Backgammon

Backgammon is a reasoned game of chance for two players, played on a board with dice. A player wins when he takes all the pieces on the deck. Backgammon is part of the family of table games, one of the oldest board game categories.

Despite the presence of chance, strategy plays an important role there. Each dice roll, the player must choose from numerous options for moving his checkers and anticipate the actions of his opponent. Players can increase the value of the stakes during the game. There is a basic repertoire of tactics and openings.

Like many games, backgammon has been studied by computer scientists that led to the development of software capable of even beating world class players.

Equipment

• A board, often in the form of a case which can be opened flat, consisting of two compartments with 12 “arrows”;

• 2 sets of 15 checkers (commonly called draughts, stones, men, counters, pawns, discs, pips, chips, or nips) of two distinct colors;

• 2 pairs of ordinary dice (6 faces) (one per player);

• 1 doubling cube called that displays the numbers 2, 4, 8, 16, 32, 64.

Rules

The goal of a game of backgammon is to get out all his checkers from the deck. Early in the game, the checkers are placed on the deck in an imposed way. They circulate in a given direction, and depending on the outcome of the throw of two dice. On their way out, they can be blocked or “beaten” by those of the enemy.

A party may bring 1, 2 or 3 points to the winner depending on the final position of the checkers of the opponent. The duration of a game is relatively short. Also, to limit the effects of a chance due to the rolls of the dice, a backgammon match is played over an agreed number of points greater than 3. Several parties are generally required to achieve this.

The ability for players to ask, or refuse, during a part, to double or even redouble the basic points awarded to the winner, provides strategic and psychological dimension to the game. This option also has the effect of shortening a party : the opponent who does not accept the request immediately loses the game.

Description of the board

Each side of the board consists of 12 triangles called “arrows” or “points”. Both groups of 12 points are considered connected by one of their ends, the assembly thus forming a horseshoe-style track with a length of 24 cases.

(Circuits of  red and black checkers, starting position, numbering points for black checkers.)

The points are numbered from 1 to 24. Each player always moves her checkers from a higher to a lower point and counterclockwise relative to the other. Therefore, numbering points seen by the players is also reversed, point 1 of one being point 24 of the other.

In the middle, the board includes a partition, the “bar” which divides into two compartments. The point groups thus defined are called for each of the two players:

• home board or inner board: point 1-6
• outer board: points 7-12

Start of the game

Each player starts with two checkers on its point 24, 3 on its point 8 and 5 on its points 13 and 6. The starting position corresponds to that of the previous figure.

To begin, each player rolls one die in the compartment to his right, the one that gets the highest number of dots performs its movement using the result displayed by the two dice. To be valid, both dice must sit flat in the compartment and on no checker. In case this condition is not met or that the two shots show the same number of points, both players recommence the procedure.

After the initial throw, players alternate throwing two dice in turn. The dice must be always started in the right hand compartment using a horn, a kind of cup with round or oval opening, after having been shaken at least three times.

Moves

Once the two dice correctly stabilized, the player must move his checkers the number of points that each displays. For example, if the result is 6 and 3 (rated 6-3), it must advance a checker six points and another three points. The same xhwxker can be moved twice as long as the moves are distinct: six then three points, or three then six points.

If a player gets a double – both dice show the same number of points – he must play each die twice. For example, if he gets 5-5 (called “double five”), it must make four trips five points each.

If a player has the possibility to play both dice, he is obliged to do so. If he can not play any of the two dice, it has to pass. If it is possible to play one of the two dice, but not both, the highest number has to be played. For example, if a player leads 6-3 and can play only either 6 or 3, he must play the 6; if he has no opportunity to play the 6, he must play 3 if possible.

It is strictly forbidden to get in position to play only a single die while there is a solution for playing both. For example, in the case of a 6-3, 3 is not playable. However, there are two ways to play the 6, with the checker A or B. If the checker  A is advanced six points, 3 can not be played. If the checker B advanced six points, 3 can then be played. The rule dictates that the checker B must be advanced six points for the 3 can be played. In short, the rule requiring players are studying all possible solutions for both dice can be played.

Restrictions on checker moves

During his move, a checker can be placed on a free point or occupied by one or more checkers of his color.

It can also be placed on a point occupied by a single opponent checker – the checker is called a “blot”. In this case, the blot is “beaten” (also called “hit”), and is placed on the side of the opposing player bar.

A checker can never be placed on a point occupied by two opposing checkers. No point can be occupied simultaneously by checklers of different colors.

The checkers placed on the bar must return to the board on the opposing home board. A 2 shown by a die allows you to enter a checker placed on point 23, a 3 on the point 22, and so on for all the numbers from 1 to 6. A player can not move any checker in the board until all those it has on the bar are not returned in game.

