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 prodigious advantage which the repetition
of odds will amount to. Thus, 'supposing I play with an adversary who
allows me the odds of