In the following combinations there are but 1560, where there might be 76076; and if this latter number were printed and sold, some one must hold the three first drawn numbers, every ticket-holder having one chance out of 76076 of drawing the capital prize. But, in this combination, if a man were to purchase the whole of the tickets, being 1560, there would still be 49 chances against his holding the three first numbers, to one for it. As there are no two tickets holding the same three numbers, of course but one can hold the three first, which is the prize.

By a little investigation, any one may discover that his chance for drawing a prize, even of a trifling amount, is extremely small. By the following method any one may ascertain the number of combinations which any given number will produce, as in the present case, 78 × 77 × 76 = 456456 ÷ 6 = 76076, the number of combinations of three numbers each; the 78 multiplied by 77, and the product by 76, and that product divided by 6 gives the number of combinations of three numbers each, which the numbers from 1 to 78 will produce, no two combinations containing the same three numbers.

Lottery-dealers are aware of the great odds against the buyers, and are very cautious in keeping all the secrets of a fraud to themselves, by which they are robbing the public continually. But it shall not be the fault of the writer of these pages if their swindling machinations are longer concealed from the community. Thousands upon thousands of dollars are expended annually in lottery tickets in this country; and how very seldom is it that you hear of a capital prize having been drawn! If there should chance to be a prize of any magnitude awarded to a ticket-holder, it is trumpeted from one end of the Union to the other, by those most interested in lottery speculations, stimulating others to try their luck, and by that means making their very losses minister to their gain; for, in all likelihood, months and years may elapse before another large prize will be drawn from the same lottery.

It will be seen by the lottery combinations we present, how infinitely disproportionate are the chances in this species of gambling—how vastly the odds bear against the purchaser of tickets, and what mischievous results must of necessity spring from a vile system of frauds, perpetrated, as it is, by the sanction of law, and the tolerance of custom.

All the combinations used in this lottery have been given, as also the number that might be made; and, of course, the less the dealer in lotteries makes, the greater the chance in his favor, and the less in favor of the buyer. The figures heading the classes of combinations, on each page, are class-numbers, and those below the first figures, and immediately above the columns, are placed there to indicate the number of packages.

Here ends the Thirty Packages of Quarters.

The above are specimens of patterns of playing cards, that the reader may rely upon the gambler's knowing by their back as well as the generality of amusement players know by their face. The same may be said of all the patterns spoken of and presented to the view of the reader on another page of this work.

[This plate represents a lottery ticket with the numbers placed upon it. The numbers seen upon its face are of the same order as those found upon every ticket when sold, and are used to designate one ticket from another, and by comparing them with the numbers at the head of any of those packages of combinations, on another page, you will see the manner in which they are arranged, and the great advantage in favor of the managers.]

FALLACY OF LOTTERIES AS A MEANS OF REVENUE.

We are indebted for the following exposition to our moral friend, Capt. John Maginn, of New York city.

"Although they may produce, by the various deceptive allurements which they hold forth, a temporary influx into the treasury of the state, yet the prostration of industry, the formation of idle habits, intemperance and various other vices, have invariably been the consequences wherever they have been introduced. No farther evidence of this position is requisite than the fact that in England, where many of the common necessaries of life are heavily taxed, it has been satisfactorily ascertained from observation, that for several days preceding the drawing of a lottery, the consumption of such articles was very materially diminished. It is moreover equally true, that a very small proportion of the tax actually paid, through the purchase of lottery tickets, is available to the state: by far the greater part being absorbed in the expenses, profits, &c., of managers and venders."

INSURING NUMBERS, OR POLICY DEALING.

There being on the day of drawing a certain number of tickets in the wheel, out of which a particular number of them are to be drawn, it follows that there are so many chances to one against a given number being drawn as the number which are to be drawn are contained in the entire number of tickets in the wheel. To illustrate this practically, suppose you would insure the payment of $100 upon the event of a certain number being drawn from the lottery wheel to-day; suppose it is a 78 number lottery, and that 12 ballots are to be drawn; the chance then is evidently 78/12, or 6.5 to 1 that you lose: accordingly, in order to make the chances equal, you must pay 100/6.5, or $15.38, for insurance: if therefore the insurer should ask $32, there would be about $16 fraud: in other words, you would have to contend against about 100 per cent. The only inducement for the insurer to pursue this vile practice, in defiance of constitutions and laws, is a liberal per centage. This varies from 30 to 70, and even 125 per cent. Under circumstances like these, when the chances of gain are obviously so remote, it would seem incredible that any one endowed with even ordinary sagacity could be so deluded—so desperate—as to adventure; though, sad to relate, hundreds and hundreds in this city daily spend their little all in effecting insurance on numbers, and that, too, at the sacrifice of the common necessaries of life.

