1 PAULO MINORA. This essay, I need hardly say, consists of notes made before the war and put in order now, at a time when victory allows our thoughts to stray for a moment from the great tragedy in which the destinies of mankind have been at stake. For the rest, the subject, however frivolous¹ it may at first sight appear, sometimes touches or seems to touch problems which it is not unfitting to examine, were it only to realize that they are perhaps illusive². Moreover it is unfortunately probable that, when peace is restored, our allies will visit in too numerous and confiding³ crowds the dubious⁴ havens⁵ of delight which we are about to enter. I have no pretension⁶ to serve them as a guide nor to teach them how to fight against the whims⁷ of fortune; but a handful of them[134] may find in these lines, if not useful hints or profitable advice, at least some few reflections or observations which will pave the way for their own experiments or render them easier.
 
2
Let us then pay a last visit to one of those green tables which spread their length in the somewhat disreputable place of which I have written elsewhere[2] as the “Temple of Chance.” To-day I would rather call it the Factory of Chance, for it is here that, for more than half a century, without respite⁹ or repose¹⁰, on weekdays, Sundays and holidays alike, daily from ten o’clock in the morning till twelve o’clock at night, with croupiers unintermittently relieving one another, men have obstinately¹¹ manufactured Chance and doggedly¹³ consulted the formless and featureless god that shrouds¹⁴ good luck and ill within his shadow.
 
[135]We do not yet know what he is nor what he wants; we are not even sure that he exists; but surely it would be astonishing if no result of any kind, no clue to the tantalizing¹⁵ puzzle, had emerged from this endless effort, the most gigantic, the most costly¹⁶, the most methodical that has ever been made on the brink¹⁷ of this gloomy abyss, if nothing had been born of all this furious work, however trivial, however unhealthy and useless it may appear.
 
In any case, at these tables, as at all places where passions become intensified¹⁸, we are able to make interesting observations and, among other things, to behold¹⁹ at first hand, violently foreshortened and harshly illuminated²⁰, certain aspects of man’s lifelong struggle with the unknown. The drama, which as a rule is long drawn²¹ out, projecting itself into space and time and breaking up amid circumstances that escape our eyes, is here knit together, gathered into a ball, held, so to speak, in the hollow of the hand. But, for all its speed, its abruptness²² of movement and its extreme[136] compression, it remains²³ as complex and mysterious as those which go on indefinitely. Until the ivory ball that rolls and hops²⁴ around the wheel falls into its red or black compartment²⁵, the unknown veiling its choice or its destiny is as impenetrable as that which hides from us the choice or the destiny of the stars. The movements of the planets can be calculated almost to a second; but no mathematical operation can measure or predict the course of the little white ball.
 
Your most skilful²⁶ players, indeed, have given up trying. Not one of them any longer seriously relies on intuition, presentiment²⁷, second sight, telepathy, psychic²⁸ forces or the calculation of probabilities in the attempt to foresee or determine the fall of a destiny no larger than a hazel-nut. All the scientific part of human knowledge has failed; and all the occult and magical side of that same knowledge has been equally unsuccessful. The mathematicians³⁰, the prophets, the seers, the sorcerers, the sensitives, the mediums, the[137] psychometrists, the spiritualists who call upon the dead for assistance, all alike are blind, confounded and impotent before the wheel and before Destiny’s thirty-seven compartments³¹. Here Chance reigns³² supreme³³; and hitherto, though it all happens before our eyes, though it is repeated to satiety³⁴ and may be held, let me say once more, in the hollow of our hand, no one has yet been able to determine a single one of its laws.
 
