Encyclopædia Britannica, Ninth Edition/Backgammon
BACKGAMMON, a game played with dice, said to have been invented about the 10th century (Strutt). The etymology of the word backgammon is disputed; it is probably Saxon, Baec, back ; gamen, game, i.e., a game in which the players are liable to be sent back. Other derivations are, Dan. bakke, tray, gammen, game (Wedgwood) ; and Welsh, bach, little, cammaun, battle (Henry).
Backgammon is played by two persons, having between them a backgammon board. (See diagram.) The board is divided into tables, each table being marked with six. points, coloured alternately white and black. The inner and outer tables are separated from each other by a projecting bar.
BLACK. Black s Home or Inner Table. Black s Outer Table. White s Home or Inner Table. White s Outer Table. WHITE. Backgammon Board.
The board is furnished with fifteen white and fifteen black men, disposed at the commencement of a game in the manner shown above. The arrangement of the men may be reversed, as it would be if the diagram were turned upside down, and the white men put where the black now stand, and vice versa, there being no rule as to whether the play shall be from right to left, or from left to right. It is usual to make the inner table (see diagram) the one nearest to the light (Academie desjeux ; regies du jeu de toute-table).
Two dice boxes are required, one for each player, and a pair of dice, which are used by both players. The dice are marked with numbers on each face from one to six, number one being called ace ; two, deuce ; three, trois (pronounced trey); four, quatre (katre); five, cinque ; and six, six (size).
The board being arranged, each player throws one die ; the one who throws the higher number has the right of playing first ; and he may either adopt the throw originally made by the two players, each throwingone die; or he may throw again, using both dice.
Each player moves his own men from point to point, the moves being determined by throws of the dice made by the players alternately. A player may move any of his men a number of points corresponding to the numbers thrown by him, provided the board is not blocked by two or more of his adversary s men occupying the point to which he wishes to move. Thus, suppose white throws cinque, six, he may move one of his men from the left-hand corner of the black s inner table to the left-hand corner of black s outer table for six ; he may, again, move the same man five points further on, viz., to the right-hand point of the same table for five, when his move is completed ; or he may leave the man first moved six, and move any other man five points, where the board is open. But white can not move a man for five, from the ace point in black s inner table, because the six point in that table (i.e., the fifth point from where white moves) is blocked by the black men. Any part of the throw which cannot be moved is of no effect ; but it is compulsory for a player to move the whole throw if he can. Thus, if the men were differently placed, and white could move a six, and having done so could not move a five, his move is completed. If, however, by moving the five first, he can afterwards move a six, he may be required to make the move in that manner. All white s moves must be in the direction indicated, viz., from black s inner table to black s outer, and from this to white s outer table, and so on to white s inner table ; and all black s moves must be in the contrary direction. Of course, where men are originally placed part of the way home, they only have to traverse the remainder of thedistance.
A player in moving must not skip a point which is blocked by his adversary s men. Thus, suppose white s first throw is fives, he cannot move a man from the ace point of black s inner table to the cinque point of black s outer, although that is free ; because in moving the first cinque he comes to a point which is occupied by black.
When two similar numbers are thrown (called doublets), the player has a double move. Thus, if he throws aces he has to move four aces instead of two, and so on for the other numbers.
When a player moves his men so as to occupy a point with two men, it is called making a point. Thus, if ace, trois are thrown and white moves one man from the three in his outer table to the cinque point in his inner table, for trois, and then moves a man from the six point to the cinque point of his inner table, for ace, he makes a point there.
If a player leaves only a single man on a point, or places a single man on an unoccupied point, it is called leaving a blot. Thus, if the first throw is six, cinque, and white carries a man from black s inner table as far as he will go, white leaves a blot on the ace point of his opponent s home table.
When a blot is left the man may be taken up, or the blot maybeAzV, if, while it remains, the adversary throws a number which will enable him to place a man on that point. For example, if a blot is left on black s ace point, as in the case previously supposed, and black throws a five, or numbers that make up five, he can hit the blot from his six point ; or similarly, if he throws seven, or numbers that make up seven, he can hit the blot from the three men posted in his outer table. The man hit is placed on the bar, and has to enter black s inner table again at white s next throw.
