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Backgammon
is a board game for two players in which checkers (also called pieces, stones, men, counters, pawns or chips) are moved after each
roll of the dice. A player wins by removing all of his checkers from the board. There are many variants of backgammon, most of which
share common traits. Backgammon is a member of the tables family, one of the oldest classes of board games in the world.
Although luck plays an important role, there is a large scope for
strategy. With each roll of the dice a player must choose from numerous options for moving his checkers and anticipate possible
counter-moves by the opponent. Players may raise the stakes during the game. There is an established repertory of common tactics
and occurrences.
Rules
The objective of backgammon is to move all
of one\'s own checkers past those of one\'s opponent and then remove them from the board. 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 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,
and are numbered from 1 to 24. 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. The two players move their checkers in opposing directions, each from his own
24-point towards his 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 the numbers shown. 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 a player must, if possible, move his
checkers according to the number of pips shown on each die. For example, if the player rolls a 6 and a 3 (noted as "6-3"),
that player must move one checker six points forward, and another 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, but not all nine at once. If a player
rolls two of the same number, called doubles, that player must play each die twice. For example, upon rolling a 5-5 that player
must move four checkers forward five spaces each.
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; such a lone piece is called a 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 hitting
player\'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 the 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. In other words 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 piece 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 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 normally used. The doubling cube is a six-sided die marked with the numbers 2, 4, 8, 16, 32, and 64. Before
rolling the dice on his turn, a player may demand that the game be played for twice the current stakes. His opponent must
either accept the new stakes or resign the game immediately. Thereafter, the right to redouble belongs exclusively to the
player who last accepted a double. Whenever a player accepts doubled stakes, the cube is placed with the corresponding power of two
facing upward.
The game is rarely redoubled beyond four times the original
stake, but there is no limit on the number of doubles. 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.
The Jacoby rule 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 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 used in tournament match play.
Strategy and Tactics
Backgammon has an established opening theory, although it is less detailed than that
of games like chess. The tree 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 may not 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.
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, a player may position all of his blots in
such a way that his opponent must roll a 2 in order to hit any of them, reducing the probability of being hit. "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
techniques to determine pip counts in live play.
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