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

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 or red 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. This 8x8 checkered grid is shared with chess, and commercial chess sets often include draughts as a secondary game, sometimes with backgammon, which would use the same pieces on a board on the inside of the traditional folding chessboard/storage box.
• 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, but red and black are common in the U.S., and light- and dark-stained wood are supplied with more expensive sets. There are two classes 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 dark spaces of 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:
  • A simple move involves sliding a piece one space diagonally forwards (also diagonally backwards in the case of kings) to an adjacent unoccupied dark square.
  • A jump is a move from a square diagonally adjacent to one of the opponent's pieces to an empty square on the directly opposite side, therefore "jumping over" the square containing the opponent's piece. Again, an uncrowned piece can only jump diagonally forwards, but 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, even if the jump is in a different direction. If a jumping move is available, that move must be made even if other non-jumping moves are available, and similarly, if multiple jumps are possible they must be made as well. When multiple jumping moves are available, whether with one piece in different directions or multiple pieces that can make the same or different jumps, the player may choose which piece to jump with and which jump or sequence of jumps to make. The jumping sequence chosen does not necessarily have to be the one that would have resulted in the most captures; however, one must make all available captures in the chosen sequence. (Under traditional draughts rules jumping is not mandatory, but 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. A piece is normally "crowned" by placing a second piece on top of it; some sets have pieces with a crown molded, engraved or painted on one side, allowing the player to simply turn the piece over or to place the crown-side up on the crowned piece, further differentiating Kings from ordinary pieces.
• 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 (In such a case, any available capture can be made at the player's choice)
• 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)

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]

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]

See also

• List of draughts players

References

1. ↑ The Proceedings of the Association for Computing Machinery Meeting, Toronto, 1952.
2. ↑ Computer Checkers Program Is Invincible - New York Times
3. ↑ Computer can't lose checkers - USATODAY.com
4. ↑ Checkers 'solved' after years of number crunching - tech - 19 July 2007 - New Scientist Tech
5. ↑ Checkers Is Solved - Schaeffer et al. 317 (5844): 1518 - Science

External links

• English Draughts Association

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