Backgammon

Backgammon

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Backgammon is one of the oldest board game
Board game
A board game is a game which involves counters or pieces being moved on a pre-marked surface or "board", according to a set of rules. Games may be based on pure strategy, chance or a mixture of the two, and usually have a goal which a player aims to achieve...

s for two players. The playing pieces are moved according to the roll of dice
Dice
A die is a small throwable object with multiple resting positions, used for generating random numbers...

, and players win by removing all of their pieces from the board. There are many variants of backgammon, most of which share common traits. Backgammon is a member of the tables
Tables (board game)
Tables is a general name given to a class of board games similar to backgammon, played on a board with two rows of 12 vertical markings called "points". Players roll dice to determine the movement of pieces...

 family, one of the oldest classes of board games in the world.

Although luck is involved and factors into the outcome, strategy plays a more important role in the long run. With each roll of the dice, players must choose from numerous options for moving their checkers and anticipate possible counter-moves by the opponent. Players may raise the stakes during the game. There is an established repertoire of common tactics and occurrences.

Like chess
Chess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...

, backgammon has been studied with great interest by computer scientists
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...

. Owing to this research, backgammon software has been developed capable of beating world-class human players.

Rules



Backgammon playing pieces are known variously as checkers, draughts
Draughts
Draughts is a group of abstract strategy board games between two players which involve diagonal moves of uniform pieces and mandatory captures by jumping over the enemy's pieces. Draughts developed from alquerque...

, stones, men, counters, pawns, or chips.

The objective is to remove (bear off) all of one's own checkers from the board before one's opponent can do the same. The checkers are scattered at first and may be blocked or hit by the opponent. As the playing time for each individual game is short, it is often played in matches, where victory
Victory
Victory is successful conclusion of a fight or competition..Victory may refer to:**strategic victory**tactical victory** Pyrrhic victory, a victory at heavy cost to the victorious party**Victory columns**Victory Monuments**Victory personified...

 is awarded to the first player to reach a certain number of points.

Setup


Each side of the board has a track of 12 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
Horseshoe
A horseshoe, is a fabricated product, normally made of metal, although sometimes made partially or wholly of modern synthetic materials, designed to protect a horse's hoof from wear and tear. Shoes are attached on the palmar surface of the hooves, usually nailed through the insensitive hoof wall...

, and are numbered from 1 to 24. Players begin with two checkers on their 24-point, three checkers on their 8-point, and five checkers each on their 13-point and their 6-point. The two players move their checkers in opposing directions, from the 24-point towards the 1-point.

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

Movement


To start the game, each player rolls one die, and the player with the higher number moves first using both the numbers shown. If the players roll the same number, they must roll again as the first move can not be a doublet. Both dice must land completely flat on the right hand side of the gameboard. The players then alternate turns, rolling two dice at the beginning of each turn.

After rolling the dice players must, if possible, move their checkers according to the number of pips shown on each die. For example, if the player rolls a 6 and a 3 (notated as "6-3"), that player must move one checker six points forward, and another or the same 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. If a player rolls two of the same number, called doublets, that player must play each die twice. For example, upon rolling a 5-5 that player may move up to four separate checkers forward five spaces each. For any roll, if a player can move both dice, that player is compelled to do so. If players cannot move either die in a roll, given the position of their checkers then that turn is over and the turn passes to the opponent. If either one die or the other but not both can be moved, the higher must be used. When removing checkers from the board ("bearing off"), the exact roll must be used unless a die is greater than any checker can use to bear off; in that case the die is played by taking a checker from the highest-numbered point off the board. If one die is unable to be moved, but such a move is made possible by the moving of the other die, that move is compulsory.

In the course of a move, a checker may land on any point that is unoccupied or is occupied only by a player's own checkers. It may also land on a point occupied by exactly one opposing checker, or "blot". In this case, the blot has been hit, and is placed in the middle of the board on the bar that divides the two sides of the playing surface. 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 simultaneously.

Checkers placed on the bar re-enter the game through the opponent's home board. A roll of 2 allows the checker to enter on the 23-point, a roll of 3 on the 22-point, and so forth. A player may not move any other checkers until all checkers on the bar belonging to that player have re-entered the game.

When all of a player's checkers are in that player's home board, that player may start removing them; this is called bearing off. A roll of 1 may be used to bear off a checker from the 1-point, a 2 from the 2-point, and so on. A die may not be used to bear off checkers from a lower-numbered point unless there are no checkers on any higher points. For example if a player rolls a 6 and a 5, but has no checkers on the 6-point, though 2 checkers remain on the 5-point, then the 6 and the 5 must be used to bear off the 2 checkers from the 5-point. When bearing off, a player may also move a lower die roll before the higher even if that means 'the full value of the higher die' is not fully utilized. For example, if a player has exactly 1 checker remaining on the 6-point, and rolls a 6 and a 1, the player may move the 6-point checker 1 place to the 5-point with the lower die roll of 1, and then bear that checker off the 5-point using the die roll of 6; this is sometimes useful tactically.

If one player has not borne off any checkers by the time that player's opponent has borne off all fifteen, then the player has lost a gammon, which counts for double a normal loss. If the losing player has not borne off any checkers and still has checkers on the bar or in the opponent's home board, then the player has lost a backgammon, which counts for triple a normal loss.

