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Backgammon

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Backgammon
A modern backgammon set, consisting of a board, two sets of 15 checkers, two pairs of dice, and a doubling cube
Players2
Setup time10–30 seconds
Playing time5–30 minutes
ChanceMedium (Dice)
Age range5+
SkillsStrategy, Probability

Backgammon is a board game for two players in which pieces are moved according to the roll of dice and the winner is the first to remove all his pieces from the board. Many variants have developed throughout the world, but most share the same common elements. It is a member of the tables family of games.

The game is essentially a race, and luck plays a measurable role, but backgammon offers a significant scope for strategy. With each roll of the dice, a player must choose between numerous options for moving the checkers, and plan for possible counter-moves by his opponent. Opportunities for raising the stakes of the game introduce more strategic intricacies. Players have developed a vocabulary for common tactics and occurrences.

Like chess, backgammon has been studied considerably by computer scientists. Research has resulted in backgammon software that is capable of beating world-class human players.

History

Game recovered from the Vasa, sunk in 1628

The ancient Egyptians played a game called senet, which resembled backgammon,[1] with moves controlled by the roll of dice. The Royal Game of Ur, played in ancient Mesopotamia, is a more likely ancestor of modern tables games. Recent excavations at the "Burnt City" in Iran showed that a similar game existed there around 3000 BC. The artifacts include two dice and 60 pieces, and the set is believed to be 100 to 200 years older than the sets found in Ur.[2]

The ancient Romans played a number of games with remarkable similarities to backgammon. Ludus duodecim scriptorum ("game of twelve lines") used a board with three rows of 12 points each, and the pieces were moved across all three rows according to the roll of dice. Not much specific text about the gameplay has survived.[3] Tabula, meaning "table" or "board", was a game mentioned in an epigram of Byzantine Emperor Zeno (AD 476–481). It was similar to modern backgammon in that a board with 24 points was used, and the object of the game was to be the first to bear off all of one's checkers. Three dice were used instead of two, and opposing checkers moved in opposite directions.[4][5]

In the 11th century Shahnameh, the Persian poet Ferdowsi credits Burzoe with the invention of the tables game nard in the 6th century. He describes an encounter between Burzoe and a Raja visiting from India. The Raja introduces the game of chess, and Burzoe demonstrates nard, played with dice made from ivory and teak.[6][7]

The jeux de tables, predecessors of modern backgammon, first appeared in France during the 11th century and became a frequent pastime for gamblers. In 1254, Louis IX issued a decree prohibiting his court officials and subjects from playing the games.[7][8] Tables games were played in Germany in the 12th century, and had reached Iceland by the 13th century. While it is mostly known for its extensive discussion of chess, the Alfonso X manuscript Libro de los juegos, completed in 1283, describes rules for a number of dice and tables games.[9] By the 17th century, tables games had spread to Sweden. A wooden board and checkers were recovered from the wreck of the Vasa among the belongings of the ship's officers.[10]

In the 16th century, Elizabethan laws and church regulations had prohibited playing tables, but by the 18th century backgammon was popular among the English clergy.[7] Edmund Hoyle published A Short Treatise on the Game of Backgammon in 1743; this book described the rules of the game and was bound together with a similar text on whist.[11] The game described by Hoyle is, in most respects, the same as the game played today.[7]

Name

  • In English, the word "backgammon" is most likely derived from "back" and Middle English "gamen", meaning "game" or "play". The earliest use documented by the Oxford English Dictionary was in 1650.[12]
  • In Arabic, the game is called tawilat el-nard (طاولة النرد) or tawilat el-zahr (طاولة الزهر), meaning "board of dice".
  • In Chinese, the game is called shuang lu (双陆), meaning "double sixes".[7]
  • in Dutch, the game is called triktrak.
  • In Greek, it is referred to as portes and is played as one of the three games in a tavli match.
  • In Hebrew, it is called shesh besh (שש בש), derived from the Persian and Turkish for "six" and "five"[13]
  • In Japanese, sugoroku (双六) refers to backgammon as well as other racing games.[7]
  • In Persian, backgammon is called takhte nard, meaning "battle on a wooden board".
  • In Portuguese, backgammon is called gamão.
  • In Romanian, backgammon is called table.
  • In Turkish, the game is called tavla.

Rules

The objective of backgammon is to move all of one's own checkers past those of one's opponent and then remove them from the board. The pieces are scattered at first and may be blocked or hit by the opponent. Because the playing time for each individual game is short, it is often played in matches, where victory is awarded to the first player to reach a certain number of points.

