This game is played with dice upon a table by two persons, upon which there are twenty-four black and white spaces, called points. Each adversary has fifteen men, black and white, to distinguish them, and they are disposed of in the following manner. Supposing the game to be played into the right hand table, two are placed upon the ace point in the adversary’s table, five upon the six point in the opposite table, three upon the cinque point in the hithermost table, and five on the sixth point in the right hand table. The grand object in this game is for each player to bring the men round into his right hand table, by throwing with a pair of dice those throws that contribute towards it, and at the same time prevent the adversary doing the like. The first best throw upon the dice is esteemed aces, because it stops the six point in the outer table, and secures the cinque in the thrower’s table, whereby the adversary’s two men upon the thrower’s ace point cannot get out with either quatre, cinque, or six. This throw is an advantage often given to the antagonist by the superior player. When he carries his men home in order to lose no point, he is to carry the most distant man to his adversary’s bar point, that being the first stage he is to place it on; the next stage is six points farther, viz. in the place where the adversary’s five men are first placed out of his tables. He must go on this method till all his men are brought home, except two, when, by losing a point, he may often save the gammon, by throwing two fours or two fives. When a hit is only played for, he should endeavour to gain either his own or adversary’s cinque point, and if that fails by his being hit by the adversary, and he finds him forwarder than himself, in that case he must throw more men into the adversary’s tables, which is done in this manner: he must put a man upon his cinque or bar point, and if the adversary fails to hit it, he may then gain a forward game instead of a back game; but if the adversary hit him, he should play for a back game, and then the greater number of men which are taken up makes his game the better, because by these means he will preserve his game at home, and then he should endeavour to gain both his adversary’s ace and trois points, and take care to keep three men upon the adversary’s ace point, that, in case he hits him from thence, that point may remain still secure to himself. A back game should not be played for at the beginning of a set, because it would be a great disadvantage, the player running the risk of a gammon to win a single hit.

A variety of instructions with regard to this curious game are given by Mr. Hoyle, who calculates the odds of the game with great accuracy. The following particulars, however, may be of use to the generality of players. If a player has taken up two of the adversary’s men, and happens to have two, three, or more points made in his own tables, he should spread his own men, that he may either take a new point in his tables, or be ready to hit the man which the adversary may happen to enter. If he finds upon the adversary’s entering, that the game is upon a par, or that the advantage is on his own side, he should take the adversary’s man up whenever he can, it being twenty-five to eleven that he is not hit, except when he is playing for a single hit only, then, if playing, the throw otherwise gives him a better chance for it, he ought to do it. As it is five to one against his being hit with double dice, he should never be deterred from taking up any one man of the adversary’s. If he has taken up one of the adversary’s men, and should happen to have five points in his own tables, and forced to leave a blot out of his tables, he should endeavour to leave it upon doublets preferable to any other chance; because the odds are thirty-five to one that he is not hit, whereas it is only seventeen to one but he is hit upon another chance. When the adversary is very forward, a player should never move a man from his own quatre, trois, or deuce points, thinking to bear that man from the point where he put it, as nothing but high doublets can give him any chance for the hit. Instead of playing an ace or a deuce from any of these points, he should play them from his own size or highest points, so that throwing two fives or two fours, his size and cinque points being eased, would be a considerable advantage to him, whereas, had they been loaded, he must have been obliged to play otherwise. It is the interest of the adversary to take up the player as soon as he enters. The blot should be left on the adversary’s lowest point, that is to say, upon his deuce point, rather than upon his trois point, or upon his trois point rather than upon his quatre point, or upon his quatre point preferable to his cinque point, for a reason before-mentioned; all the men the adversary plays upon his trois or his deuce points are deemed lost, being greatly out of play, so that those men not having it in their power to make his cinque point, and his game being crowded in on one point, and open in another, the adversary must be greatly annoyed by the player. If the player has two of his adversary’s men in his tables, he has a better chance for a hit than if he had more, provided his game is forwarder than that of his antagonist, for if he had three or more of his adversary’s men in his tables, he would stand a worse chance to be hit. When a player is running to save the gammon, if he should have two men upon his ace point, and several men abroad, although he should lose one point or two in his putting his men into his tables, it is his interest to leave a man upon his adversary’s ace point, because it will prevent his adversary from bearing his men to the best advantage, and at the same time the player will have a chance of the adversary’s making a blot which he may chance to hit. However, if a player finds, upon a throw, that he has a probability of saving his gammon, he should never wait for a blot, as the odds are greatly against his hitting it, but should embrace that opportunity.