Doubling cube



To speed up match play and to provide an added dimension for strategy, a doubling cube is usually used. The doubling cube is not a die to be rolled but rather a marker, in the form of a cube with the numbers 2, 4, 8, 16, 32, and 64 inscribed on its sides, denoting the current stake. At the start of each game, the doubling cube is placed on the bar with the number 64 showing; the cube is then said to be "centered, on 1". When the cube is centered, the player about to roll may propose that the game be played for twice the current stakes. His opponent must either accept ("take") the doubled stakes or resign ("drop") the game immediately. If the opponent takes, the cube, now showing the doubled stake, is moved to the opponent's side of the board. This is done to indicate that the right to re-double belongs exclusively to the player who last accepted a double. Whenever a player accepts doubled stakes, the cube is placed on his side of the board with the corresponding power of two
Power of two
In mathematics, a power of two means a number of the form 2n where n is an integer, i.e. the result of exponentiation with as base the number two and as exponent the integer n....

 facing upward. If the opponent drops the doubled stakes, he loses the game at the current value of the doubling cube. For instance, if the cube showed the number 2 and a player wanted to redouble the stakes to put it at 4, the opponent choosing to drop the redouble would lose two, or twice the original stake.

The game is rarely redoubled beyond four times the original stake, but there is no limit on the number of redoubles. Although 64 is the highest number depicted on the doubling cube, the stakes may rise to 128, 256, and so on. In money games, a player is often permitted to "beaver" when offered the cube, doubling the value of the game again, while retaining possession of the cube.

A variant of the doubling cube "beaver" is the "raccoon." Players who doubled their opponent, seeing the opponent beaver the cube, may in turn then double the stakes once again ("raccoon") as part of that cube phase before any dice are rolled. The opponent retains the doubling cube. E.g. White doubles Black to 2 points, Black accepts then beavers the cube to 4 points; White, confident of a win, raccoons the cube to 8 points, whilst Black retains the cube. Such a move adds greatly to the risk of having to face the doubling cube coming back at 8 times its original value when first doubling the opponent (offered at 2 points, counter offered at 16 points) should the luck of the dice change.

Some players may opt to invoke The Murphy rule or the "automatic double rule." If both opponents roll the same opening number, the doubling cube is incremented on each occasion yet remains in the middle of the board, available to either player. The Murphy rule may be invoked with a maximum number of automatic doubles allowed and that limit is agreed to prior to a game or match commencing. When a player decides to double the opponent, the value is then a double of whatever face value is shown (e.g. if two automatic doubles have occurred putting the cube up to 4, the first in-game double will be for 8 points). The Murphy rule is not an official rule in backgammon and is rarely, if ever, seen in use at officially sanctioned tournaments.

The Jacoby rule, named after Oswald Jacoby
Oswald Jacoby
Oswald Jacoby was an American contract bridge player and author, considered one of the greatest bridge players of all time. He also excelled at, and wrote about, other games including backgammon, gin rummy, and poker.Born in Brooklyn, he was taught to play whist at the age of six and played his...

, allows gammons and backgammons to count for their respective double and triple values only if the cube has already been offered and accepted. This encourages a player with a large lead to double, possibly ending the game, rather than to play it to conclusion hoping for a gammon or backgammon. The Jacoby rule is widely used in money play but is not used in match play.

The Crawford rule, named after John R. Crawford
John R. Crawford
John Randolph Crawford was an American bridge and backgammon player...

, 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, that player's opponent will always want to double as early as possible in order to catch up. Whether the game is worth one point or two, the trailing player must win to continue the match. To balance the situation, the Crawford rule requires that when a player first reaches a score one point short of winning, 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. The Crawford rule is routinely used in tournament match play. It is possible for a Crawford game never to occur in a match.

If the Crawford rule is in effect, then another option is the Holland rule, which stipulates that after the Crawford game, a player cannot double until after at least two rolls have been played by each side. It was common in tournament play in the 1980s but is now rarely used.

Variants




There are many variants of standard backgammon rules. Some are played primarily throughout one geographic region, and others add new tactical elements to the game. Variants commonly alter the starting position, restrict certain moves, or assign special value to certain dice rolls, but in some geographic regions even the rules and directions of the checkers movement change, rendering the game fundamentally different.

Acey-deucey
Acey-deucey
Acey-deucey is a variant of backgammon. Since World War I, it has been a favorite game of the United States Navy, Marine Corps, and Merchant Marine. Some evidence shows that it was played in the early 1900s aboard U.S. Navy ships...

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, after moving the 1 and the 2, to select any desired doubles move. A player also receives an extra turn after a roll of 1-2 or of doubles.

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
Solved game
A solved game is a game whose outcome can be correctly predicted from any position when each side plays optimally. Games which have not been solved are said to be "unsolved"...

, meaning that exact equities
Expected value
In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...

 are available for all 32 million possible positions.

Nackgammon is a variant of backgammon invented by Nick "Nack" Ballard in which players start with one fewer checker on the six point and midpoint and two checkers on the 23 point.

Russian backgammon is a variant in which players start with no checkers on the board, and both players move in the same direction to bear off in a common home board. In this variant, doubles are more powerful: four moves are played as in standard backgammon, followed by four moves according to the difference of the dice value from 7, and then the player has another turn (with a few exceptions).

Gul Bara
Gul bara
Gul Bara is a backgammon variant. It is also called as ‘Rosespring Backgammon’ or ‘Crazy Narde’. The motive of the game is to move all of your checkers around the board and bear them off. The first player who bears off all his checkers wins the game...

and Tapa
Tapa (game)
Tapa is a version of Backgammon played in Bulgaria and Macedonia. It is also played in Greece, where it is known as Plakoto. The word tapa means bottle cap....

are also variants of the game popular in southeastern Europe and Turkey. The play will iterate among Backgammon, Gul Bara, and Tapa until one of the players reaches a score of 7 or 5.

Another simple variant of Backgammon is to only allow a maximum of five checkers on any point. This variation is not part of the official rules, but has proved popular with casual players in some regions (e.g., Britain).