Setup

Each side of the board has a track of twelve long triangles, called points. The points are considered to be connected across one edge of the board, forming a continuous track in the shape of a horseshoe, numbered from 1 to 24. Each player begins with two checkers on his 24-point, three checkers on his 8-point, and five checkers each on his 13-point and his 6-point. The two players move their checkers in opposite directions, each from his own 24-point toward his 1-point. [14] [15]

Path of movement for blue and green; checkers are in starting position

Points 1 to 6 are called the home board or inner board, and points 7 to 12 are called the outer board. The 7-point is referred to as the bar point and the 13-point as the mid point.[14][15][16]

Movement

At the start of the game, each player rolls one die, and the player with the higher number moves first. The players then alternate turns, rolling two dice at the beginning of each turn.[14][15][16]

After rolling the dice a player must, if possible, move checkers according to the number of pips showing on each die. For example, if he rolls a 6 and a 3 (noted as "6-3") he must move one checker six points forward, and another checker three points forward. The same checker may be moved twice as long as the two moves are distinct: six and then three, or three and then six, but not all nine at once. If a player rolls two of the same number (doubles) he must play each die twice. For example, upon rolling a 5-5 he must move four checkers forward five spaces each.[14][15][16]

A checker may land on any point that is either unoccupied or is occupied only by a player's own checkers. It may also land on a point occupied by exactly one opposing checker; such a lone piece is called a blot. In the latter case, the blot has been hit, and is placed in the middle of the board on the bar, the divider between the home boards and the outer boards. A checker may never land on a point occupied by two or more opposing checkers, thus, no point is ever occupied by checkers from both players at the same time. [14][15][16]

Medieval players, from the 14th century Codex Manesse

Checkers placed on the bar re-enter the game through the opponent's home field. A roll of 2 allows the checker to enter on the 23-point, a roll of 3 on the 22-point, etc. A player may not move any other checkers until all of his checkers on the bar have first re-entered the opponent's home field.[14][15][16]

When all of a player's checkers are in his home board, he must bear off, removing the checkers from the board. A roll of 1 may be used to bear off a checker from the 1-point, a 2 from the 2-point, etc. A die may not be used to bear off checkers from a lower-numbered point unless there are no checkers on any higher points.[14][15][16]

If one player has not borne off any checkers by the time his opponent has borne off all fifteen, he has lost a gammon, which counts for double a normal loss. If the losing player still has checkers on the bar or in his opponent's home board, he has lost a backgammon, which counts for triple a normal loss.[14][15][16]

Doubling cube

Backgammon set, 19th century

To speed up match play and to provide an added dimension for strategy, a doubling cube is normally used. The doubling cube is a 6-sided die marked with the numbers 2, 4, 8, 16, 32 and 64. If a player believes his position to be superior he may, before rolling the dice on his turn, double, demanding that the game be played for twice the current stakes. The doubling cube is then placed with the 2 side face up to show that the game's value has been doubled. His opponent must either accept the new stakes or resign the game immediately. Thereafter the right to redouble belongs exclusively to the player who last accepted a double. When this occurs, the cube is placed with the face of the next power of two showing.[14][15][16]

The game is rarely redoubled beyond four times the original stake, but there is no theoretical limit on the number of doubles. Although 64 is the highest number depicted on the doubling cube, the stakes may rise to 128, 256, 512 and so on.

In money games, a player is often permitted to beaver when offered a double, doubling the value of the game again, while retaining possession of the cube.[15]

The Jacoby rule allows gammons and backgammons to count for their respective double and triple values only if there has been at least one use of the doubling cube in the game. This encourages a player with a large lead in a game to double, possibly ending the game, rather than to play the game to its conclusion in hopes of a gammon or backgammon. The Jacoby Rule is widely used in money play but is not used in match play.[15]

The Crawford rule is designed to make match play more equitable for the player in the lead. If a player is one point away from winning a match, his opponent has no incentive not to double; whether the game is worth one point or two, the outcome of the match is unaffected.[15] To balance the situation, the Crawford rule requires that when a player first reaches a score one point short of winning the match, neither player may use the doubling cube for the following game, called the Crawford game. After the Crawford game, normal use of the doubling cube resumes.[15] The Crawford rule is used in most match play.

