The laws of luck E-Book

Richard A. Proctor

• Herausgeber: Books on Demand
• Kategorie: Lebensstil
• Sprache: Englisch
• Veröffentlichungsjahr: 2019

Seitenzahl: 342

Beschreibung

To the student of science, accustomed to recognise the operation of law in all phenomena, even though the nature of the law and the manner of its operation may be unknown, there is something strange in the prevalent belief in luck. In the operations of nature and in the actions of men, in commercial transactions and in chance games, the great majority of men recognise the prevalence of something outside law-the good fortune or the bad fortune of men or of nations, the luckiness or unluckiness of special times and seasons-in fine (though they would hardly admit as much in words), the influence of something extranatural if not supernatural. This is true alike of great things and of small; of matters having a certain dignity, real or apparent, and of matters which seem utterly contemptible. Napoleon announcing that a certain star (as he supposed) seen in full daylight was his star and indicated at the moment the ascendency of his fortune, or William the Conqueror proclaiming, as he rose with hands full of earth from his accidental fall on the Sussex shore, that he was destined by fate to seize England, may not seem comparable with a gambler who says that he shall win because he is in the vein, or with a player at whist who rejoices that the cards he and his partner use are of a particular colour, or expects a change from bad to good luck because he has turned his chair round thrice; but one and all are alike absurd in the eyes of the student of science, who sees law, and not luck, in all things that happen.

Leseprobe

The laws of luck

The laws of luckLaws of LuckGamblers’ Fallacies Fair and Unfair WagersBetting on RacesLotteriesGambling in SharesFallacies and CoincidencesNotes on PokerMartingales; or, Sure(?) Gambling SystemsCopyright

The laws of luck

Richard A. Proctor

Laws of Luck

To the student of science, accustomed to recognise the operation of law in all phe-nomena, even though the nature of the law and the manner of its operation may beunknown, there is something strange in the prevalent belief in luck. In the operationsof nature and in the actions of men, in commercial transactions and in chance games,the great majority of men recognise the prevalence of something outside law—thegood fortune or the bad fortune of men or of nations, the luckiness or unluckinessof special times and seasons—in fine (though they would hardly admit as much inwords), the influence of something extranatural if not supernatural. [For to the manof science, in his work as student of nature, the word ‘natural’ implies the action oflaw, and the occurrence of aught depending on what men mean by luck would besimply the occurrence of something supernatural.]This is true alike of great thingsand of small; of matters having a certain dignity, real or apparent, and of matterswhich seem utterly contemptible.Napoleon announcing that a certain star (as hesupposed) seen in full daylight washisstar and indicated at the moment the ascen-dency of his fortune, or William the Conqueror proclaiming, as he rose with handsfull of earth from his accidental fall on the Sussex shore, that he was destined byfate to seize England, may not seem comparable with a gambler who says that heshall win because he is in the vein, or with a player at whist who rejoices that thecards he and his partner use are of a particular colour, or expects a change from badto good luck because he has turned his chair round thrice; but one and all are alikeabsurd in the eyes of the student of science, who sees law, and not luck, in all thingsthat happen. He knows that Napoleon’s imagined star was the planet Venus, boundto be where Napoleon and his officers saw it by laws which it had followed for pastmillions of years, and will doubtless follow for millions of years to come.He knowsthat William fell (if by accident at all) because of certain natural conditions affect-ing him physiologically (probably he was excited and over anxious) and physically,not by any influence affecting him extranaturally.But he sees equally well that thegambler’s superstitions about ‘the vein,’ the ‘maturity of the chances,’ about luckand about change of luck, relate to matters which are not only subject to law, butmay be dealt with by processes of calculation. He recognises even in men’s belief inluck the action of law, and in the use which clever men like Napoleon and Williamhave made of this false faith of men in luck, a natural result of cerebral development,of inherited qualities, and of the system of training which such credulous folk havepassed through.Let us consider, however, the general idea which most men have respecting whatthey call luck.We shall find that what they regard as affording clear evidence thatthere is such a thing as luck is in reality the result of law.Nay, they adopt such acombination of ideas about events which seem fortuitous that the kind of evidencethey obtain must have been obtained, let events fall as they may.Let us consider the ideas of men about luck in gambling, as typifying in small theideas of nearly all men about luck in life.In the first