Strategy and tactics


Backgammon has an established opening theory
Backgammon opening theory
The first moves of a backgammon game are the opening moves, collectively referred to as the opening, and studied in the backgammon opening theory. Backgammon opening theory is not developed in as much detail as opening theory in chess, which has been widely studied...

, although it is less detailed than that of games like chess. The tree
Game tree
In game theory, a game tree is a directed graph whose nodes are positions in a game and whose edges are moves. The complete game tree for a game is the game tree starting at the initial position and containing all possible moves from each position; the complete tree is the same tree as that...

 of positions expands rapidly because of the number of possible dice rolls and the moves available on each turn. Recent computer analysis has offered more insight on opening plays, but the midgame is reached quickly. After the opening, backgammon players frequently rely on some established general strategies, combining and switching among them to adapt to the changing conditions of a game.

The most direct strategy is simply to avoid being hit, trapped, or held in a stand-off. A "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. When this fails, one may opt for a "holding game", maintaining control of a point on one's opponent's side of the board, called an anchor. As the game progresses, this player may gain an advantage by hitting an opponent's blot from the anchor, or by rolling large doubles that allow the checkers to escape into a running game.

The "priming game" involves building a wall of checkers, called a prime, covering a number of consecutive points. This obstructs opposing checkers that are behind the prime. A checker trapped behind a six-point prime cannot escape until the prime is broken. A particularly successful priming effort may lead to a "blitz", which is a strategy of covering the entire 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, often with a gammon.

A "backgame" is a strategy of placing two or more anchors in an opponent's home board, while building a prime in one's own board. The anchors obstruct the opponent's checkers and create opportunities to hit them as they move home. 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.

"Duplication" refers to the placement of checkers such that one's opponent needs the same dice rolls to achieve different goals. For example, players may position all of their blots in such a way that the opponent must roll a 2 in order to hit any of them, reducing the probability of being hit more than once. "Diversification" refers to a complementary tactic of placing one's own checkers in such a way that more numbers are useful.

Many positions require a measurement of a player's standing in the race, for example, in making a doubling cube decision, or in determining whether to run home and begin bearing off. The minimum total of dice rolls needed to move a player's checkers around and off the board is called the "pip count". The difference between the two players' pip counts is frequently used as a measure of the leader's racing advantage. Players often use mental calculation
Mental calculation
Mental calculation comprises arithmetical calculations using only the human brain, with no help from calculators, computers, or pen and paper. People use mental calculation when computing tools are not available, when it is faster than other means of calculation , or in a competition context...

 techniques to determine pip counts in live play.

Backgammon is played in two principal variations, "Money" and "Match" play. Money play means that every point counts evenly and every game stands alone, whether money is actually being wagered or not. "Match" play means that the players play until one side scores (or exceeds) a certain number of points. The format has a significant effect on strategy. In a match, the objective is not to win the maximum possible number of points, but rather to simply reach the score needed to win the match. For example, a player leading a 9-point match by a score of 7-5 would be very reluctant to turn the doubling cube, as his opponent could take and make a costless redouble to 4, placing the entire outcome of the match on the current game. Conversely, the trailing player would double very aggressively, particularly if he has chances to win a gammon in the current game. In money play, the theoretically correct play would never vary based on the score or the value of the doubling cube.

Social and competitive play



Club and tournament play


Enthusiasts have formed club
Club
A club is an association of two or more people united by a common interest or goal. A service club, for example, exists for voluntary or charitable activities; there are clubs devoted to hobbies and sports, social activities clubs, political and religious clubs, and so forth.- History...

s 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. A few clubs offer additional services, maintaining their own facilities or offering computer analysis of troublesome plays. Some club leaders have noticed a recent growth of interest in backgammon, and attribute it to the game's popularity on the Internet
Internet
The Internet is a global system of interconnected computer networks that use the standard Internet protocol suite to serve billions of users worldwide...

.

A backgammon chouette
Backgammon chouette
The backgammon chouette is a variant of backgammon for three or more players. Traditionally played in person, today, the internet allows this form of backgammon to be played across different countries and various platforms...

 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.

Backgammon clubs may also organize tournaments. Large club tournaments sometimes draw competitors from other regions, with final matches viewed by hundreds of spectators. The top players at regional tournaments often compete in major national and international championships. Winners at major tournaments may receive prizes of tens of thousands of dollars.

International competition



The first world championship competition in backgammon was held in Las Vegas
Las Vegas, Nevada
Las Vegas is the most populous city in the U.S. state of Nevada and is also the county seat of Clark County, Nevada. Las Vegas is an internationally renowned major resort city for gambling, shopping, and fine dining. The city bills itself as The Entertainment Capital of the World, and is famous...

, Nevada in 1967. Tim Holland
Tim Holland (backgammon)
Tim Holland was a world-champion backgammon player, highly-compensated teacher of the game, author of three backgammon books and successful gambler who has won more major backgammon tournaments than anyone in history....

 was declared the winner that year and at the tournament the following year. For unknown reasons, there was no championship in 1969 or 1970, but in 1971, Tim Holland again won the title. The competition remained in Las Vegas until 1975, when it moved to Paradise Island
Paradise Island
Paradise Island is an island in the Bahamas formerly known as Hog Island. The island is located just off the shore of the city of Nassau, which is itself located on the northern edge of the island of New Providence. It is best known for the sprawling 'Vegas-by-the-sea resort' Atlantis.Paradise...

 in the Bahamas. The years 1976, 1977 & 1978 saw "dual" World Championships, one in the Bahamas attended by the Americans, and the European Open Championships in Monte Carlo
Monte Carlo
Monte Carlo is an administrative area of the Principality of Monaco....

 with mostly European players. In 1979, Lewis Deyong, who had promoted the Bahamas World Championship for the prior three years, suggested that the two events be combined. Monte Carlo was universally acknowledged as the site of the World Backgammon Championship and has remained as such for thirty years. The Monte Carlo tournament draws hundreds of players and spectators, and is played over the course of a week.

