived 24 June 2003 at the Wayback Machine
  15. Schaeffer, Jonathan; Burch, Neil; Björnsson, Yngvi; Kishimoto, Akihiro; Müller, Martin; Lake, Robert; Lu, Paul; Sutphen, Steve (14 September 2007). "Checkers Is Solved". Science. 317 (5844): 1518–1522. doi:10.1126/science.1144079. PMID   17641166.
  16. Jonathan Schaeffer, Yngvi Bjornsson, Neil Burch, Akihiro Kishimoto, Martin Muller, Rob Lake, Paul Lu and Steve Sutphen. Solving Checkers, International Joint Conference on Artificial Intelligence (IJCAI), pp. 292-297, 2005. Distinguished Paper Prize
  17. "Chinook - Solving Checkers Publications". www.cs.ualberta.ca. Archived from the original on 16 April 2008. Retrieved 22 December 2007.
  18. 1 2 Fraenkel, Aviezri S.; Garey, M. R.; Johnson, David S.; Yesha, Yaacov (1978). "The complexity of checkers on an N × N board". 19th Annual Symposium on Foundations of Computer Science. p. 55. doi:10.1109/SFCS.1978.36.
  19. Robson, J. M. (May 1984). "N by N Checkers is EXPTIME complete". SIAM Journal on Computing. 13 (2): 252–267. doi:10.1137/0213018.

Sources

Draughts associations and federations

History, articles, variants, rules

Online play