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 maybe AzV, 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 throwing until he is obliged to open a point on his inner table.
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 preferred, 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:—
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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
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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.