By the 21st century, the largest international tournaments had established the basis of a tour for top professional players. Major tournaments are held yearly worldwide. PartyGaming
PartyGaming
bwin.Party Digital Entertainment Plc is an online gambling company, formed by the March 2011 merger of PartyGaming plc and bwin. The world's largest publicly traded online gambling firm, it is best known for its online poker room PartyPoker.com and its sports betting brand Bwin. It is...

 sponsored the first World Series of Backgammon
World Series of Backgammon
World Series of Backgammon is a major televised live tour. The television shows capture the match action, jeopardy and background around some of the world’s largest backgammon tournaments, and have broadcast throughout Europe on Eurosport 1 and 2 whilst being distributed worldwide by ESPN...

 in 2006 from Cannes and later the 'Backgammon Million' tournament held in the Bahamas in January 2007 with a prize pool of one million dollars, the largest for any tournament to date. In 2008, the World Series of Backgammon
World Series of Backgammon
World Series of Backgammon is a major televised live tour. The television shows capture the match action, jeopardy and background around some of the world’s largest backgammon tournaments, and have broadcast throughout Europe on Eurosport 1 and 2 whilst being distributed worldwide by ESPN...

 ran the world's largest international events in London, the UK Masters, the biggest tournament ever held in the UK with 128 international class players; the Nordic Open which instantly became the largest in the world with around 500 players in all flights and 153 in the Championship, and Cannes, which hosted the Riviera Cup, the traditional follow-up tournament to the World Championships. Cannes also hosted the WSOB Championship, the WSOB finale which saw 16 players play three-point shootout matches for €160,000. The event was recorded for television in Europe airing on Eurosport.

The World Backgammon Association (WBA) has been holding the biggest backgammon Tour of the circuit since 2007, the "European Backgammon Tour" (EBGT), regrouping tournaments such as "Portuguese Open", "Georgian Open", "French Open", "Cyprus Open", "City of Venice", etc. With a total payout of around US$1,000,000, it is the richest circuit in backgammon, bringing the best players of the world together. WBA also stages the "US Open" and other events around the globe. WBA has contributed to a high stakes event called "Crowns Cup" broadcast on several TV-channels. In 2011, the WBA has announced collaborating with the online backgammon provider Play65
Play65
Play65 is an online backgammon operator established in 2004 by an Israeli-based company, SkillEmpire, that hosts real-time backgammon games and tournaments. With its client software available in 21 languages, including English, Arabic, Chinese, Danish, Dutch, etc. Play65 has more than 5,000,000...

 for the 2011 season of the European Backgammon Tour. The Play65/EBGT season has eight stops, seven in several European locations and one in the US (in collaboration with the American Backgammon Tour), and a corresponding number of online qualifiers. The season will be finished with a Grand Finale in Lefkosa, Northern Cyprus, where €25,000 will be split between the three finalists.

Gambling


When backgammon is played for money
Gambling
Gambling is the wagering of money or something of material value on an event with an uncertain outcome with the primary intent of winning additional money and/or material goods...

, the most common arrangement is to assign a monetary value to each point, 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 casino
Casino
In modern English, a casino is a facility which houses and accommodates certain types of gambling activities. Casinos are most commonly built near or combined with hotels, restaurants, retail shopping, cruise ships or other tourist attractions...

s. Before the commercialization of neural network
Neural network
The term neural network was traditionally used to refer to a network or circuit of biological neurons. The modern usage of the term often refers to artificial neural networks, which are composed of artificial neurons or nodes...

 programs, proposition bet
Proposition bet
In gambling, the term "proposition bet" has two definitions.-Primary definition:...

s on specific positions were very common among backgammon players and gamblers. As with most gambling games, successful play requires a combination of luck and skill, as a single dice roll can sometimes significantly change the outcome of the game.

Internet play


Backgammon software has been developed not only to play and analyze games, but also to facilitate play between humans over the internet
Internet
The Internet is a global system of interconnected computer networks that use the standard Internet protocol suite to serve billions of users worldwide...

. Dice rolls are provided by random or pseudorandom number generator
Pseudorandom number generator
A pseudorandom number generator , also known as a deterministic random bit generator , is an algorithm for generating a sequence of numbers that approximates the properties of random numbers...

s. Real-time online play began with the First Internet Backgammon Server
First Internet Backgammon Server
First Internet Backgammon Server is the earliest backgammon server on the Internet, operating since July 19, 1992.FIBS allows Internet users to play backgammon in real-time against other people and tracks player performance using a modified version of the Elo rating system. It was created by...

 in 1992. It is the longest running non-commercial backgammon server.

Play and analysis



Backgammon has been studied considerably by computer scientists
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...

. Neural networks
Artificial neural network
An artificial neural network , usually called neural network , is a mathematical model or computational model that is inspired by the structure and/or functional aspects of biological neural networks. A neural network consists of an interconnected group of artificial neurons, and it processes...

 and other approaches have offered significant advances to software for gameplay and analysis.

