Against hitting with the
amount of two dice, the chances against 7, 8, and 9 are 5 to 1;
against 10 are 11 to 1; against 11 are 17 to 1; and against
sixes, 35 to 1.
The probabilities of throwing required totals with two dice,
depend on the number of ways in which the totals can be made up
by the dice;--2, 3, 11, or 12 can only be made up one way each,
and therefore the chance is but 1/36;--4, 5, 9, 10 may be made up
two ways, or 1/8;--6, 7, 8 three ways, or 1/12. The chance of
doublets is 1/36, the chance of PARTICULAR doublets 1/216.
The method was largely applied to lotteries, cock-fighting, and
horse-racing. It may be asked how it is possible to calculate
the odds in horse-racing, when perhaps the jockeys in a great
measure know before they start which is to win?
In answer to this a question may be proposed:--Suppose I toss up
a half-penny, and you are to guess whether it will be head or
tail--must it not be allowed that you have an equal chance to win
as to lose? Or, if I hide a half-penny under a hat, and I know
what it is, have you not as good a chance to guess right, as if
it were tossed up? My KNOWING IT TO BE HEAD can be no hindrance
to you, as long as you have liberty of choosing either head or
tail.
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