place, gamblers recognise some men as always lucky. I do not mean, ofcourse, that they suppose some men always win, but that some men never have spellsof bad luck.They arealways‘in the vein,’ to use the phraseology of gamblers likeSteinmetz and others, who imagine that they have reduced their wild and wanderingnotions about luck into a science.Next, gamblers recognise those who start on a gambling career with singular goodluck, retaining that luck long enough to learn to trust in it confidently, and thenlosing it once for all, remaining thereafter constantly unlucky.Thirdly, gamblers regard the great bulk of their community as men of varyingluck—sometimes in the ‘vein’ sometimes not—men who, if they are to be successful,must, according to the superstitions of the gambling world, be most careful to watchthe progress of events. These, according to Steinmetz, the great authority on all suchquestions (probably because of the earnestness of his belief in gambling superstitions),may gamble or not, according as they are ready or not to obey the dictates of gamblingprudence. When they are in the vein they should gamble steadily on; but so soon as ‘the maturity of the chances’ brings with it a change of luck they must withdraw. Ifthey will not do this they are likely to join the crew of the unlucky.Fourthly, there are those, according to the ideas of gamblers, who are pursued byconstant ill-luck. They are never ‘in the vein.’ If they win during the first half of anevening, they lose more during the latter half. But usually they lose all the time.Fifthly, gamblers recognise a class who, having begun unfortunately, have had achange of luck later, and have become members of the lucky fraternity. This changethey usually ascribe to some action or event which, to the less brilliant imaginationsof outsiders, would seem to have nothing whatever to do with the gambler’s luck.For instance, the luck changed when the man married—his wife being a shrew; orbecause he took to wearing white waistcoats; or because so-and-so, who had been asort of evil genius to the unlucky man, had gone abroad or died; or for some equallypreposterous reason.Then there are special classes of lucky or unlucky men, or special peculiarities ofluck, believed in by individual gamblers, but not generally recognised.Thus there are some who believe that they are lucky on certain days of the week,and unlucky on certain other days.The skilful whist-player who, under the name ‘Pembridge,’ deplores the rise of the system of signals in whist play, believes that heis lucky for a spell of five years, unlucky for the next five years, and so on continually.Bulwer Lytton believed that he always lost at whist when a certain man was at thesame table, or in the same room, or even in the same house.And there are othercases equally absurd.Now, at the outset, it is to be remarked that, if any large number of persons set towork at any form of gambling—card play, racing, or whatever else it may be—theirfortunesmustbe such, let the individual members of the company be whom theymay, that they will be divisible into such sets as are indicated above. If the numbersare only large enough, not one of those classes, not even the special classes mentionedat the last, can fail to be represented.Consider, for instance, the following simple illustrative case:—Suppose a large number of persons—say, for instance, twenty millions—engage insome game depending wholly on chance, two persons taking part in each game, so thatthere are ten million contests.Now, it is obvious that, whether the chances in eachcontest are exactly equal or not, exactly ten millions of the twenty millions of personswill rise up winners and as many will rise up losers, the game being understood tobe of such a kind that one player or the other must win. So far, then, as the resultsof that first set of contests are concerned, there will be ten million persons who willconsider themselves to be in luck.Now, let the same twenty millions of persons engage a second time in the sametwo-handed game, the pairs of players being not the same as at the first encounter,but distributed as chance may direct. Then there will be ten millions of winners andten millions of losers.Again, if we consider the fortunes of the ten million winnerson the first night, we see that, since the chance which, each one of these has of beingagain a winner is equal to the chance he has of losing,aboutone-half of the winningten millions of the first night will be winners on the second night too.Nor shall wededuce a wrong general result if, for convenience, we sayexactlyone-half; so long aswe are dealing with very large numbers we know that this result must be near thetruth, and in chance problems of this sort we require (and can expect) no more. Onthis assumption, there are at the end of the second contest five millions who havewon in both encounters, and five millions who have won in the first and lost in thesecond.The other ten millions, who lost in the first encounter, may similarly bedivided into five millions who lost also in the second, and as many who won in thesecond.Thus, at the end of the second encounter, there are five millions of playerswho deem themselves lucky, as they have won twice and not lost at all; as many whodeem themselves unlucky, having lost in both encounters; while ten millions, or halfthe original number, have no reason to regard themselves as either lucky or unlucky,having won and lost in equal degree.Extending our investigation to a third contest,we find that 2,500,000 will beconfirmed in their opinion that they are very lucky,since they will have won inall three encounters; while as many will have lost in all three, and begin to regardthemselves, and to be regarded by their fellow-gamblers, as hopelessly unlucky.Ofthe remaining fifteen millions of players, it will be found that 7,500,000 will have wontwice and lost once, while as many will have lost twice and won once.