The first strong computer opponent was BKG 9.8. It was written by Hans Berliner
Hans Berliner
Hans Jack Berliner , a Professor of , is a former World Correspondence Chess Champion, from 1965–68. He is a Grandmaster of Correspondence Chess, and an International Master for over-the-board chess. He directed the construction of the chess computer HiTech. Berliner is also a chess writer.-Life...

 in the late 1970s on a DEC PDP-10
PDP-10
The PDP-10 was a mainframe computer family manufactured by Digital Equipment Corporation from the late 1960s on; the name stands for "Programmed Data Processor model 10". The first model was delivered in 1966...

 as an experiment in evaluating board game positions. Early versions of BKG played badly even against poor players, but Berliner noticed that its critical mistakes were always at transitional phases in the game. He applied principles of fuzzy logic
Fuzzy logic
Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1...

 to improve its play between phases, and by July 1979, BKG 9.8 was strong enough to play against the reigning world champion Luigi Villa
Luigi Villa
Luigi Villa is a backgammon player from Milan, Italy. In 1979, he was the winner of the World Championship held in Monte Carlo.The same year, he was defeated in a 7-point match by Hans Berliner's computer program BKG 9.8, becoming the first world champion in any board game to be defeated by a...

. It won the match, 7–1, becoming the first computer program to defeat a world champion in any board game. Berliner stated that the victory was largely a matter of luck, as the computer received more favorable dice rolls.

In the late 1980s, backgammon programmers found more success with an approach based on artificial neural network
Artificial neural network
An artificial neural network , usually called neural network , is a mathematical model or computational model that is inspired by the structure and/or functional aspects of biological neural networks. A neural network consists of an interconnected group of artificial neurons, and it processes...

s. TD-Gammon
TD-Gammon
TD-Gammon was a computer backgammon program developed in 1992 by Gerald Tesauro at IBM's Thomas J. Watson Research Center. Its name comes from the fact that it is an artificial neural net trained by a form of temporal-difference learning, specifically TD-lambda....

, developed by Gerald Tesauro of IBM
IBM
International Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...

, was the first of these programs to play near the expert level. Its neural network was trained using temporal difference learning
Temporal difference learning
Temporal difference learning is a prediction method. It has been mostly used for solving the reinforcement learning problem. "TD learning is a combination of Monte Carlo ideas and dynamic programming ideas." TD resembles a Monte Carlo method because it learns by sampling the environment according...

 applied to data generated from self-play. According to assessments by Bill Robertie
Bill Robertie
Bill Robertie is a backgammon, chess, and poker player and author. He is one of three backgammon players to have won the Monte Carlo World Backgammon Championship twice . Robertie also won the Pro-Am in the Bahamas in the year 1993 and the Istanbul World Cup in 1994. In chess, Robertie won the 1970...

 and Kit Woolsey
Kit Woolsey
Kit Woolsey is an American bridge and backgammon player. He graduated from Oberlin College in 1964. He earned a master's degree in mathematics from the University of Illinois at Urbana-Champaign in 1965....

, TD-Gammon's play was at or above the level of the top human players in the world. Woolsey said of the program that "There is no question in my mind that its positional judgment is far better than mine."

Tesauro proposed using rollout analysis to compare the performance of computer algorithms against human players. In this method, a Monte-Carlo evaluation of positions is conducted (typically thousands of trials) where different random dice sequences are simulated. The rollout score of the human (or the computer) is the difference of the average game results by following the selected move versus following the best move, then averaged for the entire set of taken moves.

Neural network research has resulted in three modern proprietary programs
Proprietary software
Proprietary software is computer software licensed under exclusive legal right of the copyright holder. The licensee is given the right to use the software under certain conditions, while restricted from other uses, such as modification, further distribution, or reverse engineering.Complementary...

, JellyFish, Snowie and eXtreme Gammon as well as the shareware
Shareware
The term shareware is a proprietary software that is provided to users without payment on a trial basis and is often limited by any combination of functionality, availability, or convenience. Shareware is often offered as a download from an Internet website or as a compact disc included with a...

 BGBlitz and the free software
Free software
Free software, software libre or libre software is software that can be used, studied, and modified without restriction, and which can be copied and redistributed in modified or unmodified form either without restriction, or with restrictions that only ensure that further recipients can also do...

 GNU Backgammon. These programs not only play the game, but offer tools for analyzing games and offering detailed comparisons of individual moves. The strength of these programs lies in their neural networks' weights tables, which are the result of months of training. Without them, these programs play no better than a human novice. For the bearoff phase, backgammon software usually relies on a database containing precomputed equities for all possible bearoff positions.

History


The history of backgammon goes back approximately 5,000 years.

Persia (Ancient Iran)


See Also: Nard
Nard (game)
Nard is a board game for two players in which the playing pieces are moved according to the roll of dice. It's similar to backgammon, uses the same board, but it has different initial positions and rules.- History :...

 


Excavations at Shahr-e Sokhteh (Persian
Persian language
Persian is an Iranian language within the Indo-Iranian branch of the Indo-European languages. It is primarily spoken in Iran, Afghanistan, Tajikistan and countries which historically came under Persian influence...

 شهر سوخته, literally "The Burnt City") in Iran
Iran
Iran , officially the Islamic Republic of Iran , is a country in Southern and Western Asia. The name "Iran" has been in use natively since the Sassanian era and came into use internationally in 1935, before which the country was known to the Western world as Persia...

 have shown that a similar game existed there around 3000 BC. The artifacts include two dice and 60 checkers, and the set is believed to be 100 to 200 years older than the sets found in Ur, and on the board found at Shahr-e Sokhteh the fields are fashioned by the coils of a snake.

Touraj Daryaee
Touraj Daryaee
Touraj Daryaee is a contemporary Persian Iranologist and historian.His elementary and secondary schooling was in Tehran, Iran and Athens, Greece. Daryaee took his Ph.D. in History at the University of California, Los Angeles in 1999...

