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odds of entering a single man upon any given number of points, and the game should be played accordingly.
4. If you are obliged to leave a blot, by recourse to the calculations for hitting it, you will find the chances for and against you, and be enabled to judge how to play your game to the greatest advantage.
5. You will also find by the calculations the odds for and against you, upon being hit by double dice, and consequently you will have it in your power to choose such a melbod of play as is most to your advantage.
6. If it is necessary to make a run, in order to win a hit, and you would know to a point which is most for: ward, your adversary or you;
Reckon how many points you must have to bring home to your size point in your own tables the man that is at the greatest distance from it, and do the like by every other man that is abroad; when the numbers are summed up, add to them the following numbers for thase already on your own tables (supposing the men that were abroad as on your size point, for bearing) namely, six for every man to the size point, five for every man on the cinque point, four every man on the quatre point, three for every man on the trois point, two for every man on the deuce point. Do the like to your adversary's game, and then you will know which of you is forwardest, and likeliest to win the hit.
Directions for a Learner to bear his Men. 1. If your adversary is much before you, never play a man from your quatre, trois, or deuce points, in order to bear that inan from the point where you put it, because nothing but high doublets can give you any chance for the hit. always play them from your size or highest point; so that throwing two fives, or two fours, will, upon having eased your size and cinque points, be of advantage; whereas, had your size point remained loaded, you must, perhaps, be obliged to play at length those fives and fours.
2. Whenever you have taken up two of your adversary's men, and have two, three, or more points, made in your own tables, spread your men, in order either to take a new point in your tables, or be ready to hit the man which your adversary may enter. As soon as he enters one of his med, compare bis game with yours;
VOI say lay
and if you find that the game is upon a par, or better, never fail taking his man up if you can, it being 25 to 11 against his hitting you; which chance being so much in your favour, you should always run that risk, when you have already two of his men up.
An exception may be made to this rule: if you play for a single hit only, and your playing that throw otherwise gives you a superior chance for the hit, you ought not to take up that man.
3. Never be deterred from taking up any one man of your adversary's by the fear of his hitting you with double dice, because the fairest probability he has of hitting you is 5 to 1 against him.
4. If you have five points in your tables, and have Inken up one of your adversary's men, and are forced to leave a blot out of your tables, leave it upon doublets, in preference to any other chance; because doublets are 35 to 1 against his hitting you, and any other chance is but 17 to 1 against him.
5. Two of your adversary's men in your tables are betier for a hit than if you had more, provided your game is more forward; because his having three or more men in your tables gives him more chances to hit you, than if he had but two men in them.
6. If you are to leave a blot upon entering a man upon your adversary's tables, or otherwise, leave it upon the point most disadvantageous to him. For example, if it is his interest to hit you or take you up as soon as you enter, leave the blot upon his lowest open point, because (as has been stated before) all the men your adversary plays upon his trois or his deuce points are decmed lost, being greatly out of play, and his game will be crowded there, and open elsewhere, whereby he must be greatly annoyed.
7. To prevent your adversary from bearing his men to the greatest advantage, at the time you are running to save your gammon, it is your advantage to leave a man upon your opponent's ace point, which will prevent his bearing his men to his greatest advantage, and will also give you the chance of bis making a blot, which you may chance to hit. However, if, upon a calcula. tion, you find tbat you have a throw, or a probability of saving your gammon, never wait for a blot, because the odds are greatly against hitting it.
Cases 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 ad. versary 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 a 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 nearly, 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 fire highest points.
Question. Whether the probability is for the adversary's gammoning me or not? Answer.
Points. For his bearing three men from his 6th point is 1
5th points 4th point 13 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,
· Remains 6
New 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 od 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 u be hit but by double dice; to hit the one, that cast must 25 be eight, and the other must be nine; so that iny adversary has only one die to hiterther of them.
The odds are 25 to 11 against hitting either of those blots. een 4. Suppose I leave two other blots ihan the former, les which cannot be hit but by double dice, the one must 20: be hit by eight, and the other by seven : print It is 2 to i that I am not hit.
. A critical Game to play.
Suppose A and B place their men in the following #i manner for a hit: Eine 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 in 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
im lay as many blots as possible, to teinpt B to hit him; e r every time that B hits them will be to A's advan.
age, 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. lation 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 blots as may be taken up by his adversary, that he may give him a chance for taking up another mau, 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; A has borne thir. teen men, and has two men to bear upon his deuce point; B has thirteen men in his own tables, and two men to enter B is 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 point. B also calls two aces for A, and therefore A cap neither bear a man nor play one: thep B calls for two sixes for himseif, and carries one man home upon his size point in his or'n 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 those points, and saves his 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 par point to carry home, which lie in wait to catch your man, and that if you pass him 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 ventura?
Answer. That of 7, for the following reasons :
First. Because the chances of being hit by 7 or 8 arc equal.
Second. If he does not bit 7, you will then have in