on the single account of the advantage" target="_blank" title="n.不利(条件)；损失">disadvantage of the play, they lost
one-eighth part of all the money played for. But the master of

the ball maintained that they had no reason to complain, since he
would undertake that any particular point of the ball should come

up in two and twenty throws; of this he would offer to lay a
wager, and actually laid it when required. The seeming

contradiction between the odds of one and thirty to one, and
twenty-two throws for any chance to come up, so perplexed the

adventurers that they began to think the advantage was on their
side, and so they went on playing and continued to lose.

The doctrine of chances tends to explode the long-standing
superstition that there is in play such a thing as LUCK, good or

bad. If by saying that a man has good luck, nothing more were
meant than that he has been generally a gainer at play, the

expression might be allowed as very proper in a short way of
speaking; but if the word 'good luck' be understood to signify a

certain predominant quality, so inherent in a man that he must
win whenever he plays, or at least win oftener than lose, it may

be denied that there is any such thing in nature. The asserters
of luck maintain that sometimes they have been very lucky, and at

other times they have had a prodigious run of bad luck against
them, which whilst it continued obliged them to be very cautious

in engaging with the fortunate. They asked how they could lose
fifteen games running if bad luck had not prevailed strangely

against them. But it is quite certain that although the odds
against losing so many times together be very great, namely,

32,767 to 1,--yet the POSSIBILITY of it is not destroyed by the
greatness of the odds, there being ONE chance in 32,768 that it

may so happen; therefore it follows that the succession of lost
games was still possible, without the intervention of bad luck.

The accident of losing fifteen games is no more to be imputed to
bad luck than the winning, with one single ticket, the highest

prize in a lottery of 32,768 tickets is to be imputed to good
luck, since the chances in both cases are perfectly equal. But

if it be said that luck has been concerned in the latter case,
the answer will be easy; for let us suppose luck not existing, or

at least let us suppose its influence to be suspended,--yet the
highest prize must fall into some hand or other, not as luck

(for, by the hypothesis, that has been laid aside), but from the
mere necessity of its falling somewhere.

Among the many curious results of these inquiries according to
the doctrine of chances, is the prodigiousadvantage which the

repetition of odds will amount to. Thus, 'supposing I play with
an adversary who allows me the odds of 43 to 40, and agrees with

me to play till 100 stakes are won or lost on either side, on
condition that I give him an equivalent for the gain I am

entitled to by the advantage of my odds;--the question is, what I
am to give him, supposing we play at a guinea a stake? The

answer is 99 guineas and above 18 shillings,[52] which will seem
almost incredible, considering the smallness of the odds--43 to

40. Now let the odds be in any proportion, and let the number of
stakes played for be never so great, yet one general conclusion

will include all the possible cases, and the application of it to
numbers may be worked out in less than a minute's time.'[53]

[52] The guinea was worth 21s. 6d. when the work quoted was
written.

[53] De Moivre, Doctrine of Chances.
The possible combinations of cards in a hand as dealt out by

chance are truly wonderful. It has been established by
calculation that a player at Whist may hold above 635 thousand

millions of various hands! So that, continuallyvaried, at 50
deals per evening, for 313 evenings, or 15,650 hands per annum,

he might be above 40 millions of years before he would have the
same hand again!

The chance is equal, in dealing cards, that every hand will have
seven trumps in two deals, or seven trumps between two partners,

and also four court cards in every deal. It is also certain on
an average of hands, that nothing can be more superstitious and

absurd than the prevailing notions about luck or ill-luck. Four
persons, constantly playing at Whist during a long voyage, were

frequently winners and losers to a large amount, but as
frequently at 'quits;' and at the end of the voyage, after the

last game, one of them was minus only one franc!
The chance of having a particular card out of 13 is 13/52, or 1

to 4, and the chance of holding any two cards is 1/4 of 1/4 or
1/16. The chances of a game are generally inversely as the

number got by each, or as the number to be got to complete each
game.

The chances against holding seven trumps are 160 to 1; against
six, it is 26 to 1; against five, 6 to 1; and against four nearly

2 to 1. It is 8 to 1 against holding any two particular cards.
Similar calculations have been made respecting the probabilities

with dice. There are 36 chances upon two dice.
It is an even chance that you throw 8. It is 35 to 1 against

throwing any particular doublets, and 6 to 1 against any doublets
at all. It is 17 to 1 against throwing any two desired 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