Draughts

Draughts (; British English) or checkers (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. The name 'draughts' derives from the verb to draw or to move, whereas 'checkers' derives from the checkered board which the game is played on.
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 a team of Canadian computer scientists led by 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. 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.
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.
History.
Ancient games.
Similar games have been played for millennia. A board resembling a draughts board was found in Ur dating from 3000 BC. 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. Plato mentioned a game, πεττεία or "petteia", as being of Egyptian origin, and Homer also mentions it. 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. 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").
Alquerque.
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. Al qirq was also the name for the game that is now called nine men's morris. Al qirq was brought to Spain by the Moors, 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". In about 1100, probably in the south of France, the game of Alquerque was adapted using backgammon pieces on a chessboard. 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.
Crowning.
The rule of crowning was used by the 13th century, as it is mentioned in the Philip Mouskat's "Chronique" in 1243 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. 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. 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.
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 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, showing that a game of draughts will always end in a draw if neither player makes a mistake. 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 generalisation of the drawing rule in standard Checkers), then the problem is in PSPACE, thus it is PSPACE-complete. However, without this bound, Checkers is EXPTIME-complete.
However, other problems have only polynomial complexity:
National and regional variants.
Russian Column draughts.
Column draughts (Russian towers), also known as Bashni, 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 colour than removed as a result of fight, the tower becomes a tower of the rival. Rules for the movement of draughts and kings correspond to the rules of Russian draughts.
Bashni has inspired the games Lasca and Emergo.
External links.
Draughts associations and federations
History, articles, variants, rules