Backgammon

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Backgammon
A modern backgammon set, consisting of a board, two sets of 15 checkers, 2 pairs of dice, and a doubling cube
Players2 (3+ players in some variants)
Setup time10–30 seconds
Playing time5–30 minutes (single game)
ChanceMedium (Dice rolling)
Age range5+
SkillsStrategy, Probability, Dice rolling

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.

While the game is essentially a race, in that each player is trying to move his checkers around the board and then remove them before his opponent does so, it incorporates a significant scope for strategy. With each dice roll, the 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. Today, the best backgammon software can defeat a world-class human player.

History

Old backgammon game recovered from the Vasa, sunk in 1628

Backgammon is one of the oldest board games played today, and can be most clearly traced to the ancient game tabula, which appears in an epigram of Byzantine Emperor Zeno (AD 476–481).[1]

The ancient Egyptians played a game called senet, which resembled backgammon,[2] 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. The set is believed to be 100 to 200 years older than the sets found in Ur.[3]

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.[4] Tabula, meaning "table" or "board", 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.[1][5]

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.[6] 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.[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.[8] The game described by Hoyle is, in most respects, the same as the game played today.

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.[9]

Rules

Backgammon is a game of moderate complexity but with deep strategic elements. It does not take long to learn to play, although obscure situations do arise which require careful interpretation of the rules. Because the playing time for each individual game is short, it is often played in matches, where, for example, victory is awarded to the player who first wins five points.

In short, a player tries to get all of his pieces past his opponent's pieces and then off the board. This is difficult because the pieces are scattered at first and may be blocked or captured by the opponent.

Setup

Each side of the board has a track of twelve adjacent spaces, called points, usually represented by long triangles of alternating (but meaningless) color. The tracks are imagined to be connected across the break in the middle and on just one edge of the board, making a continuous line (but not a circle) of twenty-four points. The points are numbered from 1 to 24, with checkers always moving from higher-numbered points to lower-numbered points. The two players move their checkers in opposite directions, so the 1-point for one player is noted as the 24-point for the other. Some recorded games, however, keep the numbering of the points constant from the perspective of one player. 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.[10] [11]

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

Points 1 to 6, where the player must attempt to move his pieces, are called the home board or inner board. A player may not bear off any checkers unless all of his checkers are in his home board. Points 7 to 12 are called the outer board, points thirteen to eighteen are the opponent's outer board, and points nineteen to twenty-four are the opponent's home board. The 7-point is often referred to as the bar point and the 13-point as the mid point.[10][11][12]

Movement

At the start of the game, each player rolls one die. Whoever rolls higher moves first, using the numbers on the already-rolled dice. In the case of a tie, the players roll again. The players then alternate turns, rolling two dice at the beginning of each turn after the first.[10][11][12]

After rolling the dice a player must, if possible, move checkers according to the number of points 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 one three points forward. The dice may be played in either order. 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 nine all at once.[10][11][12]

If a player has no legal moves after rolling the dice, because all of the points to which he might move are occupied by two or more enemy checkers, he forfeits his turn. However, a player must play both dice if it is possible. If he has a legal move for one die only, he must make that move and then forfeit the use of the other die. If he has a legal move for either die, but not both, he must play the higher number.[10][11][12]

Medieval backgammon players

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 play four checkers forward five spaces each. As before, a checker may be moved multiple times as long as the moves are distinct.[10][11][12]

A checker may land on any point occupied by no checkers or by friendly checkers. Also it may land on a point occupied by exactly one enemy checker (a lone piece is called a blot). In the latter case the blot has been hit, and is temporarily placed in the middle of the board on the bar, that is, the divider between the home boards and the outer boards. A checker may never land on a point occupied by two or more enemy checkers. Thus, no point is ever occupied by checkers from both players at the same time.[10][11][12]

Checkers 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 with one or more checkers on the bar may not move any other checkers until all of the checkers on the bar have re-entered the opponent's home field.[10][11][12]

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 number may not be used to bear off checkers from a lower point unless there are no checkers on any higher points.[10][11][12] For example, a 4 may be used to bear off a checker from the 3-point only if there are no checkers on the 4-, 5-, or 6-point.