 (2006)— on the subject of the first written mention of early precursors of backgammon—writes:
"The game of backgammon is first mentioned in Bhartrhari’s Vairagyasataka (p. 39), composed around the late sixth or early seventh century AD. The use of dice for the game is another indication of its Indic origin, since dice and gambling were a favorite pastime in ancient India. The rules of the game, however, first appeared in the Middle Persian
Middle Persian
Middle Persian , indigenously known as "Pârsig" sometimes referred to as Pahlavi or Pehlevi, is the Middle Iranian language/ethnolect of Southwestern Iran that during Sassanid times became a prestige dialect and so came to be spoken in other regions as well. Middle Persian is classified as a...

 text Wızarisnı Catrang ud Nihisnı New Ardaxsır (Explanation of Chess and Invention of Backgammon), composed in the sixth century during the rule of the Sasanian king Khosrow I (530–571). The text assigns its invention to the Persian sage Wuzurgmihr (Persian) Buzarjumihr/Bozorgmehr
Burzoe
Borzūya was a Persian physician in the late Sassanid era, at the time of Khosrow I.He translated the Indian Panchatantra from Sanskrit into the Middle Persian language of Pahlavi. But both his translation and the original Sanskrit version he worked from are lost...

, who was the minister of King Khosrow I
Khosrau I
Khosrau I , also known as Anushiravan the Just or Anushirawan the Just Khosrau I (also called Chosroes I in classical sources, most commonly known in Persian as Anushirvan or Anushirwan, Persian: انوشيروان meaning the immortal soul), also known as Anushiravan the Just or Anushirawan the Just...

, as a challenge for the Indian sages."


In the 11th century Shahnameh
Shahnameh
The Shahnameh or Shah-nama is a long epic poem written by the Persian poet Ferdowsi between c.977 and 1010 AD and is the national epic of Iran and related societies...

, the Persian poet Ferdowsi
Ferdowsi
Ferdowsi was a highly revered Persian poet. He was the author of the Shahnameh, the national epic of Iran and related societies.The Shahnameh was originally composed by Ferdowsi for the princes of the Samanid dynasty, who were responsible for a revival of Persian cultural traditions after the...

 credits Burzoe
Burzoe
Borzūya was a Persian physician in the late Sassanid era, at the time of Khosrow I.He translated the Indian Panchatantra from Sanskrit into the Middle Persian language of Pahlavi. But both his translation and the original Sanskrit version he worked from are lost...

 with the invention of the tables game nard in the 6th century. He describes an encounter between Burzoe and a Raja
Raja
Raja is an Indian term for a monarch, or princely ruler of the Kshatriya varna...

 visiting from India. The Raja introduces the game of chess
Chess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...

, and Burzoe demonstrates nard, played with dice made from ivory
Ivory
Ivory is a term for dentine, which constitutes the bulk of the teeth and tusks of animals, when used as a material for art or manufacturing. Ivory has been important since ancient times for making a range of items, from ivory carvings to false teeth, fans, dominoes, joint tubes, piano keys and...

 and teak
Teak
Teak is the common name for the tropical hardwood tree species Tectona grandis and its wood products. Tectona grandis is native to south and southeast Asia, mainly India, Indonesia, Malaysia, and Burma, but is naturalized and cultivated in many countries, including those in Africa and the...

. Today, Nard is the name for the Persian version of backgammon, which has different initial positions and objectives. H.J.R. Murray details many versions of Backgammon; modern Nard is noted there as being the same as backgammon and maybe dating back to 300 - 500 AD in the Babylonian Talmud.

Egypt and Iraq


Board games have existed for millennia in Ancient Egypt
Ancient Egypt
Ancient Egypt was an ancient civilization of Northeastern Africa, concentrated along the lower reaches of the Nile River in what is now the modern country of Egypt. Egyptian civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh...

 and Southwest Asia
Southwest Asia
Western Asia, West Asia, Southwest Asia or Southwestern Asia are terms that describe the westernmost portion of Asia. The terms are partly coterminous with the Middle East, which describes a geographical position in relation to Western Europe rather than its location within Asia...

. The ancient Egyptian game senet
Senet
Senet is a board game from predynastic and ancient Egypt. The oldest hieroglyph representing a Senet game dates to around 3100 BC. The full name of the game in Egyptian was zn.t n.t ḥˁb meaning the "game of passing."- History :...

, was excavated, along with illustrations, from ancient Egyptian royal tombs. The Royal Game of Ur
Royal Game of Ur
The Royal Game of Ur, also known as the Game of Twenty Squares, refers to two game boards found in the Royal Tombs of Ur in Iraq by Sir Leonard Woolley in the 1920s. The two boards date from the First Dynasty of Ur, before 2600 BC, thus making the Royal Game of Ur probably the oldest set of board...

, played in ancient Mesopotamia
Mesopotamia
Mesopotamia is a toponym for the area of the Tigris–Euphrates river system, largely corresponding to modern-day Iraq, northeastern Syria, southeastern Turkey and southwestern Iran.Widely considered to be the cradle of civilization, Bronze Age Mesopotamia included Sumer and the...

, may also be an ancestor of modern day table games.

Rome


The ancient Romans
Ancient Rome
Ancient Rome was a thriving civilization that grew on the Italian Peninsula as early as the 8th century BC. Located along the Mediterranean Sea and centered on the city of Rome, it expanded to one of the largest empires in the ancient world....

 played a number of games remarkably similar to backgammon. Ludus duodecim scriptorum
Ludus duodecim scriptorum
Ludus duodecim scriptorum, or XII scripta, was a tables game popular during the time of the Roman Empire. The name translates as "game of twelve markings", probably referring to the three rows of 12 markings each found on most surviving boards...