Output of checkers

When a player has brought all his checkers into his own home board, he can begin to remove them from the deck – this phase of the game is called “exit”. A 1 displayed by a die can be used to exit a checker of the point 1, a 2 for point 2, and so on for the other number from 1 to 6. It is also possible to advance the checkers on a lower point instead of an exit. A die can not be used to exit a checker of a lower point unless there are more checkers on the higher points. In this case it is essential to exit a checker of the highest point.

For example, if the dice show 5 and 6, but there is no checker on the point 6, although two checkers remain on point 5, then 6 and 5 can be used to exit the two checkers from the point 5. During the check out, a player can also play a smaller die before stronger even if it means that the total sum of the points brought by the two dice is not fully used. For example, if a player has a checker on the point 6, and that the dice show a 6 and a 1, he may move his checker from the point 6 to the point 5 by using the 1, then go out the same checker from the point 5 outside the board using 6; This is sometimes very useful from a tactical point of view.

If a blot gets hit in the output phase, the player will again have to wait to have brought all her checkers in his home board before hr can output them.

In summary:

• If the player has a checker on the point indicated by the dice:
  • It can get out from this point a checker or
  • It can perform a movement of a checker located on a higher point.
• If the player does not have a checker on the point indicated by the dice:
  • If he has one or more checkers to a higher point: he must play one of the checkers in the forward.
  • If he no longer has any checkers on higher points: it must output a checker of the highest space it occupies.

Ways to win

• Ordinary: If a player has output at least one of his checkers when the opponent took out all his own, he lost in an ordinary way.
• Gammon: If a player has not borne off any checker when his opponent pulled out all his own, he lost a “gammon”, which is double of an ordinary loss.
• Backgammon: If the loser has not output any of his checkers, and he still has at least one checker on the bar or in the home board of the opponent he lost a “backgammon”, three times a ordinary loss.

Doubling die or cube

(Doubler die or “cube”)

To reduce the duration of a game and strengthen the strategic side of the game, a doubling cube can be used. It is called cube, it is a six-sided die marked with the numbers 2, 4, 8, 16, 32, and 64. At the beginning of the game, the doubling cube display 64 is placed on the deck – the middle of the bar or the lateral sides; the doubling cube is then said centric 1. When the cube is centered, in turn to play and before rolling the dice, a player can offer to double the stake. His opponent then has two options: either he accepts – it takes – or he abandons the current game. If he agrees, the doubling cube displaying 2 is moved from its side of the deck. From that moment, the opportunity to double again belong to him exclusively.

The multiplier applied this way rarely exceeds the value of 4, but there is theoretically no limit. Although 64 is the highest coefficient displayed on the doubling cube, you can raise to 128, 256 and more.

When backgammon is played for money, a player is often permitted to redouble immediately and keep the doubling cube when his opponent offers to double the previous issue – this process that multiplies the previous issue by 4 instead of 2 is called beaver.

A variant of the beaver is the racoon. A player in turn proposes to double, his opponent accepts and beaver immediately doubling, the initial player doubles again immediately and let the doubling cube to his opponent. As result on the same throw, last issue is multiplied by 8 if accepted by the person who made a beaver. This system greatly increases the risks associated with the demand of doubling the stake.

The racoon and beaver are not part of the official rules of backgammon: it is necessary to agree on opportunities to intensify with the opponent in the early game.

Murphy rule

Some players opt for the application of the “Murphy rule” – the automatic double rule. If both players at the beginning of the game bring the same value of the dice, the doubling cube remains positioned in the center but shows for each double brought this way the double value of the previous (2 for the first doublet, 4 for the following possible, and so on). However the rule is requiring players agree in advance the maximum number of allowed automatic successive doubles. Murphy’s rule is not an official rule of backgammon and is rarely, if ever, used in official tournaments.

Jacoby rule

A rule developed by Oswald Jacoby can not count the gammons and backgammon as double and triple, respectively – which is the traditional rule – only if the cube left the center. This encourages a player with the advance, to offer the doubling cube to finish a game when he is left with only 2 or 3 points, while without the Jacoby rule, he could just attempt a gammon or backgammon. The Jacoby rule is widely used in parts for cash but not in the meetings.

Crawford rule

The Crawford rule, invented by John Crawford and commonly used in the tournament, aims to make the game fairer for the player who leads: it prohibits the use the doubling cube when one of the players is one point of winning the game. This part without doubling cube is called “the part of Crawford.” This being terminated without any player has won the game, the following games are played with the doubling cube again.

Indeed, if a player is at a point of winning the match, his opponent will tend to ask twice as early as possible in the current game to try to catch up. If the game reports a point or two, the player behind must absolutely win to continue the meeting.