(There willbe 2,500,000 who won the first two games and lost the third, as many who lost thefirst two and won the third, as many who won the first, lost the second, and won thethird, and so on through the six possible results for these fifteen millions who hadmixed luck.) Half of the fifteen millions will deem themselves rather lucky, while theother half will deem themselves rather unlucky.None, of course, can have had evenluck, since an odd number of games has been played.Our 20,000,000 players enter on a fourth series of encounters.At its close thereare found to be 1,250,000 very lucky players, who have won in all four encounters,and as many unlucky ones who have lost in all four. Of the 2,500,000 players who hadwon in three encounters, one-half lose in the fourth; they had been deemed lucky, butnow their luck has changed.So with the 2,500,000 who had been thus far unlucky:one-half of them win on the fourth trial.We have then 1,250,000 winners of threegames out of four, and 1,250,000 losers of three games out of four. Of the 7,500,000who had won two and lost one, one-half, or 3,750,000, win another game, and must beadded to the 1,250,000 just mentioned, making three million winners of three gamesout of four.The other half lose the fourth game, giving us 3,750,000 who have hadequal fortunes thus far, winning two games and losing two.Of the other 7,500,000,who had lost two and won one, half win the fourth game, and so give 3,750,000 morewho have lost two games and won two: thus in all we have 7,500,000 who have hadequal fortunes. The others lose at the fourth trial, and give us 3,500,000 to be addedto the 1,250,000 already counted, who have lost thrice and won once only.At the close, then, of the fourth encounter, we find a million and a quarter ofplayers who have been constantly lucky,and as many who have been constantlyunlucky.Five millions, having won three games out of four, consider themselves tohave better luck than the average; while as many, having lost three games out of four,regard themselves as unlucky.Lastly, we have seven millions and a half who havewon and lost in equal degree.These, it will be seen, constitute the largest part ofour gambling community, though not equal to the other classes taken together. Theyare, in fact, three-eighths of the entire community.So we might proceed to consider the twenty millions of gamblers after a fifthencounter, a sixth, and so on. Nor is there any difficulty in dealing with the matter inthat way. But a sort of account must be kept in proceeding from the various classesconsidered in dealing with the fourth encounter to those resulting from the fifth, fromthese to those resulting from the sixth, and so on.And although the accounts thusrequiring to be drawn up are easily dealt with, the little sums (in division by two,and in addition) would not present an appearance suited to these pages. I thereforenow proceed to consider only the results, or rather such of the results as bear mostupon my subject.After the fifth encounter there would be (on the assumption of results being alwaysexactly balanced, which is convenient, and quite near enough to the truth for ourpresent purpose) 625,000 persons who would have won every game they had played,and as many who had lost every game. These would represent the persistently luckyand unlucky men of our gambling community. There would be 625,000 who, havingwon four times in succession, now lost, and as many who, having lost four times insuccession, now won. These would be the examples of luck—good or bad—continuedto a certain stage, and then changing. The balance of our 20,000,000, amounting toseventeen millions and a half, would have had varying degrees of luck, from those whohad won four games (not the first four) and lost one, to those who had lost four games(not the first four) and won but a single game.The bulk of the seventeen millionsand a half would include those who would have had no reason to regard themselves aseither specially lucky or specially unlucky. But 1,250,000 of them would be regardedas examples of a change of luck, being 625,000 who had won the first three gamesand lost the remaining two, and as many who had lost the first three games and wonthe last two.Thus, after the fifth game, there would be only 1,250,000 of those regarded (forthe nonce) as persistently lucky or unlucky (as many of one class as of the other),while there would be twice as many who would be regarded by those who knew oftheir fortunes, and of course by themselves, as examples of change of luck, markedgood or bad luck at