3
Yet such laws seem to exist; and thousands of players have ruined themselves in following their forms or their elusive³⁵ and deceptive³⁶ traces. Let us take a bundle of those records or permanences, published at Monte Carlo, which give day by day the list of all the numbers that have come up at one of the roulette or trente-et-quarante tables. As everybody knows, these numbers are arranged in long parallel columns, the black on the left and the red on the right. When we look at one[138] of these sheets, containing as a rule ten columns of sixty-five numbers each—dead and harmless cyphers now, though once so dangerous, once destructive of so many hopes and perhaps inspiring more than one disaster—we observe a tendency towards a fairly perceptible equilibrium³⁷ between the red and the black. Most often the two chances balance each other, singly or in little groups, a black, a red, two blacks, three reds, three blacks, two reds and so on. When we come upon a series of five, six, seven, eight, sometimes eight, nine, ten, eleven, twelve consecutive³⁸ blacks, we are almost certain of finding not far away a compensating³⁹ series of five, six, seven, eight or ten reds. There is a very real rhythm, a sort of breathing or a cadenced⁴⁰ movement to and fro of the mysterious creature which we call Chance. This rhythm or balance is moreover confirmed by the final statistics of the day, from which we learn that, in a total of six hundred and so many spins of the ball, the difference between the[139] black and the red very seldom exceeds twenty or thirty; and this difference is even smaller in the total for the week, that is to say, in a total of nearly five thousand spins, when it is usually reduced to a few units.
 
4
The monster has other strange habits. We see, for instance, that it is not uncommon⁴¹ for a number to come up twice in succession; and it is undeniable that, in each day’s play, two or three numbers are obviously favoured, so much so that we may hurl⁴² out a challenge to logic⁴³ and declare that the more frequently a number occurs the more chances it has of reappearing. This seems to conflict with the law of equilibrium which we have remarked; but it must be observed that this equilibrium will be recovered later, that by the end of the week the difference will no longer be very great and that they will almost disappear when the month is over. The equilibrium is more slowly restored because we must[140] multiply the number of series by eighteen and a half to reach the proportions of the even chances.
 
Players note yet another law which, for that matter, is but a corollary of the former habit, but which has something curiously⁴⁴ human about it: the chances which lag behind show a greater eagerness to regain⁴⁵ their lost ground at the moment that follows more or less closely upon a halt, as though they had recovered their breath after a brief rest on the landing of a staircase.
 
Let us add at once that it is wise to distrust these fluctuating habits and these gropings after laws. For instance, red has been known to beat black by seventy per cent. in the course of a day’s play. Black, on the other hand, as people still remember at Monte Carlo, one day came up twenty-nine times in succession and the second dozen twenty-eight times without a break. Chance has not our nerves; it is not, like us, impatient to make good its losses or to carry off its gains. It takes its[141] time, awaits its hour and does not trouble to keep step with our ways of life.
 
5
Players as a rule attribute these habits or caprices to a trick of the croupier’s hand. This is hardly tenable. After all, we know how the thing is done. The ball drops into its compartment and the croupier announces, for instance:
 
“13, black, impair⁴⁶ and manque.”
 
The losses are raked in, the winnings are paid out, the players renew their stakes, there is sometimes a brief dispute, somebody asks for change and so on. These operations vary a good deal in length; and all this time the wheel carrying the ball is making hundreds of revolutions. The croupier stops it at last, takes the ball, reverses the wheel and sends the ball spinning in the opposite direction. It is impossible under these conditions for his particular trick of the hand to exercise any influence whatever. Besides, we can easily see from the chart of the permanences that[142] the change of croupier does not perceptibly affect the rhythm of the even chances. It is not the man who controls the rhythm but the rhythm that controls the man.
 
6
These gropings after laws in what would seem a negation⁴⁷ of all or any law; these strivings on the part of Chance to quit its own domain⁴⁸ and to organize its chaos⁴⁹; this god who denies himself and seeks to destroy himself by his own hand; these incomprehensible stammerings, these awkward efforts to achieve utterance⁵⁰ and assume consciousness are rather curious, we must admit. For the rest, it is these efforts, these hankerings after equilibrium, this embryonic⁵¹ rhythm that constitute the gamblers’ good and bad luck. If Chance were simply Chance as we conceive it on first principles, one would stake any sum anyhow and at any moment. I am well aware that, according to the most learned theorists on roulette, each coup⁵² is independent of all the others and begins as if nothing[143] had happened before, as if nothing were to happen afterwards, as if the table were fresh from the shop, the wheel from the factory and the croupier from the hands of God. In theory this is quite accurate; but we have just seen that in practice it does not seem to be so. For that matter, it seems impossible to explain the reason. Players are satisfied to observe the fact, while yielding to a dangerous but very human tendency to exaggerate the scope and the certainty of their observations.
 
