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Rage on, and make thee equally unblefs'd,
In what thou want'ft, and what thou haft poffeft;
In vain thou hop'ft for blifs on this poor clod,
Return, and feek thy father, and thy God:
Yet think not to regain thy native sky,
Born on the wings of vain philofophy;
Myfterious paffage! hid from human eyes;
Soaring you'll fink, and finking you will rife:
Let humble thoughts thy wary footsteps guide,
Regain by meekness what you loft by pride.

HUYGENS de Ratiociniis in Ludo Alea: Tranflated into English by Dr. ARBUTHNOT.

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The PRE FAC E.

Tis thought as necessary to write a Preface before a Book, as it is judged civil, when you invite a Friend to Dinner, to proffer him a Glafs of Hock be. forehand for a Whet: And this being maim'd enough for want of a Dedication, I am refolved it shall not want an Epistle to the Reader too. I shall not take upon me to determine, whether it is lawful to play at Dice or not, leaving that to be difputed betwixt the Fanatick Parfons and the Sharpers; I am fure it is lawful to deal with Dice as with other Epidemic Difempers; and I am confident that the writing a Book about it, will contribute as little towards its Encouragement, as Fluxing and Precipitates do to Whoring.

It will be to little purpofe to tell my Reader, of how great Antiquity the playing at Dice is, I will only let him know, that by the Alex Ludus, the Antients comprehended all Games, which were fubjected to the Determina

Determination of mere Chance; this fort of Gaming was ftrictly forbid by the Emperor Juftinian, Cod. Lib. 3. Tit. 43. under very fevere Penalties; and Phocius Nomocan. Tit. 9. Cap. 27. acquaints us, that the Ufe of this was altogether denied the Clergy of that time. Seneca fays very well, Aleator quantò in arte eft melior, tantò eft nequior; That by how much the one is more skilful in Games, by fo much he is the more culpable; or we may say of this, as an ingenious Man fays of Dancing, that to be extraordin ary good at it, is to be excellent in a Fault; therefore I hope no body will imagine I had fo mean a Defign in this, as to teach the Art of Playing at Dice.

A great part of this Difcourfe is a Tranflation from Monf. Huygens's Treatife, De ratiociniis in ludo Alex; one, who in his Improvements of Philofophy, has but, one Superior, and I think few or no› Equals. The whole I undertook for my own Divers tifement, next to the Satisfaction of fome Friends, who would now and then be wrangling about the Proportions of Hazards in fome Cafes that are here decided.: All it required was a few fpare Hours, and but little Work for the Brain; my Defign in publishing it, was to make it of more general Use, and perhaps per fuade a raw Squire, by it, to keep his Money in his Pocket; and if, upon this account, I fhould incur the Clamours of the Sharpers, I do not much regard it, fince they are a fort of People the World is not bound to provide for.

You will find here a verydplain and eafy Method of the Calculation of the Hazars of Game, which a Man may understand, without knowing the Quadratures of Curves, the Doctrine of Series's, or the Laws of Concentripetation of Bodies, or the Periods of the Satellites of Jupiter; yea, without fo much as the Elements of Euclid. There is nothing required for the emp rehending the whole, but common Sense and prac

tical Arithmetick; faving a few Touches of Algebra, as in the first Three Propofitions, where the Reader, without fufpicion of Popery, may make use of a strang implicit Faith; tho' I must confefs, it does not much recommend itself to me in thefe Purposes; for I had rather he would enquire, and I believe he will find the Speculation not unpleasant.

