English draughts

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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.

English draughts board

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

[edit] Rules

As in all draughts variant, English draughts is played by two people, on opposite sides of a playing board, alternating moves. One player has dark pieces, and the other has light pieces. 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 dark and light squares, called a checkerboard (forming a "checkered" pattern, from which the game gets its North American name). 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. U.S. checkers sets typically consists of red and black plastic pieces with ridges on the perimeter to aid stacking. The board is red and black, with play on the black squares only. On these sets, black plays first. Often, the checkers board is also equipped with a backgammon board on the reverse, with 15 of each color piece supplied for playing that game.

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 forward to an adjacent and unoccupied dark square, or "jumping" a piece of the opposing player. It is possible for a piece to be "jumped" if on one side there is an opposing piece and the opposite side is vacant. In this case, one piece would "jump over" the other into the vacant square on the opposite side. 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 opposing piece with a vacant square on the opposite side. 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.
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 "kinged" and gains the ability to move in both forward and backward directions. If player's piece jumps into the kings row, the move terminates (it cannot jump out (as in a multiple-jump move) until that move has ended and the piece has been kinged).
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 the1950s. 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, though still used in some homes, 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)
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

[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. See the Proceedings of the Association for Computing Machinery Meeting, Toronto, 1952.

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. Samuel didn't mention his opponent was blind!

In the 1990s, the strongest program was Chinook written by a team led by Jonathan Schaeffer. Marion Tinsley, world champion from 1955-1962 and 1975-1991, won a match against the machine in 1992. In 1994, he had to resign in the middle of an even match because of health reasons; he died shortly thereafter. Chinook defended its man-machine title against Don Lafferty, and won the US national tournament in 1996 by a large margin. Chinook was retired after that tournament. The man-machine title was never contested again.

The best computer programs of today are stronger than the best humans, and also stronger than Chinook was at the time when it won the man-machine title. In addition, today's computers are much faster than Chinook's hardware.

[edit] Computational complexity

It is a common misconception that English draughts has been solved. The best computers can now beat all humans, but English draughts is not yet completely solved. It is generally expected that English draughts will be solved by the 2010s.

The number of legal positions in English draughts is estimated to be 10¹⁸, and it has a game-tree complexity of approximately 10³¹.

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.

In August 2004, the Chinook team announced that the tournament opening in English draughts called the White Doctor (10-14 22-18 12-16) has proven to be a draw.