Backgammon is a game for two players, played on a board consisting of twenty-four narrow triangles called @cindex points points. The triangles alternate in color and are grouped into four quadrants of six triangles each. The quadrants are referred to as a player's home board and outer board, and the opponent's home board and outer board. The home and outer boards are separated from each other by a ridge down the center of the board called the bar.
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| @image{rulfig1} | Figure 1. A board with the checkers | in their initial position. An alternate arrangement is the reverse of the one shown here, with the home board on the left and the outer board on the right.
The points are numbered for either player starting in that player's home board. The outermost point is the twenty-four point, which is also the opponent's one point. Each player has fifteen checkers of his own color. The initial arrangement of checkers is: two on each player's twenty-four point, five on each player's thirteen point, three on each player's eight point, and five on each player's six point.
Both players have their own pair of dice and a dice cup used for shaking. A doubling cube, with the numerals 2, 4, 8, 16, 32, and 64 on its faces, is used to keep track of the current stake of the game.
The object of the game is for a player to move all of his checkers into his own home board and then bear them off. The first player to bear off all of his checkers wins the game.
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| @image{rulfig2} | Figure 2. Direction of movement of | White's checkers. Red's checkers move in the opposite direction.
To start the game, each player throws a single die. This determines both the player to go first and the numbers to be played. If equal numbers come up, then both players roll again until they roll different numbers. The player throwing the higher number now moves his checkers according to the numbers showing on both dice. After the first roll, the players throw two dice and alternate turns.
The roll of the dice indicates how many points, or pips, the player is to move his checkers. The checkers are always moved forward, to a lower-numbered point. The following rules apply:
| @image{rulfig3} | Figure 3. Two ways that White can | play a roll of 53.
A point occupied by a single checker of either color is called a blot. If an opposing checker lands on a blot, the blot is hit and placed on the bar.
Any time a player has one or more checkers on the bar, his first obligation is to enter those checker(s) into the opposing home board. A checker is entered by moving it to an open point corresponding to one of the numbers on the rolled dice.
For example, if a player rolls 4 and 6, he may enter a checker onto either the opponent's four point or six point, so long as the prospective point is not occupied by two or more of the opponent's checkers.
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| @image{rulfig4} | Figure 4. If White rolls 64 with a | checker on the bar, he must enter the checker onto Red's four point since Red's six point is not open.
If neither of the points is open, the player loses his turn. If a player is able to enter some but not all of his checkers, he must enter as many as he can and then forfeit the remainder of his turn.
After the last of a player's checkers has been entered, any unused numbers on the dice must be played, by moving either the checker that was entered or a different checker.
Once a player has moved all of his fifteen checkers into his home board, he may commence bearing off. A player bears off a checker by rolling a number that corresponds to the point on which the checker resides, and then removing that checker from the board. Thus, rolling a 6 permits the player to remove a checker from the six point.
If there is no checker on the point indicated by the roll, the player must make a legal move using a checker on a higher-numbered point. If there are no checkers on higher-numbered points, the player is permitted (and required) to remove a checker from the highest point on which one of his checkers resides. A player is under no obligation to bear off if he can make an otherwise legal move.
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| @image{rulfig5} | Figure 5. White rolls 64 and bears | off two checkers.
A player must have all of his active checkers in his home board in order to bear off. If a checker is hit during the bear-off process, the player must bring that checker back to his home board before continuing to bear off. The first player to bear off all fifteen checkers wins the game.
Backgammon is played for an agreed stake per point. Each game starts at one point. During the course of the game, a player who feels he has a sufficient advantage may propose doubling the stakes. He may do this only at the start of his own turn and before he has rolled the dice.
A player who is offered a double may refuse, in which case he concedes the game and pays one point. Otherwise, he must accept the double and play on for the new higher stakes. A player who accepts a double becomes the owner of the cube and only he may make the next double.
Subsequent doubles in the same game are called redoubles. If a player refuses a redouble, he must pay the number of points that were at stake prior to the redouble. Otherwise, he becomes the new owner of the cube and the game continues at twice the previous stakes. There is no limit to the number of redoubles in a game.
At the end of the game, if the losing player has borne off at least one checker, he loses only the value showing on the doubling cube (one point, if there have been no doubles). However, if the loser has not borne off any of his checkers, he is gammoned and loses twice the value of the doubling cube. Or, worse, if the loser has not borne off any of his checkers and still has a checker on the bar or in the winner's home board, he is backgammoned and loses three times the value of the doubling cube.
The following optional rules are in widespread use.