Draughts



Draughts 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 derives from the verb to draw or to move.

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 an 8×8, and Canadian checkers is played on a 12×12 board.

The 8×8 variant of 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 (or checkers) 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. Capturing is mandatory in most official rules, although some rule variations make capturing optional when presented. 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 forward, and capture an opponent's piece by moving two consecutive steps in the same line, jumping over the piece on the first step. Multiple opposing pieces may 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 but may "zigzag" (change diagonal direction). In English draughts men can capture only forward, but in international draughts and Russian draughts they may also capture (diagonally) backwards.

Kings


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

In international draughts, kings (sometimes 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. Since captured pieces remain on the board until the turn is complete, it is possible to reach a position in a multi-capture move where the flying king is blocked from capturing further by a piece already captured.

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

Once a game has been gridlocked, where only back and forth moves between same locations on the board avoid jumps, the player with the majority of free space wins the games.

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" 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 (the men are known as "pawns").

Sport
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 in the 3-Move division. However the women's championship in English draughts is more recent than the women's championship in International draughts and started in 1993. On the women's side the winners have been from Ireland, Turkmenistan, and the Ukraine.

The World Championship in international draughts began in 1885 in France, since 1948 organized by the World Draughts Federation (FMJD, Fédération Mondiale du Jeu de Dames). The championship occurs every two years. In the even year following the tournament must take place the World Title match. 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. Since 1971, was played the World Junior Championship. Also held European Championships — since 1965 (men) and 2000 (women).

The World Championship in Brazilian draughts began in 1985, in Russian draughts began in 1993. First official Turkish draughts World Championships were in 2014.

Invented variants

 * Cheskers: A variant invented by Solomon Golomb. Each player begins with a bishop and a camel (which jumps with coordinates (3,1) rather than (2,1) so as to stay on the black squares), and men reaching the back rank promote to a bishop, camel, or king.
 * Damath: A variant utilizing math principles and numbered chips popular in the Philippines.
 * Dameo: A variant played on an 8×8 board, move and capture rules are similar to those of Armenian draughts. A special "sliding" move is used for moving a line of checkers similar to the movement rule in Epaminondas. By Christian Freeling (2000).
 * Hexdame: A literal adaptation of international draughts to a hexagonal gameboard. By Christian Freeling (1979).
 * Island Checkers: Uses a 6×6 board, allows trapping and swapping pieces, and jumping your own.
 * Lasca: A checkers variant on a 7×7 board, with 25 fields used. Jumped pieces are placed under the jumper, so that towers are built. Only the top piece of a jumped tower is captured. This variant was invented by World Chess Champion Emanuel Lasker.
 * Les Vauriens (or Mule Checkers): A variant in which some pieces affect the outcome as in Suicide checkers, while the rest are treated normally.
 * Philosophy shogi checkers: A variant on a 9×9 board, game ending with capturing opponent's king. Invented by Inoue Enryō and described in Japanese book in 1890.
 * Standoff: An American checkers variant using both checkers and dice.
 * Suicide checkers (also called Anti-checkers, Giveaway checkers, or Losing draughts): The misère version of checkers. The winner is the first player to have no legal move: that is, all of whose pieces are lost or blocked.
 * Tiers: A complex variant which allows players to upgrade their pieces beyond kings.
 * 10×8 board for Russian draughts (2 additional columns, labelled 'i' and 'k').
 * Vladimir Vigman draughts – in which each player has 24 pieces (two full sets) — one on the white squares, second on the black. Each player plays two games simultaneously: one game at white squares, other game at dark squares. Total result is sum results of both games.

Games sometimes confused with draughts variants

 * Chinese checkers: Based on Halma, but uses a star-shaped board divided into equilateral triangles.
 * Halma: A game in which pieces move in any direction and jump over any other piece (but no captures), friend or enemy, and players try to move them all into an opposite corner.
 * Konane: "Hawaiian checkers".

Ancient games
A similar game has been played for thousands of years. 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.

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 generalization 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:


 * Can one player remove all the other player’s pieces in one move (by several jumps)?
 * Can one player king a piece in one move?