Roger Caillois
trans. Meyer Barash
Man, Play and Games (1961)
[129]
CHAPTER IX
Revivals in the Modern World
Since mimicry and ilinx are always tempting to man, it is not easy to eliminate them from social life at the point where they have become merely children's amusements or aberrant behavior. ... It may therefore be necessary to concede them some outlet,...
...their major force derives from their being paired. In order to subdue them more easily there is nothing better than to divide their strength and ban their combining. ... Henceforth they can no longer be present, except in disjointed, at-
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tenuated, and isolated form, in a world that denies them and which prospers only to the degree that it succeeds in containing or duping their irresponsible violence.
In effect, the mask necessarily loses its power of metamorphosis in a society freed from bondage to the mimicry-ilinx combination. The wearer of the mask no longer feels that he is the reincarnation of the monstrous powers whose inhuman visage he has donned. Those whom he frightens can no longer be harmed by the strange apparition. The mask itself has changed its appearance and also, in large measure, its purpose. In fact, it has acquired a new, strictly utilitarian role. As a means of disguise for the malefactor seeking to hide his identity, it does not intrude a new presence but protects him from being recognized . ...
The Mask and the Uniform ... The black mask, the mask reduced to its essentials, elegant and abstract, has long been associated with erotic fetes and with conspiracies. ... It is the symbol of amorous or political intrigue. ... In a world in which sexual relationships are subject to many taboos, it is
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noteworthy that the black mask, named after a wild and predatory beast, traditionally symbolizes the means and often the announced decision to violate these taboos.
...
In origin, the carnival is an explosion of license that, even more than the costume ball, requires disguise and is founded upon the liberty that it facilitates. ... Carnival masks involve instead indecencies, jostling, provocative laughter,... The passer-by, playing the game, makes believe that he is afraid, or conversely, that he is not afraid. If he becomes angry, he is disqualified. In refusing to play, he fails to understand that the social conventions have been momentarily replaced by others intended to flout them. ...
Even this is too much. Order and moderation are soon imposed upon this effervescence, and it all ends in parades, blos-
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som festivals, and costume competitions. On the other hand, the authorities are so well aware that masks are a vital source of release that they were content merely to ban them alone as in Rio de Janeiro, when the general frenzy threatened for a dozen consecutive years, to reach proportions incompatible with the simple functioning of public services.
In a police state , the uniform replaces the mask of a vertiginous society. The uniform is almost the exact opposite of the mask, and always symbolizes a type of authority founded on entirely opposing principles . The mask aimed to dissimulate and terrify. ... The uniform is also a disguise, but it is official, permanent, regulated, and, above all, leaves the face exposed. It makes the individual a representative and a servant of an impartial and immutable rule, rather than the delirious prey of contagious vehemence. ... Perhaps there is no better or more striking indication of the contrast between these two types of society than in these two distinctive appearances —one that disguises and the other that proclaims —and between those upon whom devolves the responsibility for preserving such contrasting types of social order.
The Traveling Fair Apart from modest resort to rattles and drums, roundelays and farandoles, the carnival is strangely lacking in instruments and occasions of vertigo. ... The proper domain of vertigo is elsewhere, as if a special wis-
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dom had prudently dissociated the powers of ilinx and mimicry. Fairgrounds and amusement parks, where by contrast the wearing of masks is not customary, in compensation constitute special places in which are found the seeds, snares, and lures of vertigo. These surroundings exhibit the basic characteristics of playing fields. ... Where traveling fairs are involved, their seasonal character also adds a time dimension to the spatial separation, thus opposing a time of paroxysm to the monotonous routine of daily life.
...
Lotteries are everywhere. ... Fakirs, fortune-tellers, and astrologers predict the future or read the stars. ...
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Mimicry is also present. Jesters, clowns, ballerinas, and mummers parade and cavort in order to lure the public. They are examples of the attraction of simulation and the power of travesty, which they monopolize, since the crowd on this occasion is not permitted to wear disguises.
However, the dominant atmosphere is that of vertigo. ...
...physical sensations are reinforced by many related forms of fascination... This is the function of labyrinths of mirrors and of freak shows exhibiting giants, dwarfs, mermaids,...
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Games involving glass, special effects, and ghosts all lead to the same result—the creation of a fictional world in desired contrast with the ordinary life that is dominated by the conventonal species and from which demons have been banished. ... ...[to] supplement on another level the wholly physical thrill by which the vertiginous machines momentarily distort one's sensory stability.
Is a reminder necessary that all of this is still play, i.e. free, isolated, limited, and regulated?