starting, and then bad or good luck.So the games would proceed, half of the persistently lucky up to a given game goingout of that class at the next game to become examples of a change of luck, so thatthe number of the persistently lucky would rapidly diminish as the play continued.So would the number of the persistently unlucky continually diminish, half going outat each new encounter to join the ranks of those who had long been unlucky, but hadat last experienced a change of fortune.After the twentieth game, if we suppose constant exact halving to take place asfar as possible, and then to be followed by halving as near as possible, there would beabout a score who had won every game of the twenty. No amount of reasoning wouldpersuade these players, or those who had heard of their fortunes, that they were notexceedingly lucky persons—not in the sense of being lucky because theyhadwon,but of beinglikelier to winat any time than any of those who had taken part in thetwenty games. They themselves and their friends—ay, and their enemies too—wouldconclude that they ‘could not lose.’ In like manner, the score or so who had not wona single game out of the twenty would be judged to be most unlucky persons, whomit would be madness to back in any matter of pure chance.Yet—to pause for a moment on the case of these apparently most manifest examples of persistent luck—the result we have obtained has been to show that inevitablythere must be in a given number of trials about a score of these cases of persistentluck, good or bad, and about two score of cases where both good and bad are countedtogether.We have shown that, without imagining any antecedent luckiness, goodor bad, there must be what, to the players themselves, and to all who heard of orsaw what had happened to them, would seem examples of the most marvellous luck.Supposing, as we have, that the game is one of pure chance, so that skill cannot in-fluence it and cheating is wholly prevented, all betting men would be disposed to say, ‘These twenty are persons whose good luck can be depended on; we must certainlyback them for the next game: and those other twenty are hopelessly unlucky; we maylay almost any odds against their winning.’But it should hardly be necessary to say that that whichmusthappen cannotbe regarded as due to luck.There must besomeset of twenty or so out of ourtwenty millions who will win every game of twenty; and the circumstance that thishas befallen such and such persons no more means that they are lucky, and is nomore a matter to be marvelled at, than the circumstance that one person has drawnthe prize ticket out of twenty at a lottery is marvellous, or signifies that he would bealways lucky in lottery drawing.The question whether those twenty persons who had so far been persistently luckywould be better worth backing than the rest of the twenty millions, and especiallythan the other twenty who had persistently lost, would in reality be disposed of atthe twenty-first trial in a very decisive way: for of the former score about half wouldlose, while of the latter score about half would win. Among a thousand persons whohad backed the former set at odds there would be a heavy average of loss; and thelike among a thousand persons who had laid against the latter set at odds.It may be said this is assertion only, that experience shows that some men arelucky and others unlucky at games or other matters depending purely on chance, andit must be safer to back the former and to wager against the latter.The answer isthat the matter has been tested over and over again by experience, with the resultthat, as`a priorireasoning had shown, some men are bound to be fortunate again andagain in any great number of trials, but that these are no more likely to be fortunateon fresh trials than others, including those who have been most unfortunate.Thesuccess of the former shows only that theyhave been, not that theyarelucky; whilethe failure of the others shows that theyhavefailed, nothing more.An objection will—about here—have vaguely presented itself to believers in luck,viz. that, according to the doctrine of the ‘maturity of the chances,’ which must applyto the fortunes of individuals as well as to the turn of events, one would rather expectthe twenty who had been so persistently lucky to lose on the twenty-first trial, andthe twenty who had lost so long to win at last in that event. Of course, if gamblingsuperstitions might equally lead men to expect a change of luck and continuanceof luck unchanged, one or other view might fairly be expected to be confirmed byevents. And on a single trial one or other event—that is, a win or a loss—mustcomeoff, greatly to the gratification of believers in luck. In one case they could say, ‘I toldyou so, such luck as A’s was bound to pull him through again’; in the other, ‘I toldyou so, such luck was bound to change’: or if it were the loser of twenty trials who wasin question, then, ‘I told you so, he was bound to win at last’; or, ‘I told you so, suchan unlucky fellow was bound to lose.’ But unfortunately, though the believers in luckthus run with the hare and hunt with the hounds, though they are prepared to findany and every event confirming their notions about luck, yet when a score of trialsor so are made, as in our supposed case of a twenty-first game, the chances are thatthey would be contradicted by the event.The twenty constant winners would notbe more lucky than the twenty constant losers; but neither would they be less lucky.The chances are that about half would win and about half would lose.If one whoreally understands the laws of probability could be supposed foolish enough to wagermoney on either twenty, or on both, he would unquestionably regard the betting asperfectly even.Let us return to the rest of our twenty millions of players, though we need by nomeans consider all the various classes into which they may be divided, for the numberof these classes amounts, in fact, to more than a million.The great bulk of the twenty millions would consist of players who had won aboutas many games as they had lost.The number who had wonexactlyas many gamesas they had lost would no longer form a large proportion of the total, though it wouldform the largest individual class.There would be nearly 3,700,000 of these, whilethere would be about 3,400,000 who had won eleven and lost nine, and as many whohad won nine and lost eleven; these two classes together would outnumber the winnersof ten games exactly, in the proportion of 20 to 11 or thereabouts. Speaking generally,it may be said that about two-thirds of the community would consider they had hadneither good luck nor bad, though their opinion would depend on temperament inpart. For some men are more sensitive to losses than to gains, and are ready to speakof themselves as unlucky, when a careful examination of their varying fortunes showsthat they have neither won nor lost on the whole, or have won rather more than theyhave lost.On the other hand, there are some who are more exhilarated by successthan dashed by failure.The number of those who, having begun with good luck, had eventually been somarkedly unfortunate, would be considerable.It might be taken to include all whohad won the first six games and lost all the rest, or who had won the first seven orthe first eight, or any number up to, say, the first fourteen, losing thence to the end;and so estimated would amount to about 170, an equal number being first markedlyunfortunate, and then constantly fortunate. But the number who had experienced amarked change of luck would be much greater if it were taken to include all who hadwon a large proportion of the first nine or ten games and lost a large proportion ofthe remainder, orvice versˆa. These two classes of players would be well represented.Thus, then, we see that, setting enough persons playing at any game of purechance, and assuming only that among any large number of players there will beabout as many winners as losers, irrespective of luck, good or bad, all the five classeswhich gambling folk recognise and regard as proving the existence of luck,mustinevitably make their appearance.Even any special class which some believer in luck, who was more or less fanciful,imagined he had recognised among gambling folk, must inevitably appear among ourtwenty millions of illustrative players. For example, there would be about a score ofplayers who would have won the first game, lost the second, won the third, and so onalternately to the end; and as many who had also won and lost alternate games, buthad lost the first game; some forty, therefore, whose fortune it seemed to be to winonly after they had lost and to lose only after they had won.Again, about twentywould win the first five games, lose the next five, win the third five, and lose the lastfive; and about twenty more would lose the first five, win the next, lose the third five,and win the last five: about forty players, therefore, who seemed bound to win andlose always five games, and no more, in succession.Again, if anyone had made a prediction that among the players of the twentygames there would be one who would win the first, then lose two, then win three,then lose four, then win five, and then lose the remaining five—and yet a sixth ifthe twenty-first game were played—that prophet would certainly be justified by theresult. For about a score would be sure to have just such fortunes as he had indicatedup to the twentieth game, and of these, nine or ten would be (practically) sure to winthe twenty-first game also.Wesee,then,thatallthedifferentkindsofluck—good,bad,indifferent,orchanging—which believers in luck recognise,are bound to appear when any con-siderable number of trials are made; and all the varied ideas which men have formedrespecting fortune and her ways are bound to be confirmed.It may be asked by some whether this is not proving that there is such a thingas luck instead of over-throwing the idea of luck. But such a question can only arisefrom a confusion of ideas as to what is meant by luck.If it be merely asserted thatsuch and such men have been lucky or unlucky, no one need dispute the proposition;for among the millions of millions of millions of purely fortuitous events affectingthe millions of persons now living, it could not but chance that the most remarkablecombinations, sequences, alternations, and so forth, of events, lucky or unlucky, musthave presented themselves in the careers of hundreds. Our illustrative case, artificialthough it may