The following table shews the plan of the game.

The Caster wins

The Setter wins by the

Caster's crabbing

When the caster throws a Main, which must be either 5, 6, 7, 8 or 9, as per table, he is then to throw his chance, which must be either 4, 5, 6, 7, 8, 9 or 10; if he neither nicks nor crabs it, he is then to abide by the chance; and if he throws that chance before the main, he wins all the money set; but if he should throw the main before the chance, then he loses all.

When 7 is the main, 'tis seven to two against the caster's nicking it, there being six ways to throw 7, and two to throw 11, either of which is the nick, as per table: so that the six ways for 7, and two for 11, being equal to eight, which taken from thirty-six (the whole number of chances) leaves a remainder of twenty-eight; that is twenty-eight

to eight, or seven to two against the caster nicking it.

When 6 or 8 is the main, 'tis 5 to 1 against the caster nicking it, there being five ways to throw 6, or 8, and one for 12, which make six ways for the nick, which taken from 36, leaves 30; therefore there being six ways to nick, and 30 against it, is five to one against the caster nicking either 6 or 8.

5 or 9 being the main, is eight to one that the caster does not nick it, there being but four ways to nick, which make it eight to one against the caster nicking either 5 or 9.

When 7 is the main, 'tis 672 to 624, or in money 14s. to 13s, that it is off in two throws: and if 7 is connected with 6 or 8, as main and chance, it is 671 to 625, nearly 15 to 14, or 13s. 113d, to 13s. 04d. that one of them is cast in twice.

When 7 is connected with 5 or 9, 'tis 676 to 620, almost 12 to 11, that it is not off in 2 throws; or 14s. 1d. to 12s. 11d. equal to 3s. 6žd. to 3s. 23d. or 1 guinea to 19s, 3d,

When 7 is connected with either 4 or 10, 'tis 729 to 567, (9 to 7 or a little better than 5 to 4) that it is not off in 2 throws; and 26973 to 19683, (a little better than 4 to 3) that it is off in 3 throws.

When 6 or 8 is connected with 5 or 6, 'tis 729 to 567, (a little better than 5 to 4) that it is not off in 2 throws; it is the very same chance as when 7 is concerned with either 4 or 10; it being 3 to 1 against either of the mains or chances being off the first throw.

6 or 8 connected with 4 or 10, is 784 to 512, that it is not off in two throws, which is a little better than 3 to 2; and 386 to 343, or near 10 to 9, that it is off in 3 throws.

If eight and six are main and chance, it is very

near 11 to 12, that either one or the other is thrown off in two throws.

If five and eight, or nine and eight, or five and six, or nine and six, are main and chance, the probability of throwing one of them in two throws is as 7 to 9 exactly.

But if five and four, or five and ten, or nine and four, or nine and ten, are main and chance, he that undertakes to throw either main or chance in three throws, has the worst of the lay; for it is as 24 to 23 exceeding near against him.

༄།

If the main be seven, and each person stakes a guinea, the gain of the setter is about 34d. per guinea.

If the main be six or eight, the gain of the setter is 54d. in a guinea.

But if the main be five or nine, the gain of the setter is about 334d. in a guinea.

However if any person is determined to set upon the first main that is thrown, his chance, supposing each stake to be a guinea, is 4 d. exactly. Hence the probability of a main, to the probability of no main, is as 27 to 28 very near.

Any one undertaking to throw a six or an acé with two dice in one throw, ought to lay 5 to 4.

See page 141 for the odds against winning any number of successive events, and page 291 for the number of chances upon two dice.

THE GAME OF BILLIARDS.

WITH INSTRUCTIONS AND RULES FOR THE FOLLOWING GAMES, viz.

The White Winning Game.

The White Losing Game.

The White Winning and Losing Game. The Winning and Losing Carambole Game. i Red or Carambole Winning Game.

The Red Losing Game.

The Simple Carambole Game.
Fortification Billiards.

With Rules and Regulations for every Method of playing the Game.

In order to play this game well, attention must be given at first to the method of holding the mace; to the position in which the player should stand, and the manner of delivering the ball from the mace; but these are much more easily acquired by observation, or by the direction of a good player, than by any possible written rules. A person who plays with his right hand must stand with his left foot foremost; and, on the contrary, he who is left-handed, must stand with his right foot foremost, by which he will stand more steady and firm. Immoderate bursts of passion, and even fretting at trifling disappointments in the game, are usually found very prejudicial to the player; his nerves being affected, it is impossible

for him to make the stroke with that steadiness and nicety the game requires.

The games usually played till lately were the white winning and the red winning carambole games, but the winning and losing carambole game is now very much in vogue.

THE DIFFERENT GAMES OF BILLIARDS.

1. The White winning Game, played with two white balls, is twelve in number, when two persons play; and fifteen when four play; scored (independently of forfeitures) from winning hazards only.

2. The White losing Game, also twelve in number, played with two white balls, is the reverse of the winning; the points being scored from losing and double, or winning and losing hazards.

3. The White winning and losing Game, is a combination of the two preceding; all balls put in by striking the adversary's ball first, reckon towards the game.

The three preceding games should be made introductory to the knowledge of those with three or more balls, which are more complicated and difficult.

4. Choice of balls.-In which the player chuses his ball each time, an incalculable advantage, generally played against the losing and winning game.

5. The Bricole game signifies being required to strike a cushion from whence the ball is to re