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 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.