Doctrine of chances

“ But the chemist had no time to consider shells. He was intent only on getting rid of surplus stock.
The majority of people who are afraid are those who refuse to consider the doctrine of chances. The chances of their being hit may be one in ten thousand, but they disregard the odds in their favor and fix their minds on that one chance against them. ”

“ The doctrine of chances pronounces upon certain kinds of events in respect of number and magnitude; it has absolutely nothing to do with any particular person's feelings about these relations. We might as well append a corollary to the rules of arithmetic, to point out that although it is very true that twice two are four it does not follow that four, horses will give twice as much pleasure to the owner as two will. If two men play on equal terms their chances are 154 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. ”

“ If, therefore, a dextrous person foretel one hundred events, by means of any prognosticating key, or any index whose powers are previously settled,—whether stars, cards, sediments of tea, lines of the hand or forehead, entrails of animals, or dreams, signs or omens,—by the doctrine of chances it is an even, or some other fixed chance, that half, or some other portion, of such events will come to pass. Superstition will triumph if only 1 in 5, or 1 in 10, happen as foretold ”

“ Each event or contingency must, of course, be uncertain, or, at all events, unknown to the parties, that is, it represents a chance, and where the chances are agreed to be uneven the inequality is represented by odds. ”

“ Doubtless it will be seen here with interest that in considering, even in the eternal principles of reason, justice, and humanity, only the favorable chances which are constantly attached to them, there is a great advantage in following these principles and serious inconvenience in departing from them: their chances, like those favorable to lotteries, always end by prevailing in the midst of the vacillations of hazard. ”

“ For if we affirm that one chance can, after any other manner, be superior to another, we must at the same time affirm, that there is something, which gives it the superiority, and determines the event rather to that side than the other: That is, in other words, we must allow of a cause, and destroy the supposition of chance; which we had before establish'd. A perfect and total indifference is essential to chance, and one total indifference can never in itself be either superior or inferior to another. ”

“ Let us not fear to shout it from the house-tops if need be; for we now know that the idea of chance is, at bottom, exactly the same thing as the idea of gift, the one simply being a disparaging, and the other a eulogistic, name for anything on which we have no effective claim. And whether the world be the better or the worse for having either chances or gifts in it will depend altogether on what these uncertain and unclaimable things turn out to be. ”

“ In order to calculate chances, we must know that of several events one, and no more, must happen, and also not know, or have any reason to suspect, which of them that one will be. Thus, with the simple knowledge that the issue must be one of a certain number of possibilities, we may conclude that one supposition is most probable to us. ”

“ This vivid impression which we receive from the presence of events, and which allows us scarcely to remark the contrary events observed by others, is a principal cause of error against which one cannot sufficiently guard himself.
It is principally at games of chance that a multitude of illusions support hope and sustain it against unfavorable chances. The majority of those who play at lotteries do not know how many chances are to their advantage, how many are contrary to them. ”

“ If an event has never once failed, in a number of trials sufficient to eliminate chance, it really has all the certainty which can be given by an empirical law; it is certain during the continuance of the same collocation of causes which existed during the observations. If it ever fails, it is in consequence of some change in that collocation. Now, no theory of chances will enable us to infer the future probability of an event from the past, if the causes in operation, capable of influencing the event, have intermediately undergone a change. ”

“ Secondly, 'Tis suppos'd, that tho' the dye be necessarily determin'd to fall, and turn up one of its sides, yet there is nothing to fix the particular side, but that this is determin'd entirely by chance. The very nature and essence of chance is a negation of causes, and the leaving the mind in a perfect indifference among those events, which are suppos'd contingent. ”

“ Now, we have seen that the chances of independent concurrent arguments are to be multiplied together to get the chance of their combination, and, therefore, the quantities which best express the intensities of belief should be such that they are to be added when the chances are multiplied in order to produce the quantity which corresponds to the combined chance. ”

