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Suppose B to have borne thirteen men, and that A has taken up the two remaining men. And also that A has fifteen men in B‘s table, viz. three upon his six, three upon his cinque, three upon his quatre, three upon his trois, two upon his deuce, and one upon his ac‘e point. Let A bring his fifteen men home, by always securin six close points, till B has entered his two men, and brought them upon any certain point; as soon as B has done that, A must open an ace, deuce or trois, or all three; which etfected, B hits one of them, and A, taking care to have two or three men in B‘s table, is ready to hit that man ; and also, he being assured of taking up the other man, has it in his power to prolong the hit to almost 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.

6. What are the odds upon two dice, for throwing two sixes, two fives, or two tours, in thrice? Ans. Supposing 36 shillings to be the stake

depending, the thrower will be entitled to s. d.

have for his first throw - - 3 (1 That deducted, leaves 33; which divided

again into 36 parts, make so many eleven

ences, out of which the thrower is to

ave three for his second throw - 2 9

The remainder, 30 shillings and three pence,

is again to be divided into 36 parts; making so many ten pences, and the three pence divided into so many parts, make so many thirds of farthings, of which the thrower is to have three parts for his share, for his third throw - -

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Total for the thrower

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*So 'thnt it is 27:. Sid. to 8.9. 34:1. against the "thrower ; which is very nearly as 10 to 3, that two :sixes, two fives, or two fours, are not thrown in three throws. ' .

7. Rack-game. Suppose A to have two men upon 'his own six point, three' men upon his usual point in his outer table, two men upon the point where vhis five men are generally placed in his adversary’s router table, five men upon his adversary‘s ace, and three upon his adversary‘s quatre point. And B to Ihave two men upon his own six point, likewise three upon his usual point, in his outer table, two upon the point where _'his five are commonly placed in his adversary‘s outer table, five upon his adver. sary's ace, and three men upon his vadversary's trois point. Who has the fairest chance to win the Mt?"

Ans. A‘has, because he is to play either an ace or a deuce, from his adversary’s ace point, in vorder to make both those points as occasion ofi'ers, and having the quatre-poin't in “his adversary‘s stables, he may more easilybring those men away, .and will also have a resting place by the conve.niency of that'point, which at all times in the game will give him an opportunity of running for the hit, or staying, if he think proper. Whereas B cann'ot so readily come from the trois point in his adver.sary‘s tables.

8. Suppose A and B place their men in the 'fol.lowing manner for a hit: A to have three men upon his own six point, three upon . his usual point in his outer‘table, and ninemen upon 'his adver. sary's ace, deuce, and trois points, three upon . each; and suppOse'B's men to be placed in the same »order and \manner. The result .is, that the best , layer oughtto win‘the hit; and the dice are to lie thrown for, the situation being perfectly equal ,in A‘sand' B’s game. If A throw first, at him endeavour to in his adversary’s cinque point; when that is e 'ecttd, let him lay as many blots as possible, to tempt B to hit him; for every time that B hits will be in A’s favour, bricause it puts B backward; and let A take up none of B's men for the same reason. A should always endeavour to have three men upon his adversary's ace and deuce points; because when B makes a blot, these points will remain secure, and by recourse had to a former case (Numb. 5. p.324) when A has borne five, six, or more men, yet A may secure six close points out of his table, in order to prevent B from getting his man home: and by recourse had to the calculations, he may easily find out (in case he makes up his table) who has the better of the ,hit; and if he find that B is the forwardest, he must then eudeavour‘to lay ‘ such blots, as may give him a chance for taking up another man, in case B should happen to have a blot at home.

N. B. Those who play the't'oregoing game well may be ranked in the first class.

9. A has borne thirteen men, and has two men to bear upon his deuce point; B has thirteen men win his own tables, with two men'to enter. B is to threw, and to name the throws both for himself and A, but not to hit a blot of either side. What ,throwis B to name for both parties in order to save his gammon ?

Am. B calls for himself two aces, which enter his two men upon A‘s ace-point. B also calls tuO aces for A, and consequently A cannot either bear aman, or play one: then B calls for two sixes for himSelf, and carries one man home upon the six point in his own table, and the other he places upon his adversary’s bar point: B also calls six-ace for A, so that 'A has one man left to

bear, and then B calls for himself eithes two sixes, two fives, or two fours, any of which bear a_ man, in case he has men in his table upon those points.

' 10. Suppose that both yours and your adversnry‘s tables are made up. Also that you have one man to carry home, but that he has two men On your bur-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 choice to run the risk of being hit by 7 or by 8, both of which are chances upon double dice. Which of these chances is it best for you to venture?

Ans. That of 7, for the foilowing reasons, 1st, because the chances of being hit by 7 or S, are equal. 2d. If he does‘not hit 7, you will then have in your favour 23 chances to 13, that by your next throw you either hit or pass beyond him. 3d. In case our second throw should happen to be nnder’7, an that consequently you cannothit him, yet you may play that cast at home, and consequently leave the blot upon double dice. , Whereas, if, on the, contrary you had lett the blot upon 8, you would have made a bad choice. lst. Because the chances of being hit by 7 or by S, are only equal. 2d. Because, if you should escape being hit by 8, yet you would then have but ‘17 chances in your favour, against l9, for either hitting or passing beyond him by your next throw. 3d; In case your second'throw should happen to be six-ace, which is short ‘of him, you would then be obliged to play the man that is out of your table, not being able to play the six at home, and consequently to leave ablot to be hit by a single (or flat) die, which event, upon sup osition that you play for IS shillings a game, woul entitle him to ll shillings of the whole stake depending.

THE LAWS OF BACK-GAMMON

1. If you takes man or- men fromany: point; that man or men must be played.

2. You are not understood to have played any" man, till it is placed upon a point, and quilted.

3. If you play with I4 men only, there is no

penalty attending it, because with a lesser num-‘ber, you play to a disadvantage, by not having theadditional'man to make up your tables. _ 4. If you bear any number of men before you have entered a man taken up, and which consequently~ you were obliged to enter, such men, so born, must be entered again in your adversary’s tables, as well as the man taken up.

5.v If you have mistaken your throw, and played‘ it, and your adirersary have thrown, it is not in your or his choice to alter it; unless both parties agree. ‘ .

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1. THE draught table, of which the print affords an’accurate representation, must be placed with an upper white corner towards the right hand. _

2. The table beingproperly placed, I number the white squares in order from to 1 t0-32.. \,

3. The men are black and white, or yellow round'. pieces, similar to thOse used at Back-Gammon. The blank pieces are supposed to be placed upon the first twelve, and the white on the last twelve» white squares,.in all the following games.

4. Each layer alternately moves one of his' men forwar s, at a right, angle, to the next Whllt)’

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