A checker borne off from a lower point than indicated on the die still counts as the full die. For instance, suppose a player has only one checker on his 2-point and two checkers on his 1-point. Then on rolling 1-2 he may move the checker from the 2-point to the 1-point (using the 1 rolled), and then bear off from the 1-point (using the 2 rolled). He is not required to maximize the use of his rolled 2 by bearing off from the 2-point.

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 (i.e., two games toward the match in a game with normal stakes). If a player has not borne off any checkers, and still has checkers on the bar, or in his opponent's home board by the time his opponent has borne off all fifteen, or both, he has lost a backgammon, which counts for triple a normal loss (i.e., three games toward the match in a game with normal stakes).[10][11][12] In some variants, a further distinction is made between pieces in the opponent's home board, counting as a triple loss, and pieces on the bar, for a quadruple loss.

Doubling cube

Backgammon set, 19th century

To speed up match play and to increase the intensity of play and the need for strategy, a doubling cube is usually used. A doubling cube is a 6 sided die that instead of the numbers 1, 2, 3, 4, 5, 6 on it, has the numbers 2, 4, 8, 16, 32, 64 on it. If a player believes his position to be superior he may, before rolling the dice on his turn, double, i.e., demand that the game be played for twice the current stakes. The doubling cube is placed with the 2 side face up to show that the game's value has been doubled. His opponent must either accept the challenge or resign the game on the spot. Thereafter the right to redouble (double again) belongs exclusively to the player who last accepted a double. If this occurs, the cube is placed with the face of the next power of two showing.[10][11][12]

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

A common rule allows beavers, which is the right for a player to immediately redouble when offered the doubling cube while retaining the cube instead of giving it back up. The redouble must be called before the originally doubling player rolls the dice. In this way, the stakes of the game can rise dramatically.[11] A raccoon is sometimes pemitted as a response to a beaver. A player who accepts a beaver may offer a raccoon, redoubling again. Beavers and raccoons are commonly allowed when backgammon is played for money game by game and usually not allowed in matches.

The Jacoby rule allows gammons and backgammons to count for their respective double and triple points 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, and thus likely end the game, rather than see the game out 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.[11]

The Crawford rule makes match play much more equitable for the player in the lead. If a player is one point away from winning a match, his opponent has no reason not to double; after all, a win in the game by the player in the lead would cause him to win the match regardless of the doubled stakes, while a win by the opponent would benefit twice as much if the stakes are double. Thus there is no advantage towards winning the match to being one point shy of winning, if one's opponent is two points shy.[11] To remedy this situation, the Crawford rule requires that when a player becomes one single point short of winning the match, neither player may use the doubling cube for a single game, called the Crawford game. As soon as the Crawford game is over, normal use of the doubling cube resumes.[11] Not quite as universal as the Jacoby rule, the Crawford rule is widely used and generally assumed to be in effect for match play.

Sometimes automatic doubles are used, meaning that any re-rolls that players must make at the very start of a game (when each player rolls one die) have the side-effect of causing a double. Thus, a 3-3 roll, followed by a re-roll of 5-5, followed by a re-roll of 1-4 that begins the game in earnest will cause the game to be played from the start with 4-times normal stakes. The doubling cube stays in the middle, with both players having access to it. The Jacoby Rule is still in effect.[11] 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.

Strategy

Medieval tabula players, from the 13th century Carmina Burana

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.[13]

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.[13]

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.[13][14]

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.[10][13]

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.[10][13]

Duplication refers to the placement of checkers in such a way that advantageous rolls for one's opponent are duplicated among several possible moves, for example, a player positioning all of her blots in such a way that her opponent must roll a 2 in order to hit one. This reduces the probability that any blot will be hit.[10]

Gambling

Backgammon is often played for money. The most common arrangement is to assign a monetary value to each game, with the stakes raised by the doubling cube, gammons, and backgammons, and to play until a certain score is reached. Players may also simply assign a monetary value to each game, and play until either player chooses to stop. Backgammon is sometimes available in casinos.