They are too ready to see laws where there is only a mass of coincidences as fleeting⁵³ as clouds. It is of course necessary that the reds and blacks, emerging successively from nowhere, should find a place somewhere and form certain groups; and, if it is rather surprising that at the end of the month their numbers are nearly equal, it would be no less surprising if one of the colours were to prevail largely over the other. It is perfectly⁵⁴ true that, at first sight, the reds and blacks seem to balance[144] on the permanence sheets; but it is also true that, when we examine more closely, a series of five or six reds, for instance, interrupted by one or two blacks, not infrequently begins a fresh run; and ill-luck may well have it that, at this moment, the player, in his search for equilibrium, will start punting on the black and in a few coups⁵⁵ behold the disappearance⁵⁶ of all the winnings slowly and laboriously⁵⁷ wrested⁵⁸ from Chance, which is niggardly⁵⁹ when one is winning and extremely generous—to the bank—when one is losing. For that matter, he will suffer the same disappointment if he bets on the variation, in other words, against the equilibrium, and will too often discover that these laws, when he puts his trust in them, are writ⁸ in water, whereas they seem to be graven in bronze so soon as they betray him.
 
7
In order to profit by these laws, which are perhaps fallacious and in any case untrustworthy, and to secure himself against[145] their treachery, he has contrived⁶¹ a host of ingenious systems which sometimes enable him to win but most often merely retard⁶³ his ruin.
 
But, before speaking of these systems, let us begin by saying that we shall concern ourselves here only with the even chances, red or black, pair or impair, passe or manque. These are sufficiently⁶⁴ complicated in themselves and set us problems that would be enough to exhaust all the shrewdness of a human life. As for any other than the even chances, en plein, à cheval, transversales, carrés, douzaines and so forth⁶⁵, these, both in theory and in practice, escape all control, calculation or explanation.
 
Whatever system he adopt, the gambler is always tossing heads or tails against the bank. He has a chance and the bank has a chance; but zero gives the bank odds⁶⁶ against him; and, though zero is apparently⁶⁷ a very mild tax, since at rouge-et-noir in thirty-six chances the bank has only half a chance more than the player, it is bound[146] to be ruinous in the end. To escape the abruptness of a decision which, if he placed all that he possessed⁶⁸ on the red or the black, would end the game at a single stroke, the player divides his stake, so as to be able to defy a large number of chances, hoping that, thanks to a skilfully⁶⁹ graduated progression, he will end by lighting⁷⁰ on a favourable⁷¹ series in which the gains will exceed the losses. This is the underlying⁷² principle of all the systems, which are never anything but more or less ingenious, prudent⁷³ and complicated martingales. There are not, there never will be any others, in the absence of a miracle which has not yet occurred, of an intuition which foresees what the ball will decide, or of an unknown force which will oblige it to act as a player wishes.
 
8
I have no intention of reviewing all these systems, which are innumerable and of unequal value: the paroli pure and simple, that artless, violent, doubled stake[147] which leads straight to disaster; the D’Alembert and all its variants⁷⁴; the descending⁷⁵ progressions; the differential methods; the montant belge; the parolis intermittents; the snowball; the photographie; the staking of equal amounts on certain groups of figures, which is a Chinese puzzle demanding days of patient observation before it is attacked; and many others which I forget, from the most clear-cut to the most mysterious, which are sold at a high price, to credulous⁷⁶ beginners, in sealed envelopes containing what is everybody’s secret and with all or nearly all of which I have become acquainted thanks to the kindness of an erudite player. A detailed⁷⁷ account of those most frequently used will be found in D’Albigny’s treatise⁷⁸ Les Martingales modernes, in Gaston Vessillier’s Théorie des systèmes géométriques, in Hulmann’s Traité des jeux dits de hasard, in Théo d’Alost’s Théorie scientifique nouvelle des jeux de la roulette, trente-et-quarante, etc., and, above all, in the Revue de Monte Carlo, which has[148] given a system in every issue since the day of its foundation some fifteen years ago.
 
Whether mystic or transparent⁷⁹, ............