Another system of insurance, which we will proceed to analyze, is effected by what is termed a station number. The adventurer selects a number, and declares that it will come out the first or second drawn, or in some other place, for which he pays six cents, and if the number is drawn in the order indicated, he is to receive $2.50. To illustrate this, suppose you select a certain number, which you declare will be the third drawn; suppose also that it is a 78 number lottery, and that there are 12 drawn ballots. In this case there are evidently 78/12 = 6.5 chances to 1 against the selected number being drawn. It is also plain that should it be a drawn number, there are 12 chances to 1 against it being drawn in any particular order; wherefore it follows, that there are 6.5x12 = 78 chances to 1 against the selected number being the third or any other particular drawn number. Accordingly, to equalize the chances, in case of winning you should receive 78x6 = $4.68; hence, under these circumstances the insurer gains $2.18, which is nearly 100 per cent. Again, suppose it is a 98 number lottery, and that you pay 25 cents: here we have 98x25 = $24.50, the sum you ought to receive in case of winning, instead of which you only receive 25/6x2.5 = $10.626; hence the insurer gains $13.975, or more than 125 per cent.

PROF. GODDARD ON LOTTERIES.

We give below a very able memorial, from the pen of Prof. Goddard, of Brown University, to the Legislature of Rhode Island.

The undersigned, citizens of Rhode Island, have long regarded the lottery system with unqualified reprobation. They believe it to be a multiform social evil, which is obnoxious to the severest reprehension of the moralist, and which it is the duty of the legislator, in all cases, to visit with the most effective prohibitory sanctions. Entertaining these convictions, the undersigned memorialists cannot withhold them from the Hon. General Assembly of Rhode Island. They invoke the General Assembly to exercise their constitutional powers, promptly and decisively, for the correction of a long-continued, and wide-spread, and pestilent social evil. They ask them, most respectfully and earnestly, to withdraw, as soon as may be, all legislative sanction of the lottery system, and to save Rhode Island from the enduring reproach of being among the last States to abandon that system. The memorialists beg leave to disclaim, in this matter, all personal or political considerations. They are seeking neither to help nor to hurt any political party. They contemplate no aggression upon the rights or the character of individuals. They are engaged in no impracticable scheme of moral reform. They have no fondness for popular agitation. They are what they profess to be, citizens of Rhode Island, and it is only in the quality of citizens of Rhode Island, that they now ask the General Assembly to resort to the most operative penal enactments, for the entire suppression of a system which exists, and which can exist only to disgrace the character of the State, and to injure both the morals and the interests of the people. The memorialists are persuaded that a commanding majority of the citizens of every political party entertain sentiments of decided hostility to all lotteries. In praying, therefore, for legislative interposition, they feel that they are not in advance of public opinion, that they are not urging the General Assembly to anticipate public opinion, but only to imbody it; to accelerate its salutary impulses, and to augment its healthful vigour. The constitutional power of the legislature to interfere in the premises being undisputed, the memorialists beg leave to submit, for consideration, a few only of the many reasons which have forced upon their minds the conclusion—that Rhode Island should lose no time and spare no effort in extirpating the lottery system:—a system which has already worked extensive evil within her borders; which is repugnant to a cultivated moral sense; and which has been branded, both as illegal and immoral, by some of the most enlightened governments upon earth. In this connection, it should be stated, that England, and, it is believed, France likewise, have abandoned the lottery system. Some of the most populous and influential States in this Confederacy have abandoned it. Massachusetts has abandoned it; Pennsylvania has abandoned it; New York has abandoned it. Nay more, so hostile were the people of the latter State to the lottery system, that in revising its Constitution a few years since, they adopted a provision which prohibits the Legislature from ever making a lottery grant. These examples are adduced to show the progress of an enlightened public sentiment upon this subject, and to exhibit the grateful spectacle of governments, differently constituted, exercising their powers for the best interests of the people. The evils which the lottery system creates, and the evils which it exasperates, are so various and complicated, that the undersigned memorialists cannot attempt an enumeration. They are so revolting as to furnish no motive for rhetorical exaggeration. A few only of these evils the undersigned memorialists will now proceed to mention.

