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 all 36 The chances to hit six, are six and two twice 2 Five and three twice 2 Two deuces 1 Two fours 1 The chances to hit nine are six and three twice 2 Five and four twice 2 Two trois 1 —— For hitting in all 11 Chances for not hitting, remain 25 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.