seem, is in reality not merely an illustration of life and its chances,but may be regarded as legitimately demonstrating what must inevitably happen onthe wider arena and amid the infinitely multiplied vicissitudes of life. But the beliefin luck involves much more. The idea involved in it, if not openly expressed (usuallyexpressed very freely), is that some men are lucky by nature, others unlucky, thatsuch and such times and seasons are lucky or unlucky, that the progress of events maybe modified by the lucky or unlucky influence of actions in no way relating to them;as, for instance, that success or failure at cards may be affected by the choice of aseat, or by turning round thrice in the seat.This form of belief in luck is not onlyakin to superstition, itissuperstition.Like all superstition, it is mischievous.It is,indeed, the very essence of the gambling spirit, a spirit so demoralising that it blindsmen to the innate immorality of gambling. It is this belief in luck, as something whichcan be relied on, or propitiated, or influenced by such and such practices, which isshown, by reasoning and experience alike, to be entirely inconsistent not only withfacts but with possibility.But oddly enough, the believers in luck show by the form which their belief takesthat in reality they have no faith in luck any more than men really have faith insuperstitions which yet they allow to influence their conduct.A superstition is anidle dread, or an equally idle hope, not a real faith; and in like manner is it withluck.A man will tell you that at cards, for instance, he always has such and suchluck; but if you say, ‘Let us have a few games to see whether you will have yourusual luck,’ you will usually find him unwilling to let you apply the test.If you tryit, and the result is unfavourable, he argues that such peculiarities of luck never doshow themselves when submitted to test. On the other hand, if it so chances that onthat particular occasion he has the kind of luck which he claims to havealways, heexpects you to accept the evidence as decisive.Yet the result means in reality onlythat certain events, the chances for and against which were probably pretty equallydivided, have taken place.So, if a gambler has the notion (which seems to the student of science to implysomething little short of imbecility of mind) that turning round thrice in his chair willchange the luck, he is by no means corrected of the superstition by finding the processfail on any particular occasion.But if the bad luck which has hitherto pursued himchances (which it is quite as likely to do as not) to be replaced by good or even bymoderate luck, after the gambler has gone through the mystic process described, orsome other equally absurd and irrelevant manœuvre, then the superstition is con-firmed. Yet all the time there is no real faith in it. Such practices are like the absurdinvocation of Indian ‘medicine men’; there is a sort of vague hope that somethinggood may come of them, no real faith in their efficacy.The best proof of the utter absence of real faith in superstitions about luck, evenamong gambling men, the most superstitious of mankind, may be found in the incon-gruity of their two leading ideas. If there are two forms of expression more frequentlythan any others in the mouth of gambling men, they are those which relate to beingin luck or out of luck on the one hand, and to the idea that luck must change on theother.Professional gamblers, like Steinmetz and his kind, have become so satisfiedthat these ideas are sound, whatever else may be unsound, in regard to luck, thatthey have invented technical expressions to present these theories of theirs, failingutterly to notice that the ideas are inconsistent with each other, and cannot both beright—though both may be wrong, and are so.A player is said to be ‘in the vein’ when he has for some time been fortunate. Heshould only go on playing, if he is wise, at such a time, and at such a time only shouldhe be backed.Having been lucky he is likely, according to this notion, to continuelucky. But, on the other hand, the theory called ‘the maturity of the chances’ teachesthat the luck cannot continue more than a certain time in one direction; when it hasreached maturity in that direction it must change. Therefore, when a man has been ‘in the vein’ for a certain time (unfortunately no Steinmetz can say precisely howlong), it is unsafe to back him, for he must be on the verge of a change of luck.Of course the gambler is confirmed in his superstition, whichever event may befallin such cases.When he wins he applauds himself for following the luck, or for dulyanticipating a change of luck, as the case may be; when he loses, he simply regretshis folly in not seeing that the luck must change, or in not standing by the winner.And with regard to the idea that luck must change, and that in the long run eventsmust run even, it is noteworthy how few gambling men recognise either, on the onehand, how inconsistent this idea is with their belief in luck which may be trusted (or,in their slang, may be safely backed), or, on the other hand, the real way in whichluck ‘comes even’ after a sufficiently long run.A man who has played long with success goes on because he regards himself