HOYLE'S GAMES.

PART I.

GAMES OF CHANCE.

INTRODUCTION.

NOTHING, perhaps, throws out in more odious relief the weakness of human nature, or exhibits more forcibly its tendency to superstition, than Games of Chance. How often do we see gamesters who attribute their ill luck to the persons who may accidentally approach them, or to other circumstances equally fortuitous! Some make it a rule always to play with the winning cards, from the conviction that a certain good luck is inherent in them; others, on the contrary, attach themselves with obstinate pertinacity to the losing ones, impressed with the idea, that as they have lost several times, it is less probable that they will lose again; as if the past could have any influence on the future. To such an extent are these superstitious ideas carried, that many players actually refuse to shuffle the cards unless in certain situations, and who think that they will infallibly lose by the slightest deviation from these absurd

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rules. In fact, the major part seek for their advantage where it is not to be found, or neglect it altogether.

This observation will, perhaps, apply to the conduct of man in every action of his life in which chance has any share. He is governed by similar prejudices and errors, founded upon the erroneous though almost universal belief, that the distribution of good and evil, and in general of all the events of this world, are due to a fatal power which acts without order or rule; and thus he imagines it wiser to abandon himself to this blind divinity, whom he calls Fortune, rather than to force her to become favourable to him by following those rules of prudence which appear to him imaginary.

It is, therefore, not only of importance to gamesters, but to men in general, to know that chance has rules which may be discovered, and that by neglecting to make themselves masters of those rules, they are every hour committing faults, the disastrous consequences of which may with more justice be imputed to themselves than to the caprices of that destiny whom unjustly they accuse.

Impressed with this conviction, I am confident that a short analysis of the doctrine of chances will prove interesting even to those who have the least taste for abstract study. We all naturally like to see clearly into what we are about, independent of every interested motive; and a man will certainly play with more pleasure when at every variation of his game he can calculate the chances for and against him; for this knowledge will not only render him more tranquil as to the result, but will also teach him how ridiculous are the complaints in which gamesters indulge on the most trivial occasions.

If the exact knowledge of the chances of play

is not sufficient to enable a player to win, it will at least, in critical cases, serve him as an infallible rule of conduct, and will enable him to calculate the chances of those ruinous games which are every day becoming more generally introduced into this country. Moreover, it will teach him to despise the ignorant presumption of those quacks who affect to be able to turn the wheel of fortune at pleasure, and the besotted credulity of those who think that for a few pence they can purchase a system by which they may win thousands. Conduct is fate, and prudent man will leave as little to chance as possible. We cannot, it is true, draw aside the veil which hangs over futurity; but in games of chance, and likewise in many other events of life, we can calculate with mathematical precision the probability of a particular event.

Some of the greatest mathematicians have devoted much time and attention to this subject; and the result of their scientific labours ought to terrify the most reckless gamester, by laying open to him the infinite and almost certain dangers to which he exposes his fortune and his happiness, when he engages himself in that labyrinth of chances which sooner or later must overwhelm him. I have, therefore, in the present edition, given a succinct analysis of the doctrine of chances, convinced that so far from having a tendency to promote play, it will be found the surest antidote against the glittering temptations of that demon which, above all others, is the most fatal to human happiness.

THE object of the calculation of probabilities is to discover facts, the reality of which is unknown

to us.

The probability of an event may be said to be more or less, according to the number of chances by which it may happen, compared with the whole number of chances by which it may either happen or fail.

If we, therefore, constitute a fraction, whereof the numerator be the number of chances whereby an event may happen, and the denominator the number of all the chances whereby it may happen or fail, that fraction will be the proper designation of the probability of the event. Thus, if an event has 3 chances to happen and 2 to fail, the fraction will fitly represent the probability of its happening, and may be said to be the measure of it.

The same may be said of the probability of failing, which will likewise be measured by a fraction, whose numerator is the number of chances by which it may fail, and the denominator the whole number of chances for and against, as .

Thus the number of the two fractions representing the probability of the advent or not of an event is equal to unity. When one, therefore, is given, the other may be found by subtraction.

The expectation, that is, the sum which the person who has a chance for the advent of an event is entitled to, if he resign his chance to another, is always the product of the fraction representing the probability multiplied into the sum expected.

Thus, if I have 3 chances in 5 to obtain 100%.,