Backgammon

Close-up of modern backgammon set.

Backgammon set, 19th century

Backgammon is a board game for two players. Each player has fifteen pieces (checkers or men) which move between twenty-four triangles (points) according to the roll of two dice. The objective of the game is to be first to bear off, that is, to move all fifteen checkers off the board.

History

Backgammon is the oldest known recorded game. Traditionally, it was believed to have originated in ancient Egypt, Sumeria, or Mesopotamia in the Persian empire (present-day Iran). However, more recent conclusive evidence indicates that the game originated on the eastern borders of Iran, near Afghanistan.(e.g.) The Iranian chancellor and thinker of the Sassanid Empire Bozorgmehr is said to have created the ancient version of the game. In English, the word backgammon is believed to be derived from "back" plus the Middle English word "gamen" (game).

Tabula was a form of backgammon played by the ancient Romans. It was called tabula, which means 'table' or 'board', since it was played on a special board. Tabula bears some similarity to Egyptian Senet, which dates back to at least 3000 BC.

The game of Tabula was similar to modern-day Backgammon in that the same board was used with fifteen pieces alloted to each player with the object of the game being to be the first to bear off all fifteen pieces. It differed in that the game began with no pieces on the board so that these first had to be entered by the roll of the dice. Likewise, three dice were used instead of two. Finally, both players entered the board from the same table and moved around the board in the same counterclockwise direction.

Rules

Backgammon is a simple game 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. The playing time for each individual game is short, so it is often played in matches, for example the first to five points. Game and match are used in Backgammon to refer to these distinct elements, as in, "I won two games in a row, but then she won three in a row and I lost the match, three points to two."

In short, players are trying to get all of their pieces past their opponent's pieces. This is difficult because the pieces are scattered at first, and may be blocked or captured by the opponent's pieces.

Each side of the board has a track of twelve adjacent spaces, called points and 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 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.

File:Bg sg start.png

Note that the board as shown can be flipped horizontally, with starting positions and direction of play likewise flipped but with no changes to the mechanics of gameplay. The two orientations are equally common and game boards are all designed to be played both ways.

Points one to six, where the player wants to get his pieces to, 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 seven to twelve 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.

At the start of the game, each player rolls one die. Whoever rolls higher starts his first turn using the numbers on the already-rolled dice. In case of a tie, the players roll again. The players alternate turns and roll two dice at the beginning of each turn after the first.

After rolling the dice a player must, if possible, move checkers the number of points showing on each die. For example, if he rolls a 6 and a 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.

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.)

If a player rolls two of the same number (doubles) he must play each die twice. For example, upon rolling a 5 and a 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.

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, i.e., the divider between the home boards and the outfields. 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.

Checkers on the bar re-enter the game through the opponent's home field. A roll of 1 allows the checker to enter on the 24-point, a roll of 2 on the 23-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.

When all of a player's checkers are in his home board, he may remove them from the board, or bear them off. 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. 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-, and 6-points.

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 twice a normal loss. 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. Sometimes a distinction is made between pieces in the opponent's home board (triple loss) and pieces on the bar (quadruple loss).

The doubling cube

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 2 showing.

The game rarely is redoubled beyond 4 times the original stake, but there is no theoretical limit on the number of doubles. Even though 64 is the highest number on the doubling cube, the stakes may rise to 128, 256, 512 and so on.

Beavers

A common rule allows beavers - 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.

Beavers are commonly allowed when backgammon is played for money game by game, and usually not allowed in matches.

Jacoby Rule

The Jacoby Rule makes gammons and backgammons 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.

Crawford Rule

The Crawford Rule makes match play much more fair 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!

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, any further games use the doubling cube normally.

Not quite as universal as the Jacoby Rule, the Crawford Rule is widely used and generally assumed to be in effect for match play.

Automatic Doubles

When Automatic Doubles are used, 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.

Automatic Doubles are common in money games (upon agreement). They are never used in match play.

Three Basic Strategies

In very general terms, there are 3 basic strategies employed. You need to be able to switch strategies instantly as the course of the game unfolds.

The Blockade

This involves building a 6-thick wall of checkers, or at least as thick as you can manage, to block in the opponent's checkers that are on your 1-point. This is considered to be the most suitable strategy at the start of the game. You can build the wall anywhere between your 11-point and your 2-point and then shuffle it into your home board as the game progresses.

The Blitz

This involves closing your home board as quick as possible while keeping your opponent on the bar. For example, if your opponent rolls an early 2 and moves one checker from your 1-point to your 3-point and you then roll a 5-5, you can play 6/1 6/1 8/3 8/3. Your opponent is now in serious trouble because they have 2 checkers on the bar and you have closed half your inner board!