“ It follows again from this theorem that in a series of events indefinitely prolonged the action of regular and constant causes ought to prevail in the long run over that of irregular causes. It is this which renders the gains of the lotteries just as certain as the products of agriculture; the chances which they reserve assure them a benefit in the totality of a great number of throws. ”

“ Yet does not everyone believe from experience that survival is a continuous chance?
There are innumerable chances for and against one’s living another day, another hour. These chances are estimated statistically and great companies are formed to bet on them. ”

“ If the opportunity be repeated exactly as often as there are chances against the event, it is an even chance that it occurs once in that number of times. If oftener, the chances are actually in favor of its happening. It is an even chance every time whether red or black wins ”

“ The common theory, therefore, of the calculation of chances, appears to be tenable. Even when we know nothing except the number of the possible and mutually excluding contingencies, and are entirely ignorant of their comparative frequency, we may have grounds, and grounds numerically appreciable, for acting on one supposition rather than on another; and this is the meaning of Probability. ”

“ The likelihood and probability of chances is a superior number of equal chances; and consequently, when we say 'tis likely the event will fall on the side which is superior, rather than on the inferior, we do no more than affirm, that where there is a superior number of chances there is actually a superior, and where there is an inferior there is an inferior, which are identical propositions, and of no consequence. ”

“ It is not only to be considered what is the general result of the chances in the long run, but also what are the extreme limits of variation from the general result, which may occasionally be expected as the result of some smaller number of instances. ”

“ The theory of chances has been described as a method of extracting knowledge out of ignorance; it is undoubtedly a method of converting probable judgments into certain ones—though the certainty is of a peculiar kind, and its verification presents a special epistemological problem of some interest. But the probable beliefs that I now wish to distinguish from certain ones are beliefs which involve no attempt at a quantitative estimate of ‘amount of probability’ ”

“ Sustained by this belief, players often risk considerable sums at games when they know that the chances are unfavorable. In the conduct of life a similar opinion may sometimes have advantages; but most often it leads to disastrous enterprises. ”

“ Then comes in the third fallacy I have mentioned. 'The chances,' some will say, 'are bound to equalise themselves in the long run, and then one can neither win nor lose.' Dear, good, simple-minded souls! The proportion of gains to losses, I grant, will become more equalised in an infinite number of bets where the probabilities are always equal; but the amount which may be lost, and the proportion it bears to the belongings of the bettor, may ever increase with the infinity of the bets. ”

“ The theory of chance consists in reducing all the events of the same kind to a certain number of equally possible cases, such, that is to say, that we are equally undecided about, and to determine the number of cases favourable to the event, whose probability we are seeking. ”

“ Now, as the whole utility of probability is to insure us in the long run, and as that assurance depends, not merely on the value of the chance, but also on the accuracy of the evaluation, it follows that we ought not to have the same feeling of belief in reference to all events of which the chance is even. ”

“ Do you think that such a thing as chance exists? Rather an explosive sentence to start a letter with; but pray cast your mind back over your own life, and tell me if you think that we really are the sports of chance. You know how often the turning down this street or that, the accepting or rejecting of an invitation, may deflect the whole current of our lives into some other channel. Are we mere leaves, fluttered hither and thither by the wind, or are we rather, with every conviction that we are free agents, carried steadily along to a definite and pre-determined end? ”

“ The problem of chance can be only approximately explained when all conceivable chance-happenings of a given discipline are brought together and their number reduced by careful search for definite laws. Besides, the problem demands the knowledge of an extremely rich casuistry, by means of which, on the one hand, to bring together the manifoldness of chance events, and on the other to discover order. ”

“ Still others occur frequently and to many different persons; but no individual can tell when and how they will occur to him. A general average of chances in different lines of business causes some to be called safe, others extra-hazardous. Chance has its favorable as well as its unfavorable aspects. ”

“ Chance is a confession of ignorance. If man possessed infinite knowledge, the term chance would have no place in his vocabulary.
The games of chance are money making schemes supported by the gambling fraternity. ”