aslucky. A man who has played long without success goes on because he considers thatthe luck is bound to change.The latter goes on with the idea that, if he only playslong enough, he must at least at some time or other recover his losses.Now there can be no manner of doubt that if a man, possessed of sufficient means,goes on playing for a very long time, his gains and losses will eventually be very nearlyequal; assuming always, of course, that he is not swindled—which, as we are dealingwith gambling men, is perhaps a sufficiently bold assumption.Yet it by no meansfollows that, if he starts with considerable losses, he will ever recover the sum he hasthus had to part with, or that his losses may not be considerably increased.Thissounds like a paradox; but in reality the real paradox lies in the opposite view.This may be readily shown.The idea to be controverted is this: that if a gambler plays long enough there mustcome a time when his gains and his losses are exactly balanced.Of course, if thiswere true, it would be a very strong argument against gambling; for what but loss oftime can be the result of following a course which must inevitably lead you, if you goon long enough, to the place from which you started?But it is not true.If it weretrue, of course it involves the inference that, no matter when you enter on a course ofgambling, you are bound after a certain time to find yourself where you were at thatbeginning. It follows that if (which is certainly possible) you lose considerably in thefirst few weeks or months of your gambling career, then, if you only play long enoughyou must inevitably find yourself as great a loser, on the whole, as you were when youwere thus in arrears through gambling losses; for your play may be quite as properlyconsidered to have begun when those losses had just been incurred, as to have begunat any other time.Hence this idea that, in the long run, the luck must run even,involves the conclusion that, if you are a loser or a gainer in the beginning of yourplay, you must at some time or other be equally a gainer or loser. This is manifestlyinconsistent with the idea that long-continued play will inevitably leave you neither aloser nor a gainer. If, starting from a certain point when you are a thousand poundsin arrears, you are certain some time or other, if you only play long enough, to havegained back that thousand pounds, it is obvious that you are equally certain sometime or other (from that same starting-point) to be yet another thousand pounds inarrears. For there is no line of argument to prove you must regain it, which will notequally prove that some time or other you must be a loser by that same amount, overand above what you had already lost when beginning the games which were to putyou right.If, then, you are to come straight, you must be able certainly to recovertwo thousand pounds, and by parity of reasoning four thousand, and again twice that;and so onad infinitum: which is manifestly absurd.The real fact is, that while the laws of probabilities do undoubtedly assure thegambler that his losses and gains will in the long run be nearly equal, the kind ofequality thus approached is not an equality of actual amount, but of proportion.Iftwo men keep on tossing for sovereigns, it becomes more and more unlikely, the longerthey toss, that the difference between them will fall short of any given sum.If theygo on till they have tossed twenty million times, the odds are heavily in favour ofone or the other being a loser of at least a thousand pounds.But the proportion ofthe amount won by one altogether, to the amount won altogether by the other, isalmost certain to be very nearly a proportion of equality. Suppose, for example, thatat the end of twenty millions of tossings, one player is a winner of 1,000l., then hemust have won in all 10,000,500l., the other having won in all 9,999,500l. the ratio ofthese amounts is that of 100005 to 99995, or 20001 to 19999. This is very nearly theratio of 10000 to 9999, or is scarcely distinguishable, practically, from actual equality.Now if these men had only tossed eight times for sovereigns, it might very well havehappened that one would have won five or six times, while the other had only wonthrice or twice.Yet with a ratio of 5 to 3, or 3 to 1, against the loser, he wouldactually be out of pocket only 2l. in one case and 4l. in the other; while in the othercase, with a ratio of almost perfect equality, he would be the loser of a thousandpounds.But now it might appear that, after all, this is proving too much, or, at any rate,proves as much on one side as on the other; for if one player loses the other mustgain; if a certain set of players lose the rest gain: and it might seem as though, withthe prevalent ideas of many respecting gambling games, the chance of winning werea sufficient compensation for the chance of losing.Where a man is so foolish that the chance of having more money than he wants isequivalent in his mind (or what serves him for a mind) to the risk of being deprived ofthe power of getting what is necessary for himself and for his family, such reasoningmay be regarded as convincing. For those who weigh their wants and wishes rightly,it has no value whatever.On the contrary it may be shown that every wager orgambling transaction, by a man of moderate means, definitely reduces the actualvalue of his possessions, even if the wager or transaction be a fair one. If a man whohas a hundred pounds available to meet his present wants wagers 50l.against 50l.,or an equal chance, he is no longer worth 100l. Hemay, when the bet is decided, beworth 150l., or he may be worth only 50l. All he canestimatehis property at is about87l. Supposing the other man to be in the same position, they are both impoverishedas soon as they have made the bet; and when the wager is decided, the average valueof their possessions in ready money is less than it was; for the winner gains less byhaving his 100l.raised to 150l.