("Game of twelve lines") used a board with three rows of 12 points each, and the checkers were moved across all three rows according to the roll of dice. Little specific text about the gameplay has survived. Tabula
Tabula
Tabula was a board game in the tables family, and is generally thought to be the direct ancestor of modern backgammon.The earliest description of tabula is in an epigram of Byzantine Emperor Zeno , given by Agathias of Myrine , who describes a game in which Zeno goes from a strong position to a...

, meaning "table" or "board", was a game mentioned in an epigram of Byzantine
Byzantine Empire
The Byzantine Empire was the Eastern Roman Empire during the periods of Late Antiquity and the Middle Ages, centred on the capital of Constantinople. Known simply as the Roman Empire or Romania to its inhabitants and neighbours, the Empire was the direct continuation of the Ancient Roman State...

 Emperor Zeno
Zeno (emperor)
Zeno , originally named Tarasis, was Byzantine Emperor from 474 to 475 and again from 476 to 491. Domestic revolts and religious dissension plagued his reign, which nevertheless succeeded to some extent in foreign issues...

 (AD 476–481). It was similar to modern backgammon in that the object of the game was to be the first to bear off all of one's checkers. Players threw three dice and moved their checkers in opposing directions on a board of 24 points.

East Asia


It was popular for a time but then replaced by other games such as Xiangqi
Xiangqi
Xiangqi is a two-player Chinese board game in the same family as Western chess, chaturanga, shogi, Indian chess and janggi. The present-day form of Xiangqi originated in China and is therefore commonly called Chinese chess in English. Xiangqi is one of the most popular board games in China...

, which is similar to chess.

Europe


The jeux de tables (Games of Tables), predecessors of modern backgammon, first appeared in France during the 11th Century and became a favorite pastime of gamblers. In 1254, Louis IX
Louis IX of France
Louis IX , commonly Saint Louis, was King of France from 1226 until his death. He was also styled Louis II, Count of Artois from 1226 to 1237. Born at Poissy, near Paris, he was an eighth-generation descendant of Hugh Capet, and thus a member of the House of Capet, and the son of Louis VIII and...

 issued a decree prohibiting his court officials and subjects from playing. Tables games were played in Germany in the 12th century, and had reached Iceland
Iceland
Iceland , described as the Republic of Iceland, is a Nordic and European island country in the North Atlantic Ocean, on the Mid-Atlantic Ridge. Iceland also refers to the main island of the country, which contains almost all the population and almost all the land area. The country has a population...

 by the 13th century. In Spain
Spain
Spain , officially the Kingdom of Spain languages]] under the European Charter for Regional or Minority Languages. In each of these, Spain's official name is as follows:;;;;;;), is a country and member state of the European Union located in southwestern Europe on the Iberian Peninsula...

, the Alfonso X manuscript Libro de los juegos
Libro de los juegos
The Libro de los Juegos, , or Libro de acedrex, dados e tablas, was commissioned by Alfonso X of Castile, Galicia and León and completed in his scriptorium in Toledo in 1283, is an exemplary piece of Alfonso’s medieval literary legacy.Consisting of ninety-seven leaves of parchment, many with color...

, completed in 1283, describes rules for a number of dice and table games in addition to its extensive discussion of chess. By the 17th Century, tables games had spread to Sweden
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....

. A wooden board and checkers were recovered from the wreck of the Vasa
Regalskeppet Vasa
Vasa is a Swedish warship that was built from 1626 to 1628. The ship foundered and sank after sailing less than a nautical mile into its maiden voyage on 10 August 1628. It fell into obscurity after most of its valuable bronze cannons were salvaged in the 17th century...

 among the belongings of the ship's officers. Backgammon appears widely in paintings of this period, mainly those of Dutch and German painters (Van Ostade, Jan Steen
Jan Steen
Jan Havickszoon Steen was a Dutch genre painter of the 17th century . Psychological insight, sense of humour and abundance of colour are marks of his trade.-Life:...

, Hieronymus Bosch, Bruegel and others). Some surviving artworks are "Cardsharps
Cardsharps (Caravaggio)
The Cardsharps is a painting by the Italian Baroque artist Michelangelo Merisi da Caravaggio.-History:The work represents an important milestone for Caravaggio...

" by Caravaggio
Caravaggio
Michelangelo Merisi da Caravaggio was an Italian artist active in Rome, Naples, Malta, and Sicily between 1593 and 1610. His paintings, which combine a realistic observation of the human state, both physical and emotional, with a dramatic use of lighting, had a formative influence on the Baroque...

 (the backgammon board is in the lower left) and "The Triumph of Death
The Triumph of Death
The Triumph of Death is an oil painting on panel, painted c. 1562 by Pieter Bruegel the Elder. It is in the Museo del Prado in Madrid.The painting is a panoramic landscape: the sky in the distance is blackened by smoke from burning cities and the sea is littered with shipwrecks. Armies of...

" by Pieter Bruegel the Elder (the backgammon board is in the lower right). Others are the Hell of Bosch and interior of an Inn by Jan Steen.

England


In the sixteenth century, Elizabethan laws and church regulations prohibited playing tables, but by the eighteenth century backgammon was popular among the English clergy. Edmund Hoyle published A Short Treatise on the Game of Back-Gammon in 1743; this described rules and strategy for the game and was bound together with a similar text on whist
Whist
Whist is a classic English trick-taking card game which was played widely in the 18th and 19th centuries. It derives from the 16th century game of Trump or Ruff, via Ruff and Honours...

.

In English, the word "backgammon" is most likely derived from "back" and Middle English
Middle English
Middle English is the stage in the history of the English language during the High and Late Middle Ages, or roughly during the four centuries between the late 11th and the late 15th century....