Every Man's Succefs in any Affair is proportional to his Conduct and Fortune. Fortune (in the fenfe of maji People) fignifies an Event which depends onChance, agreeing with my Wish; and Misfortune fignifies fuch an one, whofe immediate Caufes I don't know, and confequently can neither foretel nor produce it (for it is no Herefy to believe, that Providence fuffers ordinary matters to run in the Channel of fecond Causes). Now I fuppofe, that all a wife Man can do in fuch a Cafe is, to lay his Bufinefs on fuch Events, as have the most powerful fecond Caufes, and this is true both in the great Events of the World, and in ordinary Games. It is impoffible for a Die, with fuch de termined force and direction which makes it fall on fuch a determined fide, only I don't know the force and direction which makes it fall on fuch a determin'd fide, and therefore I call that Chance, which: is nothing but want of Art; that only which is left to me, is to wager where there are the greatest number of Chances, and confequently the greatest probability to gain; and the whole Art of Gaming, where there is any thing of Hazard, will be reduced to this at last, viz. in dubious Cafes to calculate on which fide there are most Chances; and tho' this can't be done in the midst of Game precifely to an Unit, yet a Man who knows the Principles, may make fuch a Con jecture, as will be a fufficient direction to him; and tho it is poffible if there are any Chances against him at all, that he may lofe, yet when he chufeth the fafeft

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fide, he may part with his Money with more content (if · there can be any at all) in fuch a Cafe.

I will not debate, whether one may engage another in a disadvantageous Wager. Games may be fuppos'd to be a tryal of Wit as well as Fortune, and every Man, when he enters the Lifts with another, unlefs out of Complaifance, takes it for granted, his Fortune and Judgment are, at least, equal to thofe of bis Play-Fellows; but this I am fure of, that falfe Dice, Tricks of Leger-de-main, &c. are inexcufable, for the question in Gaming is not,Who is thebest Fugler? The Reader may bere obferve the Force of Numbers, which can be fuccessfully applied, even to thofe things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc'd to a Mathematical Rea-foning; and when they cannot, it's a fign the Knowledge of them is very small and confus'd; and where a› Mathematical reasoning can be had, it's as great folly to make ufe of any other, as to grope for a thing in the Dark, when you have a Candle Standing by you. I believe the Calculation of the Quantity of Probability might be improved to a very ufeful and pleasant Speculation, and applied to a great many Events which are accidental, befides thofe of Games; only thefe Cafes would be infinitely more confus'd, as depending on Chances which the most part of Men are ignorant of; and as I have hinted already, all the Politicks in the World, are nothing else but a kind of Analysis of the Quantity of Probability in cafual Events, and a good Politician fignifies no more, but one who is dextrous at fuch Calculations; only the Principles which are made ufe of in the Solution of fuch Problems, can't be ftudied in a Clefet, but acquired by the Obfervation of Mankind.

There is likewife a Calculation of the Quantity of Probability founded on Experience, to be made use of

in Wagers about any thing; it is odds if a Woman is with Child, but it fhall be a Boy; and if you would know the juft odds, you must confider the Proportion in the Bills that the Males bear to the Females: The. Yearly Bills of Mortality are obferved to bear fuch Proportion to the live People as 1 to 30, or 26; therefore it is an even Wager, that one of thirteen, dies within a Year (which may be a good Reason, tho' not the true, of that foolish piece of Superftition,) because, at this rate, if 1 out of 26 dies, you are no lofer. It is but 1 to 18 if you meet a Parfon in the Street, that be proves to be a Non-Juror, because there is but of 36 that are fuch. It is hardly 1 to 10, that a Woman of Twenty Years old has her Maiden-head, and almost the fame Wager, that a Town-Spark of that Age has not been clap'd. I think a Man might ven- . ture fome adds, that 100 of the Gens d'arms beats an equal Number of Dutch Troopers; and that an English Regiment ftands its ground as long as another, making Experience our Guide in all these Cafes and athers of the like Nature.

But there are no cafual Events, which are fo easily fubjected to Numbers, as thofe of Games; and I believe, there the Speculation might be improved fo far, as to bring in the Doctrine of the Series's and Logarithms. Since Gaming is become a Trade, I think it fit the Adventurers fhould be upon the Square; and therefore in the Contrivance of Games there ought to be. a friet Calculation made ufe of, that they mayn't put one Party in more probability to gain than another; and likewife, if a Man has a confiderable Venture; he ought to be allowed to withdraw his Money when be pleafes, paying according to the Circumftances he is then in: And it were easy in moft Games to make Tables, by inspection of which, a Man might know what he was either to pay or receive, in any Circum

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