Strategy and tactics

Backgammon has an established opening theory, although it is less detailed than for other games such as chess. The shaft of positions is growing rapidly because of the number of possible outputs of the dice and the possibilities of moves every time. Computer-analyzes have provided a better understanding of possible openings, but the middle part is reached quickly. After the opening, backgammon players frequently rely on conventional strategies, combining and passing from one to another to adapt to changing conditions of play.

The most direct strategy is simply to avoid being beaten, of having blocked checkers, or being unable to play. A “running game” means a strategy of moving as quickly as possible his checkers on the circuit, which is the most profitable when a player is already ahead in the race. When that fails, one can opt for a “light game” by taking control of a point inside the opponent home board – this point is called an “anchor”. The game progresses, the player can take advantage by beating a blot of opponent since that anchor or pulling large doubles that allow checkers of the anchor to escape in a racing game.

The “plugging” is to build a barrier of checkers, called “premium”, occupying several consecutive squares with at least two checkers per point. A checker blocked behind a premium of 6 points can not move forward as long as the premium is not broken. The construction of a premium of 6 points in his home board when the opponent has at least one checker on the bar is a strategy called “blitz”. In this case, the opponent can not return to the board quickly, the player can easily enjoy a racing game that leads most often to win the game, and even by gammon.

The “back game” is a strategy of placing two or more anchors in the opponent’s home board while building a premium in itsown home board. The anchors obstruct the opposing checkers and create opportunities to beat them in their travels to their home in the homeboard. The back game is usually considered only as a rescue attempt of a desperate situation where a player is far behind compared to the other; using the back game as an initial strategy is usually doomed to failure.

“Duplication” is to position his checkers so that the opponent needs the same values ​​of the dice to succeed its goals. For example, a player can position all blots so that his opponent is able to hit each of them by a 2 thereby reducing the likelihood of being beaten more than once. “Diversification” is a complementary tactic posting checkers so that more numbers supplied by the dice are needed.

Many game situations require evaluation and decision making on the part of players, for example, concerning the use of the doubling cube, or the choice to go as fast as possible to his home board to exit her checkers. The number of pips required to output all the checkers for a player at one time of a game is called the “pips account”. The difference between the counts of the pips of both players is frequently used as a measure of the advantage of a player with respect to the running to the exit. Players often use mental calculation methods suitable for determining the accounts of pips during the backgammon games.

Software

Game and analysis

Backgammon has been extensively studied by computer. Artificial neural networks and other methods have made significant advances to software for gameplay and analysis.

The first valueable software, BKG 9.8., was designed by Hans Berliner in the 1970s on a DEC PDP-10 to test the assessment of the positions of board games. Previous versions of BKG were not able to beat repeatedly novice players, but Berliner noticed that its critical errors still were in transition phases of the game. He applied the principles of fuzzy logic to improve his game during those phases, and in July 1979, BKG 9.8 became strong enough to play against the world champion Luigi Villa. He won the match 7-1, becoming the first program to beat a world champion in a board game. Berliner, however, found that the victory was due largely to chance because of a more favorable results obtained by the software.

During the 1980s, computer scientists obtained more success with an approach based on the use of artificial neural networks. TD-Gammon, developed by Gerald Tesauro at IBM, was the first such software to reach a level close to that of an experienced player. Its neural network was trained by self-learning. According to Bill Robertie and Kit Woolsey, TD-Gammon play was then at the height, and even above, to that of the best players in the world. Woolsey declared: “There is no doubt in my mind that his analysis of the positions is much higher than mine.”

Research based on artificial neural networks resulted in the generation of three modern commercial software, Jellyfish, Snowie and eXtreme Gammon, and the BGBlitz shareware and free software GNU Backgammon license. These software are not content to play backgammon, but include analysis tools for the games and presentations in order of interest of different moving options of the checkers on a given dice throw. The strength of this software is based on months of training of their neural networks, without which they could not go beyond the level of a novice player. The checkers output phase is generally treated by software from a database – obtained by computer – containing all the possible positions of the checkers at the exit.

Online game

Backgammon software has not been developed only to play and analyze the parties, but also to facilitate the clearance between two remote players through the Internet. Dice throwing are simulated by generating pseudo-random numbers. Such real-time games have been initiated with FIBS (First Internet Backgammon Server) in 1992. Still active, it is the oldest non-commercial computer server and is used daily by an international gaming community. Yahoo Games offers online backgammon room based on Java technology and MSN Games does the same in ActiveX. The commercial ISPs such as online casinos have begun to include the game of backgammon in their offerings in 2006.

Translated from Wikipedia.org