English draughts

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"Checkers" redirects here. For other uses, see Checkers (disambiguation).

English draughts board

A standard American Checkers Federation set. Smooth red and white 1.25 inch (32 mm) pieces, green and buff 2 inch (51 mm) squares.

The starting position

English draughts, also called American checkers or "straight checkers", commonly called checkers in the U.S., but commonly called draughts in some other countries, is a form of the draughts board game played on an 8×8 board with 12 pieces on each side that may only move and capture forward.

1 Rules
2 Computer players
3 Computational complexity
4 References
5 See also
6 External links

[edit] Rules

As in all draughts variants, English draughts is played by two people, on opposite sides of a playing board, alternating moves. One player has black colored pieces, and the other has white colored pieces. Most commonly, the board alternates between red and black squares. Pieces move diagonally and pieces of the opponent are captured by jumping over them.

The rules of this variant of draughts are:

Board - The board is an 8×8 grid, with alternating black and red squares, called a checkerboard (in the U.S., in reference to its checkered pattern, also the source of the name checkers). The playable surface consists of the 32 dark squares only. A consequence of this is that, from each player's perspective, the left and right corners encourage different strategies.
Pieces - The pieces are usually made of wood and are flat and cylindrical. They are invariably split into one darker and one lighter color. Traditionally, these colors are red and white. There are two kinds of pieces: "men" and "kings". Kings are differentiated as consisting of two normal pieces of the same color, stacked one on top of the other. Often indentations are added to the pieces to aid stacking.
Starting Position - Each player starts with 12 pieces on the three rows closest to their own side, as shown in the diagram. The row closest to each player is called the "crownhead" or "kings row". The black (darker color) side moves first.
How to Move - There are two ways to move a piece: simply sliding a piece diagonally forwards (also diagonally backwards in the case of kings) to an adjacent and unoccupied dark square, or "jumping" one of the opponent's pieces. In this case, one piece "jumps over" the other, provided there is a vacant square on the opposite side for it to land on. Again, a man (uncrowned piece) can only jump diagonally forwards, and a king can also move diagonally backwards. A piece that is jumped is captured and removed from the board. Multiple-jump moves are possible if, when the jumping piece lands, there is another piece that can be jumped. Jumping is mandatory and cannot be passed up to make a non-jumping move, nor can fewer than the maximum jumps possible be taken in a multiple-jump move. When there is more than one way for a player to jump, one may choose which sequence to make, not necessarily the sequence that will result in the most amount of captures. However, one must make all the captures in that sequence. (Under traditional draughts rules jumping is not mandatory. If it is not done, the opponent may either force the move to be reversed, huff the piece or carry on regardless.)
Kings - If a player's piece moves into the kings row on the opposing player's side of the board, that piece is said to be "crowned" (or often "kinged" in the U.S.), becoming a "king" and gaining the ability to move both forwards and backwards. If a player's piece jumps into the kings row, the current move terminates; having just been crowned, the piece cannot continue on by jumping back out (as in a multiple jump), until the next move.
How the Game Ends - A player wins by capturing all of the opposing player's pieces, or by leaving the opposing player with no legal moves.

In tournament English draughts, a variation called three-move restriction is preferred. The first three moves are drawn at random from a set of accepted openings. Two games are played with the chosen opening, each player having a turn at either side. This tends to reduce the number of draws and can make for more exciting matches. Three-move restriction has been played in the United States championship since 1934. A two-move restriction was used from 1900 until 1934 in the United States and in the British Isles until the 1950s. Before 1900, championships were played without restriction: this style is called go-as-you-please (GAYP).

One rule of long standing that has fallen out of favor is the "huffing" rule. In this variation, jumping is not mandatory, but a piece that could have jumped, but failed to do so, may be taken — or "huffed" — by the opposing player at the beginning of his or her next turn. After huffing the offending piece, the opponent then takes his or her turn as normal. Huffing has been abolished by both the American Checker Federation and the English Draughts Association.

Three common misinterpretations of the rules are:

that the game ends in a draw when a player has no legal move but still pieces remaining (true in chess but not in draughts; see stalemate)
that capturing with a king precedes capturing with a regular piece
a piece which in the current move has become a king can then in the same move go on to capture other pieces (see under Kings, above)

[edit] Computer players

The first computer English draughts program was written by C. S. Strachey, M.A., National Research Development Corporation, London, in the early 1950s. ^[1]

The second computer program was written in 1956 by Arthur Samuel, a researcher from IBM. Other than it being one of the most complicated game playing programs written at the time, it is also well known for being one of the first adaptive programs. It learned by playing games against modified versions of itself, with the victorious versions surviving. Samuel's program was far from mastering the game, although one win against a blind checkers master gave the general public the impression that it was very good.

In the 1990s, the strongest program was Chinook, written in 1989 by a team from the University of Alberta led by Jonathan Schaeffer. Marion Tinsley, world champion from 1955-1962 and from 1975-1991, won a match against the machine in 1992. In 1994, Tinsley had to resign in the middle of an even match for health reasons; he died shortly thereafter. In 1995, Chinook defended its man-machine title against Don Lafferty in a 32 game match where each had 1 win and 1 loss, and a record setting 30 draws. In 1996 Chinook won in the USA National Tournament by the widest margin ever, and was retired from play after that event. The man-machine title has not been contested since.

On July 2007, in an article published in Science Magazine, Chinook's developers announced that the program had been improved to the point where it could not lose a game.^[2] If no mistakes were made by either player, the game would always end in a draw. After eighteen years, they have mathematically proven a weak solution to the game of Checkers ^[3]. Using between 200 desktop computers at the peak of the project down to around 50 later on, the team made just 10¹⁴ calculations to search from the initial position to a database of positions with at most 10 pieces.^[4]

[edit] Computational complexity

The number of legal positions in English draughts is estimated to be 10²⁰, and it has a game-tree complexity of approximately 10³¹. By comparison, chess is estimated to have 10⁴⁰ legal positions.

When draughts is generalized so that it can be played on an n-by-n board, the problem of determining if the first player has a win in a given position is EXPTIME-complete.

The July 2007 announcement by Chinook's team stating that the game had been solved must be understood in the sense that, with perfect play on both sides, the game will always finish with a draw. Yet, not all positions that could result from imperfect play have been analyzed. ^[5]