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Oases by way of example, to calculate the odds of saving
or winning the Gammon. 1. If your adversary has so many men abroad as require three throws to put them into his tables; and your tables are made up, and you have taken up one of your adversary's men ; it is about an equal wager that your opponent is gammoned.
Because, in all probability, you will have borne two men before you open your tables, and when you bear the third man, you will be obliged to open your size or cinque point; in that case it is probable that your adversary is obliged to throw twice before he enters his man in your tables, and two throws more before he puts that man into his own tables, and three throws more to put the men which he has abroad into his own tables : in all seven throws: now, as you have twelve men to bear, these probably will take seven throws in bearing, because before you can bear all your men, you may twice be obliged to make an ace, or à deuce.
N. B. No mention is made of doublets of either side, that event being equal to each party.
The preceding case duly attended to, shows how to calculate, very nwarly, the odds of saving or winning a gammon upon most occasions.
2. Suppose I have three men upon my adversary's ace point, and five points in my own tables, and that my adversary has all his men in his tables, three upon each of his five highest points.
Question. Whether the probability is for the adver. sary's gammoning me or not? Answer.
Points. For his bearing three men from bis 6th point is 18
5th point 15 4th point 12 3d point 9 2d point 6
In all 60 Bringing my three men from my adversary's
ace point, to my size point in my tables, being 18 points each, make in all
Now in addition to the six points in your favour, there is a further consideration for you, which is, that your adversary may make one or two blots in bearing, as is frequently the case ; by this calculation, you have greatly the better of the probability of saving your gammon.
N. B. This case is supposed upon an equality of throwing.
3. Suppose I leave two blots, either of which cannot de hit but by double dice; to hit the one, that cast must be eight, and the other must be nine ; so that my adversary has only one die to hit either of them.
The odds are 25 to 11 against hitting either of those blots.
14. Suppose I leave two other blots than the former, which cannot be hit but by double dice, the one must be hit by eight, and the other by seven : It is 2 to l that I am not hit.
A critical Game to play. Suppose A and B place their men in the following manner for a hit:
A, three men upon his. size point in his own tables, three men out of his tables upon his usual point, and nine men upon his adversary's ace, deuce, and trois points, three upon each; and suppose B's men to be placed in his own, and in his adversary's tables, in the same manner and order.
Situated thus, the best player ought to win the hit.
Now, if A throws first, he ought to endeavour to gain his adversary's cinque point; when that is done, let him lay as many blots as possible, to tempt B to hit him; for every time that B hits them will be to A's advantage, because it puts him backward ; and let A take up none of B's men for the same reason.
A should endeavour to have three men upon each of his adversary's ace and deuce points; because when B makes a blot, these points will remain secure, and when A has borne five, six, or more men, A may yet secure six close points out of his tables, in order to prevent B from getting his man home; and by recourse to calcu. Jation he may easily find out (in case he makes out his tables, who has the best of the hit; and if he finds that B is the foremost, he should then try to lay such biots as may be taken up by his adversary, that he may give him a chance for taking up another man, in case B should have a blot at home.
Those who play the foregoing game well may rank in the first class of back-gammon players.
A Case of Curiosity. A and B play at back-gammon; À has borne thirteen men, and has two men to bear apon his deuce point; B has thirteen men in his own tables, and two men to enter. Bis to throw and to name the throws both for himself and A, but not to hit a blot of either side,
Now what throw is B to name for both parties, in or der to save his gammon?
Answer. B calls for himself two aces, which enters his two men upon A's ace points Balso calls two aces for A, and therefore A cau neither bear a man nor play one : theo В calis for two sixes for himself, and carries one man home upon his size point in his orin tables, and the other he places upon his adversary's bar point: B also calls size-ace for A, so that A has one man left to bear, and then B calls for himself either two sixes, two fives, or two fours, any of which bear a man, if he has men in his tables upon these points, and saves bis gammon.
The following question is worth attention, as being critical and instructive.
Supposing that yours and your adversary's tables are made up;
And that you have one man to carry home, but that he has two men on your bar point to carry home, which lie in wait to catch your man, and tha: if you pass bim you are to win the hit: suppose also that you have it in your option to run the risk of being hit, by 7 or 8, both of which are chances upon double dice:
Question. Which of these chances is it best for you to venture?
Answer. That of 7, for the followiny reasons :
your favour twenty-three chances to thirteen, that by your next throw you either hit him or pass beyond him.
Third. In case your second throw should be under 7, and you cannot hit him, yet you may play that cast at home, and consequently leave the blot upon double dice.
Whereas if, on the contrary, you had left the blot upon 8, you would have made a bad choice, for the fol. lowing reasons:
1. Because the chances of being hit by 7 or by 8 are equal only.
2. Because, if you should escape the being hit by 8, yet then you would have but seventeen chances in your favour, against nineteen, for either hitting him, or pass. ing beyond him, by your next throw.
3. Now in case your second throw should be size-ace, which is short of him, you would then be forced to play the man that is out of your tables, being unable to play the six at home, and consequently to leave a blot to be hit by a single die, (or flat) in which event, computing that you play for eighteen shillings a game, he would be entitled to eleven shillings of the whole depending stake.
THE LAWS OF THE GAME. 1. If the man is taken from any point, it must be played.
2. A man is not played, till it is placed upon a point and quitted.
3. If a player has only fourteen men in play, there is no penalty attending it.
4. 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.
5. 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 both parties agree to it.