 "gamen", meaning "game" or "play". The earliest use documented by the Oxford English Dictionary
Oxford English Dictionary
The Oxford English Dictionary , published by the Oxford University Press, is the self-styled premier dictionary of the English language. Two fully bound print editions of the OED have been published under its current name, in 1928 and 1989. The first edition was published in twelve volumes , and...

 was in 1650.

Greece
Greece
Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....

 and Cyprus
Cyprus
Cyprus , officially the Republic of Cyprus , is a Eurasian island country, member of the European Union, in the Eastern Mediterranean, east of Greece, south of Turkey, west of Syria and north of Egypt. It is the third largest island in the Mediterranean Sea.The earliest known human activity on the...


Backgammon
Backgammon
Backgammon is one of the oldest board games for two players. The playing pieces are moved according to the roll of dice, and players win by removing all of their pieces from the board. There are many variants of backgammon, most of which share common traits...

 is extremely popular among Greeks
Greeks
The Greeks, also known as the Hellenes , are a nation and ethnic group native to Greece, Cyprus and neighboring regions. They also form a significant diaspora, with Greek communities established around the world....

. Young and old play backgammon in coffee shops. It is a game in which Greeks usually tease their opponent and they create a lively atmosphere. The game is called "Tavli" meaning "board" in Greece. There are three games of Tavli commonly played:

Portes: This is similar to Western backgammon.

Plakoto
Plakoto
Plakoto is a tables game popular in Greece. The object of Plakoto is for the player to bring all their checkers around to their own home board and then bear them off. The player who bears off all of his checkers first wins the game. This game is usually played along with two other variants, Fevga...

: A game where one checker can trap another checker on the same point.

Fevga: A game of Turkish origin where one checker by itself can block a point.

These games are played one after another, in matches of three, five, or seven points.

Turkey


Backgammon is still a very popular game in Turkey
Turkey
Turkey , known officially as the Republic of Turkey , is a Eurasian country located in Western Asia and in East Thrace in Southeastern Europe...

, and it is customary to name the dice rolls with their Persian
Persian language
Persian is an Iranian language within the Indo-Iranian branch of the Indo-European languages. It is primarily spoken in Iran, Afghanistan, Tajikistan and countries which historically came under Persian influence...

 number names: yek (1), dü (2), se (3), cehar (4), penc (5), şeş (6).

United States


The most recent major development in backgammon was the addition of the doubling cube. It was first introduced in the 1920s in New York City
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...

 among members of gaming clubs in the Lower East Side
Lower East Side
The Lower East Side, LES, is a neighborhood in the southeastern part of the New York City borough of Manhattan. It is roughly bounded by Allen Street, East Houston Street, Essex Street, Canal Street, Eldridge Street, East Broadway, and Grand Street....

. The cube required players not only to select the best move in a given position, but also to estimate the probability of winning from that position, transforming backgammon into the expected value
Expected value
In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...

-driven game played in the 20th and 21st centuries.

Beginning in the mid-1960s, the popularity of Backgammon surged, in part due to the charisma of Prince Alexis Obolensky, who was known as “The Father of Modern Backgammon”. "Obe", as he was called by friends, co-founded the International Backgammon Association which published a set of official rules. He also established the World Backgammon Club of Manhattan, devised a backgammon tournament system in 1963, then organized the first major international Backgammon tournament in March, 1964 which attracted royalty, celebrities and the paparazzi
Paparazzi
Paparazzi is an Italian term used to refer to photojournalists who specialize in candid photography of celebrities, politicians, and other prominent people...

. The game became a huge fad and was played on college campuses, in discothèques and at country clubs; stockbrokers and bankers began playing at conservative men's clubs. People young and old all across the country dusted off their boards and checkers. Cigarette, liquor and car companies began to sponsor tournaments and Hugh Hefner
Hugh Hefner
Hugh Marston "Hef" Hefner is an American magazine publisher, founder and Chief Creative Officer of Playboy Enterprises.-Early life:...

 held backgammon parties at the Playboy Mansion
Playboy Mansion
The Playboy Mansion is the home of Playboy magazine founder Hugh Hefner. Located in the Holmby Hills area of Los Angeles, California, the mansion became famous during the 1970s through media reports of Hefner's lavish parties.-History:The house is described as being in the "Gothic-Tudor" style...

. Backgammon clubs were formed and tournaments were held, resulting in a World Championship promoted in Las Vegas
Las Vegas, Nevada
Las Vegas is the most populous city in the U.S. state of Nevada and is also the county seat of Clark County, Nevada. Las Vegas is an internationally renowned major resort city for gambling, shopping, and fine dining. The city bills itself as The Entertainment Capital of the World, and is famous...

 in 1967.

Most recently, the US Backgammon Federation (USBGF) was organized in 2009 to repopularize the game in the United States. Board and committee members include many of the top players, tournament directors and writers in the worldwide backgammon community. The USBGF has recently created a Standards of Ethical Practice to address issues on which tournament rules fail to touch.

See also



  • Backgammon notation
    Backgammon notation
    Backgammon notation is a means for recording backgammon games, developed by Paul Magriel in the 1970s. The common way of describing the movement of checkers involves numbering the points around the board from 24 to 1 as depicted in Figure 1....

  • Backgammon players (category)
  • Tables (board game)
    Tables (board game)
    Tables is a general name given to a class of board games similar to backgammon, played on a board with two rows of 12 vertical markings called "points". Players roll dice to determine the movement of pieces...

  • Table games
    Tabletop game
    Tabletop game is a general term used to refer to board games, card games, dice games, miniatures wargames, tile-based games and other games that are normally played on a table or other flat surface...



External links