1. Lotteries are liable to many of the strongest objections which can be alleged against gambling. They have thus far escaped, it is true, the infamy of gambling, but they can plead no exemption from its malignant consequences. Like gamblers, they are hostile—not to say fatal—to all composure of thought and sobriety of conduct. Like gambling, they inflame the imagination of their victims and their dupes, with visions of ease, and affluence, and pleasure, destined never to be realized. Like gambling, they seduce men, especially the credulous and the unthinking, from the pursuits of regular industry, into the vortex of wild adventure and exasperated passions. Like gambling, they ultimately create a necessity for constant vicious excitement. Like gambling, they often lead to poverty and despair, to insanity and to suicide. Like gambling, they furnish strong temptations to fraud, and theft, and drunkenness. Like gambling, they work, in but too many cases, a permanent depravation of all moral principle and all moral habits. This fearful parallel might easily be extended. The picture here presented of the evils of lotteries, however fearful it may seem, is not overdrawn. This picture will be owned as just, by many a bereaved widow and by many a forsaken wife, who trace all their woes to the temptation into which this respectable and legalized species of gambling had betrayed once affectionate husbands. It will be owned as just by many a child, who has been doomed perchance to a heritage of ignorance and poverty, by a father, for whose weak virtue the potent fascinations of the lottery were found too strong. In many respects, the lottery system may be deemed even more pernicious than ordinary gambling. It spreads a more accomplished snare; it is less offensive to decorum; it is less alarming to consciences which have not lost all sensitiveness; it numbers among its participants multitudes of those who ought to blush and to tremble for thus hazarding their own virtue, and for thus corrupting the virtues of others; it draws within its charmed circle men and women who fill up every gradation of age, and character, and fortune.

2. The lottery system, as at present constituted, presents the strongest temptations to fraud on the part of all those who are concerned either in the drawing of lotteries or in the sale of tickets. It is not known that fraud has in any case been perpetrated, though fraud is suspected. If perpetrated, it would be no easy matter to detect it. The ignorant and the credulous men and women, who seek to better their fortunes by gambling in lottery tickets, know nothing of those mystical combinations of numbers, on which their fate is suspended. Utter strangers as they are to all the "business transactions" of the lottery system, if cheated at all, they are cheated without remedy.

3. The lottery system operates as a most oppressive tax upon the community. This tax is paid, not by the rich and luxurious—but it is paid mainly by those who are struggling for independence, and by those who earn their bread by the sweat of their brow—by the servants in our kitchens—by clerks and apprentices, and day-labourers; by mechanics and traders; by the men and women who work in our factories; and in too many instances, it is to be feared, by our hardy yeomanry, who, impatient of the slow profits of agriculture, vainly expect from the chances of the lottery that which is never denied to the efforts of industry. The amount of pauperism and crime, of mental agitation and perchance of mental insanity, which the lottery system must create among these numerous classes, it would not be easy to calculate.

4. Lotteries are the parent of much of the pauperism which is to be found in this young, and free, and prosperous land. It entails poverty upon multitudes directly, by exhausting their limited means in abortive experiments to get rich by "high prizes"—and, yet more, by withdrawing multitudes from a dependence on labour, and accustoming them to hope miracles of good fortune from chance. After repeated disappointments, they discover, when it is too late to profit from the discovery, how sadly they have been duped, and how recklessly they have abandoned their confidence in themselves, and in that gracious Being who never forsakes those who put their trust in him. They sink into despondency, and, seeking to forget themselves, they bring upon their faculties the brutal stupor of intoxication, or they exhilarate them by its delirious gayety. Suicide is often the fearful issue. Dupin ascribes a hundred cases of suicide annually to the lottery system in the single city of Paris. Many years ago a lottery scheme, displaying splendid prizes, was formed in London. Adventures to a very large amount was the consequence, and the night of the drawing was signalized by fifty cases of suicide!

5. Success in lotteries is hardly less fatal than failure. The fortunate adventurer is never satisfied. He ventures again and again, till ruin overtakes him. After all the tempting promises of wealth, which are made by those concerned in this iniquitous system, how very few, except managers of lotteries and venders of lottery tickets, has it ever made rich! and well may it be asked, whom has it ever made more diligent in business, more contented, and respectable, and happy?

