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## BackgammonBackgammon is a board game for two players. Each player has fifteen pieces (checkers) 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, i.e., move all fifteen checkers off the board.Each side of the board has a track of twelve adjacent points. The tracks are imagined to be connected on one edge of the board, making a continuous chain 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.
Points one to six are called the At the start of the game, each player rolls one die. Whoever rolls higher plays the number on his own die and the number on his opponent's die as if he had rolled them both. After that players alternate turns and roll two dice at the beginning of each turn. 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 rolls two of the same number (
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 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. 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. 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.) When all of a player's checkers are in his home board, he may 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 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 when it is not played for money it is often played in matches, for example the first to five points.
## Sample Game## Backgammon as a Gambling Game## Computer BackgammonIt is interesting to contrast the development of backgammon software to chess software:
- 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.
- 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.
- 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.
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