(or increased as 2 to 3), than the loser suffers byhaving his ready money halved.Similar remarks apply to participation in lottery schemes, or the various forms ofgambling at places like San Carlo. Every sum wagered means, at the moment whenit is staked, a depreciation of the gambler’s property; and would mean that, evenif the terms on which the wagering were conducted were strictly fair.But this isnever the case. In all lotteries and in all established systems of gambling certain oddsare always retained in favour of those who work the lottery or the gambling system.These odds make gambling in either form still more injurious to those who take partin it. Winners of course there are, and in some few cases winners may retain a largepart of their gains, or at any rate expend them otherwise than in fresh gambling. Yetit is manifest that, apart from the circumstance that theeffectsof the gambling gainsof one set of persons never counterbalance theeffectsof the gambling losses of others,there is always a large deduction to be made on account of the wild and reckless wasteof money won by gambling. In many cases, indeed, large gambling gains have broughtruin to the unfortunate winner:set ‘on horseback’ by lightly acquired wealth, andunaccustomed to the position, he has ridden ‘straightway to the devil.’But the greed for chance-won wealth is so great among men of weak minds, andthey are so large a majority of all communities, that the bait may be dangled forthem without care to conceal the hook. In all lotteries and gambling systems whichhave yet been known the hook has been patent, and the evil it must do if swallowedshould have been obvious. Yet it has been swallowed greedily.A most remarkable illustration of the folly of those who trust in luck, and the coolaudacity of those who trust in such folly, with more reason but with more rascality,is presented by the Louisiana Lottery in America.This is the only lottery of thekind now permitted in America.Indeed, it is nominally restricted to the State ofLouisiana; but practically the whole country takes part in it, tickets being obtainableby residents in every State of the Union.The peculiarity of the lottery isthe calmadmission, in all advertisements, that it is a gross and unmitigated swindle.Theadvertisements announce that each month 100,000 tickets will be sold, each at fivedollars, shares of one-fifth being purchasable at one dollar.Two commissioners—Generals Early and Beauregard—control the drawings; so that we are told, and maywell believe, the drawings are conducted with fairness and honesty, and in good faithto all parties.So far all is well.We see that each month,if all the tickets aresold, the sum of 500,000 dols. will be paid in.From this monthly payment we mustdeduct 1,000 dols. paid to each, of the commissioners, and perhaps some 3,000 dols.at the outside for advertising. We may add another sum of 5,000 dols. for incidentalexpenses, machinery, sums paid to agents as commission on the sale of tickets, and soforth. This leaves 490,000 dols. monthly if all the tickets are sold. And as the lotteryis ‘incorporated by the State Legislature of Louisiana for charitable and educationalpurposes,’ we may suppose that a certain portion of the sum paid in monthly will beset aside to represent the proceeds of the concern, and justify the use of so degradinga method of obtaining money.Probably it might be supposed that 24 per cent. perannum, or 2 per cent. per month, would be a fair return in this way, the system beingentirely free from risk. This would amount to 9,800 dols., or say 10,000 dols., monthly.Those who manage the lottery are not content, however, with any such sum as this,which would leave 480,000 dols. to be distributed in prizes. They distribute 215,000dols. less, the total amount given in prizes amounting to only 265,000 dols.If the100,000 tickets are all sold—and it is said that few are ever left—the monthly profiton the transaction is not less than 225,000 dols., or 45 per cent. on the total amountreceived per month. This would correspond to 540 per cent. per annum if it were paidon a capital of 500,000 dols. But in reality it amounts to much more, as the lotterycompany runs no risk whatsoever. The Louisiana Lottery is a gross swindle, besidesbeing disreputable in the sense in which all lotteries are so. What would be thoughtif a man held an open lottery, to which each of one hundred persons admitted paid5l., and taking the sum of 500l. thus collected, were to say: ‘The lottery, gentlemengamblers, will now proceed; 265l