The Backgame

This is where you have 2 or more anchors in your opponent's home board. (An anchor is a point occupied by at least 2 of your checkers.) It should be used when you are significantly behind as it much improves your chances. The best places for anchors are towards your opponent's lower point and either on adjacent points or with a single point in between. Timing is crucial for an effective backgame: after all, there's no point having 2 nice anchors and a solid wall in your own home board if you are then forced to dismantle this straight away, while your opponent is getting their checkers home, because you don't have other spare checkers to move! In this case, it's better to have checkers on the bar so that you can preserve your position until your opponent gives you a chance to hit, so it can be a good idea to try and get your opponent to hit them in this case!

Some people go for a backgame from the outset, but this is a mistake. The backgame is a losing strategy: it's just that this strategy makes you less likely to lose if you are already losing!

Sample Game

A few turns from the beginning of a sample game will illustrate the rules of movement. To start the game blue rolls a 4 and green rolls a 1, so blue takes the first turn playing a 4,1. This is an unfavorable opening roll, arguably the worst possible, but blue uses it the best he can. He takes a checker from each of his heavy points by playing 13-9, 6-5.

It is seldom useful to have five checkers on the same point, so blue starts to spread his checkers around. He is threatening to build a prime, i.e., a blockade to prevent green's two trailing checkers from getting home. The disadvantage of blue's choice is that it isn't very safe. It leaves two blots which green might hit. Some experts prefer the less aggressive but safer move of 24-23, 13-9.

Green rolls a 4, 4. This is an extremely lucky roll. Not only can he hit both of blue's blots with 1-5*-9*, he also has two more fours to play. He may, for example play 19-23(2), moving two checkers from his 6-point to the 2-point. This leaves blue with two checkers on the bar, trying to re-enter against green's home board, which has two points blocked by green.

Green was wise to hit twice, because it disrupts blue's efforts to build a prime, and it puts blue considerably behind in the race. Those two checkers must come all the way around the board before blue can begin to bear off.

In contrast, green's decision to make the 2-point was strategically dubious. Though it may prevent blue from entering with both checkers, and there is some chance green will be able to build a strong home board before blue gets organized, increasing the chances of winning a gammon, the disadvantage is that green will now find it difficult to build a prime. If blue manages to make an advanced anchor, i.e., get two of his back checkers on green's 3-, 4-, or especially the 5- point, then green's blocking game is busted.

Green would be in better shape had he played 12-16(2), keeping open the option to block or attack depending on blue's next roll.

Blue rolls 5, 2. The only legal move is Bar-20. The two can't be played from the bar because green owns his 2-point, and until blue has played all his checkers off the bar, he can't play anywhere else. Therefore the 2 is forfeited and blue's turn is over.

Green got what he wanted, in that blue was not able to enter both checkers, but the fight is far from over. Green must hit the blot on his next roll, or else blue has a fifty-fifty chance to cover his blot and take a fairly strong position. Even if green does hit, blue has many rolls to hit back. A war for green's 5-point will shape the character of the game in the near future.

Backgammon as a Gambling Game

Backgammon is often played for money stakes. The most common ways that gamblers play is to set a wager on which player can be first to reach a certain number of points, achieved over however many games necessary; to assign a dollar value to each point, and to play until a certain number of points is reached or passed; or to assign a dollar value to each point and play games until either player chooses to stop. Backgammon is also available, though not often, at casinos.

Chouettes

A Chouette is a complicated, group version of backgammon played for money stakes. Before beginning, a monetary value is agreed upon for the value of each point. One player is the box player, and plays against all of the other players together, who are led by a captain. The captain has final say over how to play each roll, though the other players may give advice freely. Each player on the group team controls his or her own doubling cube, and may double back and forth with the box player independently of the other players.

Whoever wins the largest number of points in a game is promoted: a group player becomes captain, or the captain becomes box player. A loser is demoted: a captain becomes a mere group player, and a box player becomes a captain.

Backgammon in the Middle East and Central Asia

Backgammon is widely played in the Middle East and Central Asia, particularly in cafes. There are four main variants played in the Middle East: the European game as described above and known as ifranjiah (meaning Frankish in Arabic, "Takhte Nard" is the Iranian version, shesh besh (Shesh means six in Persian and Besh means five in Turkish) in Azerbaijan, Israel, and Uzbekistan and tavla in Turkey); mahbusa (meaning 'imprisoned'); and maghribiyya.