6. Lotteries, it is believed, are rendered especially mischievous in this country by the nature of our institutions, and by the spirit of the times. Here, the path to eminence being open to every one—but too many are morbidly anxious to improve their condition; and by means, too, which in the wisdom of Providence were never intended to command success. A mad desire for wealth pervades all classes—it feeds all minds with fantastic hope; it is hostile to all patient toil, and legitimate enterprise, and economical expenditure. It generates a spirit of reckless speculation; it corrupts the simplicity of our tastes; and, what is yet worse, it impairs, not unfrequently, in reference to the transactions of business, the obligations of common honesty. Upon these elements of our social condition and character, the lottery system operates with malignant efficacy.

The undersigned memorialists are far from thinking that, in the preceding remarks, they have exhausted the argument against the lottery system. They have dwelt, in general terms, upon only some of its more prominent evils. They do not allow themselves to believe that, aside from the ranks of those who have a direct personal interest in this system, a man of character could be found in Rhode Island to defend it. The memorialists deem lotteries to be in Rhode Island a paramount social evil. They entreat the General Assembly to survey this evil in all its phases, and then to apply the remedy. The interposition which is now asked at the hands of the Legislature has been delayed too long, either for the interests or for the character of the state. It is time that we protected our interests, and retrieved our character. It is time that the lottery had ceased to be the "domestic institution" of Rhode Island. It is time that we abandoned, and abandoned for ever, the policy of supporting schools, and building churches, with the wages of iniquity. The memorialists are aware that the General Assembly have made lottery grants, which have not yet expired. They seek not in any way to interfere with those grants; but in concluding this expression of their views, they cannot avoid repeating their earnest entreaty that the legislature would come up without unnecessary delay to the great work of reforming an abuse, which no length of time, or patronage of numbers, or policy of state, should be permitted to shelter for another hour.

EXTRACTS from a Report to the Society for the Prevention of Pauperism in the city of New York.

"It is not possible to estimate the sum that may have been drawn from the people by lottery devices. Nor is it possible to estimate the number of poor people that have engaged in lottery gambling. We have been told, that more than two hundred of these deluded people have been seen early in the mornings at the lottery offices, pressing to know their fate. There might be seen the anxiety, the disappointment, and mortification, of unfortunate beings, who had lost their all!

"Thus we see that this demoralizing contagion has spread its destructive influence over the most indigent and ignorant of the community. The injurious system of lotteries opens a wide door to gambling, fraud and imposition; of which the speculating, dishonest, idle, profligate and crafty avail themselves, and deceive the innocent and ignorant.

"If we place this subject in a pecuniary view as it relates to the public funds, the mischievous effect is more obvious. From an estimate, made by a gentleman of accurate calculation, it appears, that the expense, or the amount drawn from the people, to raise by lottery the net sum of 30,000 dollars, amounts to $170,500, including the expense of the managers and their attendants, the clerks and attendants of the lottery offices, the expense of time lost by poor people, and the amount paid the proprietors of lottery offices. This enormous sum is paid for the collection of only 30,000 dollars. This is, therefore, not only the most expensive, but also the most demoralizing method that was ever devised to tax the people.

"Upon the whole view of the subject, your committee are decidedly of opinion, that lotteries are the most injurious kind of taxation, and the very worst species of Gambling. By their insidious and fascinating influence on the public mind, their baleful effect is extended, and their mischievous consequences are most felt by the indigent and ignorant, who are seduced, deceived, and cheated out of their money, when their families are often suffering for the necessaries of life. Their principles are vitiated by lotteries, they are deceived by vain and delusive expectation, and are led into habits of idleness and vice, which produce innumerable evils, and, ultimately, end in misery and pauperism."

LOTTERY COMBINATIONS.

Rule.—Take a series of numbers, the first term of which is equal to the number of things out of which the combinations are to be made, and decreasing by 1, till the number of terms is equal to the number of things to be taken at a time, and the product of all the terms.

Then take the natural series 1, 2, 3, &c., up to the number of things to be taken at a time, and find the product of all the terms of this series.

Divide the former product by the latter, and the quotient will be the answer.

How many combinations of 3 numbers can be taken out of 78 numbers?