The following are directions for calculating the odds of saving or winning the gammon:—Suppose the adversary has so many men abroad as require three throws to bring them into his tables, and at the same time that the players’ tables are made up, and that he has taken up one of the adversary’s men, in this case it is about an equal wager that the adversary is gammoned. For, in all probability, the player has borne two men before he opens his tables, and when he bears the third man, he will be obliged to open his size or cinque point. It is then probable, that the adversary is obliged to throw twice before he enters his men in the player’s tables, twice before he puts that man into his own tables, and three throws more to put the men which are abroad into his own tables, in all seven throws. Now the player having twelve men to bear, he may be forced to make an ace or a deuce twice before he can bear all his men, and consequently will require seven throws in bearing them; so that, upon the whole, it is about equal whether the adversary is gammoned or not. Suppose a player has three men upon his adversary’s ace point, and five points on his own tables, and that the adversary has all his men in his tables, three upon each of his five highest points, has the player a probability of gammoning his adversary or not?

POINTS.
For bearing three men from his sixth point is18
From his fifth point15
From his fourth point12
From his third point9
From his second point6
——
In all60
Bringing his three men from the adversary’s ace point, to his size point in his own tables, being eighteen points each, and making together54
——
There must remain6

It is plain from this calculation, that the player has much the best of the probability of the gammon, exclusive of one or more blots which the adversary is liable to make in bearing his men, supposing at the same time the throws to be upon an equality. Suppose two blots are left, either of which cannot be hit but by double dice, one must be hit by throwing eight, and the other by throwing nine, so that the adversary has only one die to hit either of them.

The chances of two dice, being in all36
The chances to hit six, are six and two twice2
Five and three twice2
Two deuces1
Two fours1
The chances to hit nine are six and three twice2
Five and four twice2
Two trois1
——
For hitting in all11
Chances for not hitting, remain25

So that the odds are twenty-five to eleven against hitting either of these blots.

This method may be taken to find out the odds of hitting three, four, or five blots upon double dice, or blots made upon double or single dice at the same time. After knowing how many chances there are to hit any of those blots, they must be added together, and then subtracted from the number thirty-six, which are the chances of the two dices, and the question is solved.

The laws of backgammon are, first, If a man is taken from any point, it must be played, if two men are taken from it they also must be played. Second, A man is not supposed to be played till it is placed upon a point and quitted. Third, If a player has only fourteen men in play, there is no penalty inflicted; because by his playing with a less number than he is entitled to, he plays to a disadvantage for want of the deficient man to make up his tables. Fourth, If he bears 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. Fifth, If he has mistaken his throw and played it, and his adversary has thrown, it is not in the choice of either of the players to alter it, unless they both agree so to do.

The probable method of prolonging a hit at backgammon, affords a case of instruction as well as curiosity; for there is a probability of making the hit last by one of the players for many hours, although they shall both play as fast as usual. Suppose B to have borne thirteen men, and that A has his fifteen men in B’s tables, viz. three men upon his size point, as many upon his cinque, quatre, and trois points, two upon his deuce point, and one upon his ace point. A in this situation can prolong it by bringing his fifteen men home, always securing six close points till B has entered his two men, and brought them upon any certain point; as soon as B has gained that point A will open an ace, deuce, or trois point, or all of them, which done, B hits one of them, and A taking care to have two or three men in B’s tables, is ready to hit that man, and also he being certain of taking up the other man, has it in his power to prolong the hit almost to any length, provided he takes care not to open such points as two fours, two fives, or two sixes, but always to open the ace, deuce, or trois points, for B to hit him. We add the following two critical cases for a back game. First, suppose the fore game to be played by A, and that all his men are placed as usual, B has fourteen of his men placed upon his adversary’s ace point, and one man upon his adversary’s deuce point, and B is to throw who has the best of the hit; answer, A has the best of it, gold to silver, because, if B does not throw an ace to take his adversary’s deuce point, which is twenty-five to eleven against him, A will take up B’s men in his tables either singly or make points, and then if B secures either A’s deuce or trois point, A will put as many men down as possible, in order to hit and thereby get a back game. It is evident that the back game is powerful, consequently, whoever practises it must become a greater proficient at the game than he could by any other means. Second, Suppose A to have five men placed upon his size point, as many upon his quatre point, and the same number upon his deuce point, all in his own tables. At the same time let us suppose B to have three men placed upon A’s ace point, as many upon A’s trois point, and the same number upon A’s cinque point, in his own tables, and three men placed as usual out of his tables, who has the best of the hit? Answer—The game is equal till B has gained his cinque and quatre points in his own tables, which, if he can effect, and by playing two men from A’s cinque point, in order to force his adversary to blot by throwing a cane, which should B hit, he will have the best of the hit.—Strutt—Ency. Lon.—Hoyle.