The most popular of those is probably mahbusa. In this game each player's 15 checkers are all initially positioned on his 24-point. When hit, an isolated checker is not placed on the bar. Rather the hitting piece sits on top of the hit piece forming a block i.e. the same rules apply as if the point was occupied by two or more pieces of the same colour. The checker which has been hit is 'imprisoned' and cannot be moved until the opponent removes his piece: hence the name of the game. Sometimes a further rule requires that a player must bring his first checker to the opponent's home board before moving any other checkers. Whether or not this rule is applied, a rapid advance to the opponent's side of the board is desirable as imprisoning the opponent's checkers on his home table is highly advantageous.

An interesting feature of backgammon as played in some Arab countries is that Persian or Kurdish numbers, rather than Arabic ones, are called out by a player announcing his dice rolls.

People in Iranian plateau and Caucasus region, especially in Iran, Armenia, Azerbaijan, and Georgia are very fond of playing Narde. In Georgia they play mainly the "short Narde" - a bit simplified version of ifranjiah. In Iran it is called "Takhte Nard". In Armenia and Azerbaidjan experienced players prefer to play "long Narde" that requires more skill and even "knowledge" of some non-written strategic methods. As in 'mahbusa' all 15 checkers of a player are initially positioned on his 24-point. But there is a principle difference. One is forbidden to put his checker at a point occupied by opponnents checker. So there is no "hitting" and no "imprisonment" in the long Narde game. The main strategy is to secure playing "big pairs" by one's own checkers and prevent as much as possible doing the same by the opponnent.

Other variants

Brädspel

A Swedish variant of backgammon, also called Swedish Tables in English.

The main difference compared to other backgammon variants is the method of winning. You can win by bearing off, but there are also several other ways to win, such as to arrange all your checkers in certain pre-determined patterns or by hitting so many checkers that your opponent can not bring them in again.

Brädspel is played without the doubling cube.

Gul Bara

Gul bara is also called as ‘Rosespring Backgammon’ or ‘Crazy Narde’.

Old English Rule

This rule limits the number of checkers to a maximum of five on each point, thus restricting some moves that might otherwise be made. This variation of backgammon is popular in England (as well as other regions), and is viewed as making the gameplay more interesting.

Runte Rule

The Runte Rule allows the player to move his checkers both backwards and forwards within his own home board. The player cannot move the checker in such a way that it lands outside of his home board. The rule was created to increase the possibility of scoring backgammons and gammons, because it allows one to trap the opponent for longer.

Tavli

In Greece, backgammon is called tavli (related to the word tavla 'board, table', and cognate to the Latin Tabula). It consists of three main styles, Portes, Plakoto and Fevga. Portes resembles the standard game, with minor variations. Plakoto is very similar to mahbusa or Tapa, while Fevga is similar to Narde or the Turkish variant Moultezim. The three are normally played consecutively, one after another, in matches of three, five or seven points.

LongGammon

LongGammon is a variant of backgammon, the sole difference being that all fifteen of the players' checkers start on their opponent's one-point. All other rules of the game are the same as regular backgammon.

Computer Backgammon

The first strong computer opponent was BKG 9.8. It was programmed by Hans Berliner in the late 1970s on a PDP-10 as an experiment in evaluating board positions. Early versions of BKG played badly even against poor players, but Berliner noticed that the critical mistakes the program made were always at phase changes. He applied basic principles of fuzzy logic to smooth out the transition between phase changes, and by July 1979, BKG 9.8 was ready to play against then current world champion Luigi Villa. It won the match, 7-1, becoming the first computer program to defeat a world champion in any game, although this was mostly a matter of luck, as the computer happened to get better die rolls than its opponent in that match.

Beginning in the late 1980s, creators of backgammon-playing software began to have even more success with a neural network approach. TD-Gammon, developed by Gerald Tesauro of IBM, was the first of these computer programs to play at or near the expert level. This program's neural network was trained using Temporal Difference learning applied to data generated from self-play.

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. 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 child.

It is interesting to contrast the development of backgammon software with that of chess software:

1. For backgammon, neural networks work better than any other methods 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 at present unclear whether the best computer or the best human is best overall. For most other games, one or the other is unambiguously stronger.

Real-time on-line play began with the First Internet Backgammon Server on July 19, 1992. This server is active to this day, remains free, and enjoys a strong international community of backgammon players. Several commercial websites also offer on-line real-time backgammon play.

See also

• List of World Backgammon Champions
• Tables
• Hypergammon
• Tapa
• Nackgammon
• Acey-Deucey
• Nard
• Crazy Nard
• Sugoroku
• Ludus Duodecim Scriptorum

External links

• Backgammon Galore is one of the most comprehensive sites about backgammon. It also contains the rules for almost every variant.
• The Origin of Backgammon The history of backgammon.
• Gammon Links large collection of backgammon hyperlinks.
• GnuBg open source neural net based backgammon program.
• F.I.B.S. First Internet Backgammon Server
• Backgammon Exchange Backgammon Articles and Information

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