It will be observed that black in taking up -white leaves a blot himself, which subjects him to be taken up if white enters with an ace. If this should occur, black s man is placed on the bar, and has at his next throw to enter white s inner table, whence he has to start his journey home. Suppose white to have a blot as before on black s ace point, and black to throw sixes, black could then move two men from white s outer table to his own bar point (so called because it is close to the bar), and thence again to his own ace point, when he would hit white without leaving a blot.
The point in which a man is entered must not be blocked by two or more men^ belonging to the adversary. Thus, to carry on the illustration, if white now throws aces, or sixes, or six, ace, he cannot enter at all. He is not allowed to move any man while he has one to enter; consequently his throw is null and void, and black throws again. It some times happens that one player has a man up, and that his adversary occupies all the points on his own home table with two or more men (called having his table made up). In this case, the player with a man up cannot enter; and as it is useless for him to throw, his adversary continues throw ing until he is obliged to open a point on his innertable.
Two blots may be taken up at once if the adversary throws numbers that will hit them both. It is possible with doublets to take up four blots at once, but this could scarcely happen in a game between players of any proficiency.
The game proceeds by moving the men round towards home, or by hitting blots and sending them back, until one of the players gets all his men into his inner table or home. As soon as this stage is reached, the player who has accomplished it begins to take his men off the board or to bear them. Thus, suppose he has several men on every point of his table, and throws six, quatre ; he bears one man from his six point, and one from his quatre point. If his six point is unoccupied, he can bear a six from his cinque point, or from the highest point which is occupied, and so on with smaller numbers, provided the numbers thrown are higher than the points occupied; if lower, the throw must be moved. A player has the option of moving a man when he can, instead of bearing it. Thus, in the case originally given the six must be borne, because a six cannot be moved ; but the quatre may be moved if pre ferred, by moving a man from the six point to the deuce point, or from cinque point to the ace point. Doublets entitle to bear or move four men in accordance with the previous rules. The adversary similarly bears his men as soon as he gets them all home. If, after a player has commenced bearing his men, he should be hit on a blot, he must enter on his adversary s inner table, and must bring the man taken up into his own inner table before he can bear any more.
Whoever first bears all his men wins the game : a single game or hit if his adversary has borne any of his men ; a double game or gammon if the adversary has not borne a man ; and a triple game or backgammon, if, at the time the winner bears his last man, his adversary, not having borne a man, has one in the winner s inner table.
When a series of games is played, the winner of a hit has the first throw in the succeeding game ; but if a gammon is won, the players each throw a single die to determine the first move of the next game.
In order to play backgammon well, it is necessary to know all the chances on two dice, and to apply them in various ways. The number of different throws that can be made is thirty-six. (See Hazard.) By taking all the combinations of these throws which include given numbers, it is easily discovered where blots may be left with the least probability of being hit. For example, to find the chance of being hit where a blot can only be taken up by an ace; the adversary may throw two aces, or ace in combination with any other number up to six, and he may throw each of these in two different ways, so that there are in all eleven ways in which an ace may be thrown. This deducted from thirty-six (the total number of throws), leaves twenty-five ; so that it is 25 to 1 1 against being hit on an ace. It is very important to bear in mind the chance of being hit on any number. The following table gives the odds against being hit on any number within the reach of one or two dice:—
It is 25 to 11, or about 9 to 4, against being Lit on 1 3 4 5 6 7 8 9 10 11 12 J^l 22 JLA, Ul ft 1 4, or about 3
2, 21 15, or 7 5, 21 15, 7 5, 19 17, 94 8J, 30 6, 5 1, 30 6, 5 I, 31 5, 6 1, 33 3, 11 1, 34 2, 17 1, 35 1, 35 1,
The table shows that if a blot must be left within the reach of one die (i.e., on any number from 1 to 6), the nearer it is left to the adversary s man, the less probability there is of its being hit. Also, that it is long odds against being hit on a blot which is only to be reached with double dice, and that, in that case (i.e., on any number from 7 to 12), the further off the blot is, the less chance there is of its being hit.