Sometimes automatic doubles are used, meaning that any ties in the very first roll of the game automatically double the stakes. Thus, after a 3-3 roll, followed by a re-roll of 5-5, followed by a re-roll of 1-4 to begin the game itself, the game would be played for quadruple stakes. The doubling remains in the middle, with both players having access to it, and the Jacoby Rule is still in effect.[15] Again, automatic doubles are common in money games. but they are rarely, if ever, used in match play.

Variants

Main article: Tables (board game)

There are many variants to standard backgammon rules. Some are played primarily throughout one geographic region, and others add new tactical elements to the game, such as by altering the starting position, restricting certain moves, or assigning special value to certain dice rolls.

Acey-deucey

Main article: Acey-deucey

Acey-deucey is a variant of backgammon in which players start with no checkers on the board, and must bear them on at the beginning of the game. The roll of 1-2 is given special consideration, allowing the player to select doubles of her choice. A player also receives an extra turn after the roll of 1-2 or of doubles.

Hypergammon

Main article: Hypergammon

Hypergammon is a variant of backgammon in which players have only three checkers on the board, starting with one each on the 24-, 23- and 22-points. The game has been strongly solved, meaning that exact equities are available for all 32 million positions possible in the game.[17]

Nackgammon

Nackgammon is a variant devised by Nack Ballard. It differs only in its initial setup: each player starts with two checkers on the 24-point, two checkers on the 23-point, three checkers on the 8-point, and four checkers each on the 13-point and 6-point. Each side still has fifteen checkers total, but with two checkers on each side starting further back, there is more initial contact between the two sides, and less chance the game will quickly develop into a race.[18]

Old English

Old English backgammon restricts the number of checkers to a maximum of five on each point, thus forbidding some moves that might otherwise be made. A player may also opt to play one part of a roll in such a way that the rest may not be played.[19]

Strategy

Backgammon has an established opening theory, although it is less detailed than that of games like chess. The tree of checker positions expands quickly because of the number of possible dice rolls and the moves available on each turn. Recent computer analysis has offered more insight on opening moves, but the midgame is reached quickly. After the opening moves, backgammon players frequently rely on some established general strategies, and will combine and switch among them to adapt to changing conditions as a game unfolds.

The most direct and sometimes the most successful strategy is simply to avoid being hit, trapped, or getting into mutually blocked stand-offs. The running game describes a strategy of moving as quickly as possible around the board, and is most successful when a player is already ahead in the race.[20]

A holding game is a strategy wherein a player keeps a point high in his opponent's board or on his opponent's bar point, as the game progresses. The player may gain an advantage by hitting an opponent's blot from the held point, or by rolling large doubles that allow the player to advance both checkers and begin a running game.[20]

The priming game involves building a wall of checkers, called a prime, ideally covering six consecutive points. This obstructs opposing checkers that are behind the blockade. The prime is usually built somewhere between the 11-point and the 2-point, and then shuffled into the home board as the game progresses.[20][21]

A blitz describes a strategy of closing the home board as quickly as possible while keeping one's opponent on the bar. Because the opponent has difficulty re-entering from the bar or escaping, a player can quickly gain a running advantage and win the game.[14].

A backgame is a strategy of placing two or more anchors (points with two or more checkers) in one's opponent's home board, while building a prime in one's own home board. The anchors obstruct the opponent's checkers, and create opportunities to hit them as they move toward the home board. The backgame is generally used only to salvage a game wherein a player is already significantly behind; using a backgame as an initial strategy is usually unsuccessful.[14][20]

Duplication refers to the placement of checkers in such a way that advantageous dice rolls for one's opponent are the same for a number of desirable moves. For example, a player may position all of her blots in such a way that her opponent must roll a 2 in order to hit one, reducing the probability that any blot will be hit.[14][20] Diversification refers to a complementary tactic of placing one's own checkers in such a way that more numbers are useful.[20]

Social and competitive play

Medieval players, from the 13th century Carmina Burana

Club and tournament play

Enthusiasts have formed clubs for social play of backgammon. Local clubs may hold informal gatherings, with members meeting at cafés and bars in the evening to play and converse.[22][23] A few clubs offer additional services, maintaining their own facilities or offering computer analysis of troublesome plays.[24] Some club leaders have noticed a recent growth of interest in backgammon, and attribute it to the game's popularity on the internet.[25]

A backgammon chouette[26] permits three or more players to participate in a single game, often for money. One player competes against a team of all the other participants, and positions rotate after each game. Chouette play often permits the use of multiple doubling cubes.[14]

