numbers. It is 4 to 9 against
throwing a single number with either of the dice, so as to hit a blot
and enter. 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. In spite of this reasoning, there are
people who build so much upon their own opinion, that should their
favourite horse happen to be beaten, they will have it to be owing to
some fraud.

The following fact is mentioned as a 'paradox.'

It happened at Malden, in Essex, in the year 1738, that three horses
(and no more than three) started for a L10 plate, and they were all
three distanced the first heat, according to the common rules in
horse-racing, without any quibble or equivocation; and the following was
the solution:--The first horse ran on the inside of the post; the second
wanted weight; and the third fell and broke a fore-leg.(54)

(54) Cheany's Horse-racing Book.

In horse-racing the expectation of an event is considered as the
present value, or worth, of whatsoever sum or thing is depending on the
happening of that event. Therefore if the expectation on an event be
divided by the value of the thing expected, on the happening of that
event, the quotient will be the probability of happening.

Example I. Suppose two horses, A and B, to start for L50, and there are
even bets on both si