The table assumes that the board is open for every pos sible throw. If part of the throw is blocked by an interven ing point being held by adverse men, the chance of being hit may be less. Thus, a blot may be hit on an eight with dueces ; fours ; cinque, trois (twice) ; or six, deuce (twice). If the fourth point is blocked, the blot cannot be hit with deuces or fours, and consequently the chance of its being hit is reduced from 30 to 6 to 32 to 4, or from 5 to 1 to 8 to 1.
Two principles, then, have to be considered in moving the men : (1.) To make points where there is the best chance of obstructing the opponent; (2.) When obliged to leave blots, to choose the position in which they are least likely to be hit, i.e., either as near as possible to an adverse man, or as far as possible from any adverse men ; or where the intervening points are blocked by the player s own men.
At the beginning of the game it is advisable, if possible, to secure the cinque point in your own inner table, or the cinque point in your adversary s inner table, or both. If you succeed in this, you should then play a bold game in hopes of winning a gammon. The next best point to gain is your own bar point ; and the next to that the quatre point in your own inner table.
If you are fortunate enough to secure all these points, and your adversary s inner table is less favourably made up, it is then to your interest to open your bar point (in expectation of compelling your adversary to run out of your inner table with a six), and also to keep any men you may have in the outer tables spread (i.e., not to crowd a number of men on one point). In this case you have a good chance of hitting the man your adversary brings out, and also of hitting the man he has left on your ace point.
If you succeed in taking both these men, and your ad versary has a blot in his inner table, it will be to your in terest not to make up your own table, but to leave a blot there on purpose, in hopes of his entering on it. You will then have a probability of hitting a third man, which, if accomplished, will give you considerable odds (according to Hoyle, 4 to 1) in favour of winning a gammon; whereas if you have only two of his men up, the odds are against your gammoning him.
The best move for every possible throw at the commencement of a game is as follows : If you throw aces (the best of all throws), move two on your bar point and two on your cinque point. This throw is often given to inferior players by way of odds.
Ace deuce : move the ace from your adversary s ace point (if playing for a hit only), and the deuce from the five men placed in your adversary s outer table. If playing for a gammon, move the ace from the six to the cinque point in your inner table.
Ace trois : make the cinque point in your inner table.
Ace quatre and ace cinque : move the ace from your adversary s ace point, and the quatre or cinque from the five men in your ad versary s outer table. If playing for a gammon, play the ace on the cinque point in your inner table.
Ace six : make your bar point.
Deuces : move two on the quatre point in your inner table, and two on the trois point in your opponent s inner table. If playing for a gammon, move two on the quatre point in your inner table, and two from the five men in your adversary s outer table.
Deuce trois and deuce cinque : move two men from the five placed in your adversary s outer table.
Deuce quatre : make the quatre point in your own table.
Deuce six : move a man from the five in your adversary s outer table, and place him on the cinque point in your own table.
Threes : play two on the cinque point in your inner table, and three on the quatre point of your adversary s inner table. For a gammon, play two on your cinque point and two on your trois point in your inner table.
Trois quatre : move two men from the five in your opponent s outer table.
Trois cinque : make the trois point in your own table.
Trois sir : bring a man from your adversary s ace point as far as he will go.
Fours : move two on the cinque point in your adversary s inner table, and two from the five in his outer table. For a gammon, move two men from the five in your opponent s outer table to the cinque point in your own table.
Quatre cinque and quatre six : carry a man from your adversary s ace point as far as lie will go.
Fives : move two men from the fire in your adversary s outer table to the trois point in your inner table.
Cinque six : move a man from your adversary s ace point as far as lie will go.
Sixes (the second best throw) : move tro on your adversary s bo.r point, and two on your own bar point.
Subsequent moves depend on the intervening throws ; conse quently the problem becomes too complicated for analysis. Some general rules, however, may be given.
In carrying the men home carry the most distant man to your adversary s bar point, next to the six point in your outer table, and then to the six point in your inner table. By following this rule as nearly as the throws admit, you will carry the men to your inner table in the fewest number of throws. "When all are home but two, it is often advisable to lose a point, if by so doing you put it in the power of a high throw to save a gammon.
