English draughts

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

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

English draughts board

English draughts (International English) or checkers (American English and Canadian English), also called American checkers or straight checkers or in Israel damka, is a form of draughts board game. Unlike international draughts, it is played on an eight by eight squared board (with sixty-four total squares) with twelve pieces on each side. The pieces move and capture diagonally. They may only move forward until they reach the opposite end of the board, when they are "crowned" or "kinged" and may henceforth move and capture both backward and forward.

As in all draughts variants, English draughts is played by two people, on opposite sides of a playing board, alternating moves. Traditionally the pieces are either black, red, or white. The opponent's pieces are captured by jumping over them.

Game play

The starting position

• Pieces - Though pieces were traditionally made of wood, now many are made of plastic, though other materials may be used. Pieces are typically flat and cylindrical. They are invariably split into one darker and one lighter colour. Traditionally, these colours are white and red, but black and red are common in the United States, 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 colour, stacked one on top of the other. Often indentations are added to the pieces to aid stacking.
• Starting position - Each player starts with twelve pieces on the dark spaces of the three rows closest to that persons own side (as shown in the diagram). The row closest to each player is called the "crownhead" or "kings row". The player with the darker coloured pieces moves first.
• How to move - There are two ways to move a piece:
  • A simple move involves sliding a piece one space diagonally forwards 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 immediately and directly on the opposite side of the opponent's square, thus "jumping directly over" the square containing the opponent's piece. An uncrowned piece may only jump diagonally forwards, kings may jump 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 immediate piece that can be jumped; even if the jump is in a different direction. Jumping is mandatory - whenever a player has the option to jump, that person must jump (even if it's to the jumping player's disadvantage). When multiple-option jumping moves are available, whether with the one piece in different directions or multiple pieces that can make various jumping moves, the player may choose which piece to jump with and which jumping option 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. Any piece, whether it is a king or not, can jump a king.
• 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. The game ends in a draw, if neither side can force a win.

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

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 favour^{[citation needed]} is the "huffing" rule. In this variation jumping is not mandatory, but if a player does not take their jump (either deliberately or by failing to see it), the piece that could have made the jump is "blown" or "huffed", i.e. removed from the board. After huffing the offending piece, the opponent then takes their turn as normal. Huffing has been abolished by both the American Checker Federation and the English Draughts Association.^{[citation needed]}

Two common misinterpretations of the rules are:

• 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).

Notation

Main article: Portable Draughts Notation

For recording games, there is a standardised notation. All 32 reachable positions of the board are numbered in sequence. The numbering starts in black's double-corner. The blacks squares on the first rank are numbered 1 to 4, (in algebraic chess notation those being g1, e1, c1, a1. The next rank starts 5 to 8 (h2, f2, d2, b2) and so on. Moves are recorded as from-to, so a move from 9 to 14 would be 9-14. Captures are notated with an x connecting the start and end square. The result is often abbreviated as BW/RW (Black/Red wins) or WW (White wins)

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Initial position with the started numbering

A sample game. White resigned after blacks 46th move.

[Event "1981 World Championship Match, Game #37"]
[Black "M. Tinsley"]
[White "A. Long"]
[Result "1-0"]
1. 9-14 23-18 2. 14x23 27x18 3. 5-9 26-23 4. 12-16 30-26 5. 16-19 24x15 6. 10x19 23x16 7. 11x20 22-17 8. 7-11 18-15 9. 11x18 28-24 10. 20x27 32x5 11. 8-11 26-23 12. 4-8 25-22 13. 11-15 17-13 14. 8-11 21-17 15. 11-16 23-18 16. 15-19 17-14 17. 19-24 14-10 18. 6x15 18x11 19. 24-28 22-17 20. 28-32 17-14 21. 32-28 31-27 22. 16-19 27-24 23. 19-23 24-20 24. 23-26 29-25 25. 26-30 25-21 26. 30-26 14-9 27. 26-23 20-16 28. 23-18 16-12 29. 18-14 11-8 30. 28-24 8-4 31. 24-19 4-8 32. 19-16 9-6 33. 1x10 5-1 34. 10-15 1-6 35. 2x9 13x6 36. 16-11 8-4 37. 15-18 6-1 38. 18-22 1-6 39. 22-26 6-1 40. 26-30 1-6 41. 30-26 6-1 42. 26-22 1-6 43. 22-18 6-1 44. 14-9 1-5 45. 9-6 21-17 46. 18-22 BW

Computer players

The first computer English draughts program was written by Christopher Strachey, M.A. at the National Physical Laboratory, London.^[1] Strachey finished the programme, written in his spare time, in February 1951. It ran for the first time on NPL's Pilot ACE on 30 July 1951. He soon modified the programme to run on the Manchester Mark 1.

The second computer programme was written in 1956 by Arthur Samuel, a researcher from IBM. Other than it being one of the most complicated game playing programmes written at the time, it is also well known for being one of the first adaptive programmes. It learned by playing games against modified versions of itself, with the victorious versions surviving. Samuel's programme 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 programme 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 thirty-two game match. The final score was 1-0 with 31 draws for Chinook over Don Lafferty.^[2] 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.

In July 2007, in an article published in Science Magazine, Chinook's developers announced that the programme had been improved to the point where it could not lose a game.^[3] If no mistakes were made by either player, the game would always end in a draw. After eighteen years, they have computationally proven a weak solution to the game of Checkers.^[4] Using between two hundred desktop computers at the peak of the project and around fifty later on, the team made just 10¹⁴ calculations to search from the initial position to a database of positions with at most ten pieces.^[5]

Computational complexity

The number of legal positions in English draughts is estimated to be 10²⁰,^[6] and it has a game-tree complexity of approximately 10³¹.^{[citation needed]} By comparison, chess is estimated to have between 10⁴³ and 10⁵⁰ 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.^[6]

See also

• Backgammon
• Board game
• Chinese Checkers
• Game theory
• International draughts
• List of draughts players
• List of world championships in mind sports

References

1. ^ The Proceedings of the Association for Computing Machinery Meeting, Toronto, 1952.
2. ^ Details of the 1995 Man vs. Machine World Championship.
3. ^ Chang, Kenneth (July 19, 2007). "Computer Checkers Program Is Invincible - New York Times". Nytimes.com. http://www.nytimes.com/2007/07/19/science/19cnd-checkers.html?hp. Retrieved 2008-11-24. 
4. ^ Randolph, By (July 19, 2007). "Computer can't lose checkers - USATODAY.com". Usatoday.com. http://www.usatoday.com/tech/science/mathscience/2007-07-19-checkers-solved_N.htm. Retrieved 2008-11-24. 
5. ^ "Checkers 'solved' after years of number crunching - tech - 19 July 2007 - New Scientist Tech". Newscientisttech.com. http://www.newscientisttech.com/article/dn12296-checkers-solved-after. Retrieved 2008-11-24. 
6. ^ ^{a b} "Checkers Is Solved - Schaeffer et al. 317 (5844): 1518 - Science". Sciencemag.org. http://www.sciencemag.org/cgi/content/abstract/1144079. Retrieved 2008-11-24. 

External links

• World Draughts Federation
• English Draughts Association
• American Checkers Federation
• List of world checkers champions

 This article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed (1911). Encyclopædia Britannica (11th ed.). Cambridge University Press.