Backgammon clubs may also organize tournaments. Large club tournaments sometimes draw competitors from other regions, with final matches viewed by hundreds of spectators.[27] The top players at regional tournaments often compete in major national and international championships. Winners at top tournaments may receive prizes of tens of thousands of dollars.[28] One sponsor announced a purse of US$1,000,000 for a tournament held in the Bahamas in 2006.[29]

World Backgammon Championship

Prior to 1979, there was no single world championship competition in backgammon. A number of tournaments were held in Las Vegas and the Bahamas. Since 1979, the World Backgammon Championship in Monte Carlo has been widely acknowledged as the top international tournament.[30] The tournament in Monte Carlo draws thousands of players and spectators, and is played over the course of a week.[28]

Gambling

When backgammon is played for money, the most common arrangement is to assign a monetary value to each game, and to play to a certain score, or until either player chooses to stop. The stakes are raised by gammons, backgammons, and use of the doubling cube. Backgammon is sometimes available in casinos. As with most gambling games, successful play requires a combination of both luck and skill, as a single dice roll can, in some circumstances, significantly change the outcome of the game.[20]

Software

Play and analysis

A screen shot of GNU Backgammon, showing an evaluation and rollout of possible moves.

Backgammon has been studied considerably by computer scientists. Neural networks and other approaches have offered significant advances to software both for gameplay and analysis.

The first strong computer opponent was BKG 9.8. It was written by Hans Berliner in the late 1970s on a DEC PDP-10 as an experiment in evaluating board positions. Early versions of BKG played badly even against poor players, but Berliner noticed that its critical mistakes were always at phase changes. He applied principles of fuzzy logic to smooth out the transition between phases, and by July 1979, BKG 9.8 was strong enough to play against the ruling world champion Luigi Villa. It won the match, 7-1, becoming the first computer program to defeat a world champion in any game. Berliner states that the victory was largely a matter of luck, as the computer received more favorable dice rolls.[31]

In the late 1980s, creators of backgammon software began to have more success with an approach based on neural networks. TD-Gammon, developed by Gerald Tesauro of IBM, was the first of these programs to play near the expert level. Its neural network was trained using temporal difference learning applied to data generated from self-play.[32] According to assessments by Bill Robertie and Kit Woolsey, TD-Gammon plays at or above the level of the top human players in the world.[32]

This line of research has resulted in two modern commercial programs, Jellyfish and Snowie, as well as the shareware BGBlitz implemented in Java, and the free software GNU Backgammon. They also offer tools for analyzing games and offering detailed comparisons of individual moves. It is worth noting that without their associated "weights" tables, which represent hours or even months of tedious neural net training, these programs play no better than a human novice.

Internet play

Backgammon software has been developed not only to play and analyze games, but also to facilitate play between humans from different parts of the world over the internet. Dice rolls are provided by random or pseudorandom number generators. Real-time on-line play began with the First Internet Backgammon Server on July 19, 1992.[33] The server is the longest running non-commercial backgammon server and enjoys a strong international community of backgammon players. Several commercial websites also offer on-line real-time backgammon play. Yahoo! Games has offered a Java-based online backgammon game since 1997. MSN Games currently offers a backgammon game based on ActiveX. The online gambling industry began to expand its offerings to include backgammon in 2006.[34]