If, in endeavouring to gain your own or your adversary s cinque point, you have to leave a blot and are hit, and your adversary is forwarder in the game than you, you must put another man on your cinque or bar point, or into your adversary s table. If this man is not hit, you may then make a point, and so get as good a game as your opponent. If it is hit, you must play a back game (i.e., allow him to take up as many men as he likes) ; and then in entering the men taken up, endeavour to secure your adversary s ace and trois points, or ace and deuce points, and keep three men upon his ace point, so that if you hit him from there you still keep the ace point protected.
To find which is the forwardest, reckon how many points you have to bring all your men home to the six point in your inner table. Add to this six for every man on the six point iu your tables, five for every man on your cinque point, and so on ; and then make the same calculation for your adversary s men.
Avoid carrying many men upon the trois or deuce point in your own tables, as these men are out of play, and the board is left open for your adversary.
Whenever you have taken up two of your adversary s men, and have two or more points made in your inner table, spread your other men to take the best chance of making another point in your tables, and of hitting the man your adversary enters. As soon as he enters, compare his game with yours, and, if equal or better, take up his man, except when playing for a hit only, and your playing the throw gives you a better chance for the hit.
Always take up a man if the blot you leave in making the move can only be hit with double dice, except when playing for a hit only, and you already have two of your opponent s men in your tables, and your game is forwardest ; because your having three of his men in your tables gives him a better chance of hiting you with out leaving a blot than if he has only two.
In entering a man which it is to your adversary s advantage to hit, leave the blot upon the lowest point you can, e.g., ace point in pre ference to deuce point, and so on ; because this crowds his game by taking out of it the men played on the low point.
When your adversary is bearing his men, and you have two men in his table, say on his ace point, and several men in the outer table, it is to your advantage to leave one man on the ace point, because it prevents his bearing his men to the greatest advantage, and gives you the chance of his leaving a blot. But if, on calcula tion, you find that you can probably save the gammon by bringing both your men out of his table, do not wait for a blot. To make this calculation, you must ascertain in how many throws you can bring all ycur men home (a throw averaging eight points), and in how many throws he can bear all his men, on the assumption that he will bear on the average two men at each throw.
The laws of backgammon (as given by Hoyle) are as follows:—
1. When a man is taken from any point, it must be played : when two men are taken from it, they also must be played. 2. A man is not supposed to be played till it is placed upon a point and quitted. 3. If a player have only fourteen men in play, there is no penalty inflicted, because by his playing with a lesser number than he is entitled to, he plays to a disadvantage for want of the deficient man to make up his tables. 4. If he bear any number of men before he has entered a man taken up, and which of course he was obliged to enter, such men so borne must be entered again in the adversary s tables as well as the man taken up. 5. If he have mis taken his throw and played it, and his adversary have thrown, it is not in the choice of either oi the players to alter it, uulc&o they both agree so to do.
Russian Backgammon or Trio-Trac is played with the same implements as backgammon. The men are not placed on the board, but both black and white are entered in the same table by throws of the dice, and both players move in the same direction round to the opposite table. A player is not obliged to enter all his men before lie moves any; and he can take up blots on entering, although he has some of his men, which have never been entered, off the board. But, while a player has a man up, he must enter it before entering any more, or moving any of those already entered. If he cannot enter the man that is up, he losesthe benefit of the throw.
A player who throws doublets must move not only the number thrown, but also doublets of the number corresponding to the opposite side of the dice; thus, if he throws sixes, he must first enter or move the sixes, as the case may be, and then aces, and he also has another throw. If he throws doublets a second time, he moves according to the rule already given, and throws again, and so on. The privilege is sometimes restricted by not allowing this advantage to the first doublets thrown by each player. It is sometimes extended by allowing the thrower of deuce, ace, to choose any doublets he likes on the opposite sides of the dice, and to throw again. The restriction with regard to the first doublets thrown does not apply to deuce, ace, nor does throwing it remove the restriction with regard to first doublets.
A player must first bs able to complete the doublets thrown. If iiie cannot move the wLo!e throw, he cannot take the corresponding doublets , and he is not allowed another throw if he cannot move all the points to which he is entitled. In other respects the game is similar to ordinary backgammon. The chief object in the game is for the player who has his men in advance to secure as many successive points as possible, so that his adversary may be unable to pass or hit the forward men.