Chouette

Main article: Backgammon chouette

A chouette[15] 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.[10]

Computer backgammon

Play and analysis

A screen shot of GNU Backgammon, showing a game analysis and rollout.

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 current 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.[16]

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.[17]

This line of research has resulted in two modern commercial programs, Jellyfish and Snowie, the shareware BGBlitz implemented in Java, and the free software GNU Backgammon, that play on a par with the best human players in the world. These programs 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.

Comparison to computer chess

As with chess, programmers have managed to develop backgammon software which can defeat world-class human players. It is worth comparing backgammon software with chess software in terms of their approaches to gameplay:

  1. For backgammon, neural networks have worked better than any other method so far. For chess, brute force searching, with sophisticated pruning and other refinements, works better than neural networks.
  2. Every advance in the power of computer hardware has significantly improved the strength of chess programs. In contrast, additional computing power appears to improve the strength of backgammon software only marginally.
  3. For both backgammon and chess, it is presently unclear whether the best computer or the best human is the stronger player. For most other games, one or the other is unambiguously stronger. Go, for example, is considered a serious challenge in the field of artificial intelligence. The best go software can still be beaten by lower-than-average club players;[18] nine men's morris has been solved and software exists that can win or draw against any human.

Internet backgammon

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. Real-time on-line play began with the First Internet Backgammon Server on July 19, 1992.[19] The server is still active as of 2006, remains free, 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.

See also

Notes and references

  1. ^ a b Austin, Roland G. "Zeno's Game of τάβλη", The Journal of Hellenic Studies 54:2, 1934. pp 202-205.
  2. ^ 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.
  3. ^ "Iran's Burnt City Throws up World’s Oldest Backgammon." Persian Journal. December 4, 2004. Retrieved on August 5, 2006.
  4. ^ Austin, Roland G. "Roman Board Games. I", Greece & Rome 4:10, October 1934. pp. 24-34.
  5. ^ Austin, Roland G. "Roman Board Games. II", Greece & Rome 4:11, February 1935. pp 76-82.
  6. ^ Lillich, Meredith Parsons. "The Tric-Trac Window of Le Mans", The Art Bulletin 65:1, March 1983. pp. 23-33.
  7. ^ 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.
  8. ^ Allee, Sheila. "A Foregone Conclusion: Fore-Edge Books Are Unique Additions to Ransom Collection". Retrieved on August 8, 2006.
  9. ^ "backgammon", The Oxford English Dictionary. Second Edition, 1989. Retrieved on August 5, 2006. (Subscription required)
  10. ^ a b c d e f g h i j k l m n o Robertie, Bill. Backgammon for Winners, Third Edition. 2002.
  11. ^ a b c d e f g h i j k l m n o p Keith, Tom. Backgammon Galore. "Backgammon Rules". 2006. Retrieved on August 5, 2006.
  12. ^ a b c d e f g h i j Hoyle's Rules of Games, Eighty-second printing. 1983
  13. ^ a b c d e "Basic Backgammon Strategies", www.redtopbg.com. Retrieved on August 5, 2006.
  14. ^ Backgammon Galore, "Backgammon FAQ", What is a prime?. Retrieved on August 9, 2006.
  15. ^ "Chouette" is a French term, referring to owls. As slang, it can also mean "cool", "nifty", "neat". Chouette, French Wikipedia.
  16. ^ Berliner, Hans, et. al. "Backgammon program beats world champ", ACM SIGART Bulletin, Issue 69. January 1980. pp 6-9.
  17. ^ Tesauro, Gerald. "Temporal difference learning and TD-Gammon", Communications of the ACM, 38:3. March 1995. pp 58-68.
  18. ^ On 11 Jul 2006, Senseis Library mentions there is much yet to be done in the field; see computer go.
  19. ^ Schneider, Andreas, et. al. "Brief history of FIBS", FIBS, the First Internet Backgammon Server. Retrieved on August 5, 2006.

External links

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