See also

Notes and references

  1. ^ Hayes, William C. "Egyptian Tomb Reliefs of the Old Kingdom", The Metropolitan Museum of Art Bulletin, New Series 4:7. March 1946. pp 170-178.
  2. ^ "Iran's Burnt City Throws up World’s Oldest Backgammon." Persian Journal. December 4, 2004. Retrieved on August 5, 2006.
  3. ^ Austin, Roland G. "Roman Board Games. I", Greece & Rome 4:10, October 1934. pp. 24-34.
  4. ^ Austin, Roland G. "Roman Board Games. II", Greece & Rome 4:11, February 1935. pp 76-82.
  5. ^ Austin, Roland G. "Zeno's Game of τάβλη", The Journal of Hellenic Studies 54:2, 1934. pp 202-205.
  6. ^ Wilkinson, Charles K. "Chessmen and Chess", The Metropolitan Museum of Art Bulletin. New Series 1:9, May 1943. pp. 271-279
  7. ^ a b c d e f Murray, Harold James Ruthven (1952). "6: Race-Games". A History of Board-Games Other than Chess. Hacker Art Books. ISBN 0878172114.
  8. ^ Lillich, Meredith Parsons. "The Tric-Trac Window of Le Mans", The Art Bulletin 65:1, March 1983. pp. 23-33.
  9. ^ Wollesen, Jens T. "Sub specie ludi...: Text and Images in Alfonso El Sabio's Libro de Acedrex, Dados e Tablas", Zeitschrift für Kunstgeschichte 53:3, 1990. pp. 277-308.
  10. ^ "Vasamuseet — The Swedish-Tables Association", The Vasa Museum. Retrieved on August 12, 2006.
  11. ^ Allee, Sheila. "A Foregone Conclusion: Fore-Edge Books Are Unique Additions to Ransom Collection". Retrieved on August 8, 2006.
  12. ^ "backgammon", The Oxford English Dictionary. Second Edition, 1989. Retrieved on August 5, 2006. (Subscription required)
  13. ^ Stahl, Avraham. Bilingual Etymological Dictionary of Spoken Israeli Arabic and Hebrew. 1995. Cited in "shesh", Balashon — Hebrew Language Detective. May 8, 2006. Retrieved on September 15, 2006.
  14. ^ a b c d e f g h i j k l m Robertie, Bill. Backgammon for Winners, Third Edition. 2002.
  15. ^ a b c d e f g h i j k l m n Keith, Tom. Backgammon Galore. "Backgammon Rules". 2006. Retrieved on August 5, 2006.
  16. ^ a b c d e f g h Hoyle's Rules of Games, Eighty-second printing. 1983
  17. ^ "Backgammon Variants: Hyper-backgammon". Backgammon Galore. Retrieved 2006-11-19.
  18. ^ "Backgammon Variants: Nackgammon". Backgammon Galore. Retrieved 2006-11-19.
  19. ^ "Backgammon Variants: Old English Backgammon". Backgammon Galore. Retrieved 2006-11-19.
  20. ^ a b c d e f g Magriel, Paul (1976). Backgammon. Quadrangle/The New York Times Book Co. ISBN 0812906152.
  21. ^ Backgammon Galore, "Backgammon FAQ", What is a prime?. Retrieved on August 9, 2006.
  22. ^ "Tribes of Sydney — Sydney Backgammon Club", The Daily Telegraph (Australia). June 24, 2006. p. 95
  23. ^ Bray, Chris. "Backgammon", The Independent (London). June 29, 2002. p. 50
  24. ^ Bray, Chris. "Backgammon", The Independent (London). November 25, 2000. p. 19
  25. ^ Laverty, Roy. "Backgammon warriors — columnist, club member square off as board game's popularity grows", The Alameda Times-Star. May 16, 2003. Section: Bay Area Living.
  26. ^ "Chouette" is a French term, referring to owls. As slang, it can also mean "cool", "nifty", "neat". Chouette, French Wikipedia.
  27. ^ Magriel, Paul. "Backgammon: Before Planning Big Attack, Be Sure to Cover Your Rear", The New York Times. June 1, 1980, Late City Final Edition. Section 1, part 2, p. 50.
  28. ^ a b Maxa, Rudy. "Where the Rich And the Royal Play Their Games — Monte Carlo's Seven-Day Backgammon Soiree With Countesses, Princes and Other Sharpies", The Washington Post. September 6, 1981. p. H1
  29. ^ "PartyGammon.com to Stage First Ever US$1 Million Backgammon Tournament", PR Newswire. July 10, 2006. Retrieved via Lexis-Nexis on August 12, 2006.
  30. ^ Michael Crane (July 25, 2000). "Backgammon News — World Championships 2000". Mind Sports Worldwide. Retrieved 2006-09-14. {{cite web}}: Check date values in: |date= (help)
  31. ^ Berliner, Hans, et. al. "Backgammon program beats world champ", ACM SIGART Bulletin, Issue 69. January 1980. pp 6-9.
  32. ^ a b Tesauro, Gerald. "Temporal difference learning and TD-Gammon", Communications of the ACM, 38:3. March 1995. pp 58-68.
  33. ^ Schneider, Andreas, et. al. "Brief history of FIBS", FIBS, the First Internet Backgammon Server. Retrieved on August 5, 2006.
  34. ^ Lemke, Tim. "Odds favor Internet gambling — Lawmakers aim to rein in industry", The Washington Times. March 19, 2006. p. A1.

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