To illustrate these calculations still more clearly, the following table will be serviceable:

The nick of seven is 7 to 2, often laid 10 to 3. The nick of six and eight is 5 to 1

It is necessary to be perfectly master of these odds, in order to play the prudent game, and to make use of them by way of insuring bets in what is called hedging, in case the chance happens to be unlikely; for by taking the odds a ready calculator secures himself, and often stands part of his bet to a certainty. For example, if seven be the main, and four the chance, and he should have 57. depending on the main, by taking 67. to 31. he must either win 21. or 1.; and on the contrary, if he should not like his chance, by laying the odds against himself, he must save in proportion to the bet he has made.

CALCULATIONS ON HAZARD.

WHEN either 6 or 8 is connected with 7, as main and chance, it is 6 to 5 in favour of 7, there

being six ways to throw the 7, and only five for the 6, or 8.

7 connected with either 5 or 9, is 3 to 2 in favour of 7; there being six ways for the 7, and but four for 5, or 9.

7 connected with either 4 or 10, is 2 to 1 in favour of 7; there being six ways to throw the 7; but three for 4 or 10.

6 or 8 connected with either 5 or 9, is 5 to 4 in favour of 6 or 8; there being five ways to throw 6, or 8; but four for 5, or 9.

6 or 8 connected with 4 or 10, is 5 to 3 in favour of 6 or 8; there being five ways to throw 6, or 8; only three for 4 or 10.

5 or 9 connected with 4 or 10, is 4 to 3 in favour of 5 or 9; there being four ways to throw 5, or 9; but three for 4, or 10.

When 6 or 8 is backed against 7, size ace is barred, thereby reducing the 7 to four chances; and the two trois of the 6 being barred, leaves but four chances for the 6; the same by barring of the two fours in the 8; which two trois and two fours are commonly called doublets.

When 5 or 9 is backed against 6 or 8, the doub lets are barred, reducing the 6 or the 8 to only four chances; which makes the bet equal, there being four for each.

The following tables explain the various ways of throwing all the different mains and chances.

To throw 7.

6 and 1 twice........2 5 and 2 twice........2 4 and 3 twice......2

To throw 6.

5 and 1 twice........2 4 and 2 twice........2 two trois once......1

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5

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, or10; should he neither nick nor crab it, he is then to abide by the chance; and if he throw that chance before the main, he wins all the money set; but if he throw the main, before the chance, then he loses all.

When 7 is the main, it is 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, it is 5 to 1 against the caster nicking it, there being five ways to throw 6, or 8, and 1 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, 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 makes it eight to one against the caster nicking either 5 or 9.

When 7 is the main, it is 672 to 624, or in money 14s. to 13s. that it comes in two throws: and if 7 be connected with 6 or 8, as main and chance, it is 671 to 625, nearly 15 to 14, or 13s. 11 d. to 13s. 04d. that one of them is cast in twice throwing.

When 7 is connected with five or 9, it is 676 to 620, almost 12 to 11, that it is not thrown in two throws; or 14s. 1d. to 12s. 11d. equal to 3s.64d. to 3s. 2 d. or 1 guinea to 19s. 3d.

When 7 is connected with either 4 or 10, it is 729 to 567, (9 to 7 or a little better than 5 to 4)that it is not thrown in two throws: and 26973 to 19683 (a little better than four to 3) that it is in 3 throws.

When 6 or 8 is connected with 5 or 6, it is 729 to 567, (a little better than 5 to 4) that it is not thrown in two 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 thrown the first throw.

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

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

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

If five and eight, or nine and eight, or five and six, or nine and six, be 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, be main and chance, he that undertakes to throw either main or chance in three throws has the worst of the bet; for it is very near 24 to 23 against him.

If the main be seven, and each person stake 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 5 d. in a guinea.

But if the main be five or nine, the gain of the setter is about 34d. in a guinea,

However if any person be determined to set upon the first main that is thrown, his chance, supposing each stake to be a guinea, is 4ğd. exactly.

Hence the probability of a main to the probability of no main, is very nearly as 27 to 28.

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

See page 153 for the odds against winning any number of successive events, and page 307 for the number of chances upon two dice.