I do think so. Categorizing all of this as a form of Play and Games is actually mildly provocative. It also/instead belongs in the category of performance art...right where Rank-Becker would place it. The fact of seeing-and-being-seen cannot be merely incidental. Nor can the arrogation of a certain self-concept. Devolving always to an analysis of "culture" and "civilization" papers over the consideration of individual motivations, which may have little to do with reductionist accounts of a culture. But admittedly that IS quite beyond the scope of the present book.
... Sometimes the sensations are frightfully brutal, but the duration and intensity of the shock are controlled in advance. ... Everything is regulated in great detail and conforms to one of the more conservative traditions. ...
It is pleasure founded upon excitement, illusion, and disorder that has been agreed to, falling and being caught, blunted shocks and harmless collisions. ...
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...
For those old enough, on the mock auto raceway just as elsewhere at the fair,... the effects of dizziness and terror are joined to produce an added diffuse and insidious anguish and delight, that of seeking a sexual liaison. At this point one leaves the realm of play as such. ...
We might just as well conclude, then, that there is no such thing as play.
The Circus The circus is a natural part of the traveling fair. This is a segregated society with its own costumes, pride, and laws. It comprises a population jealous of its special character, proud of its isolation, and endogamous. Its professional secrets are transmitted from father to son. As far as possible, it settles its own differences without resorting to the courts.
...
This closed and rigorous universe constitutes the austere side of the fair. The decisive sanction of death is necessarily present,... It forms part of the tacit agreement that binds the performers and the spectators. It enters into the rules of a game that anticipates a total risk. ...
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...
For circus people the big top represents not merely a profession but a way of life, not really comparable to sports, casino, or stage for champions, gamblers, or professional actors. In the circus there is added a kind of hereditary fatalism and a much sharper break with ordinary life. Because of this, circus life, strictly speaking, cannot be regarded as synonymous with play. And yet, two of its traditional activities are literally and significantly associated with ilinx and mimicry. I allude to the tightrope and the universality of certain kinds of clowning.
... It is surely a special road which puts man on the brink of so fearful a spell. It has been seen how the Lacedaemonian sorcerer became a legislator and pedagogue, the masked band of wolf-men evolved into a political police, and frenzy ultimately became institutionalized. Here we have another provocative development, more fecund, more propitious for the development of grace, liberty, and invention, always oriented toward equilibrium, detachment, and irony and not toward the pursuit of an implacable and perhaps, in its turns, a vertiginous domination. Evolution does not rule out the emergence of the first fissure, destined after a thousand vicissitudes to destroy the all-powerful coalition of simulation and vertigo, through a strange, almost imperceptible innovation, apparently absurd and doubtless sacrilegious. This is the introduction into the band of masked divinities of characters of equal rank and identical authority, charged with parodying their bewitching mimes, and tempering by laughter what might end fatally in trance and hypnosis, were this antidote absent.
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Addenda
[145]How literary of them.
APPENDIX I
The Importance of Games of
Chance
Even in an industrial civilization, founded on the value of work, the taste for games of chance remains extremely powerful, the exact opposite of what is involved in earning money,... Play mocks at work and represents a competing attraction which, at least in some cases, assumes sufficient importance to partly determine the life-style of an entire society.
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The cultural creativity of these considerations is not proved, even though they sometimes contribute a socioeconomic function to games of chance. Instead they are suspected of encouraging indolence, fatalism, and superstition. It is agreed that studying their laws contributed to the discovery of the theory of probability,... But they are not regarded as capable of providing a model for depicting the real world... Moreover, fatalism and strict determinism, to the degree that they deny free will and responsibility, view the entire universe as a gigantic, general, obligatory, and endless lottery... Also, among leisure classes whose work is insufficient to absorb their energies or occupy all their available time, games of chance frequently acquire an unexpected cultural significance which influences their art, ethics, economy, and even life experience.
...
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...
I shall cite briefly several examples of the peculiar success of games of chance,... I will begin with a case in which there has been no culture contact, and the traditional values have therefore remained intact. Playing dice is very widespread in Southern Cameroun and Northern Gabon. It is played with the aid of figures cut into the exceptionally tough wood, of the consistency of bone, from a tree that provides an oil more valuable than palm oil (Baillonella Toxisperma). ...
These quasi-heraldic designs are numerous and varied. They constitute a kind of visual encyclopedia. ...
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...
These heraldic dice are also amulets which may help their owner gratify his least desire. He does not generally keep them at home, but in the woods, enclosed in a sack and hanging from a tree. On occasion they may be used to communicate messages.
As for the game itself, it is relatively simple. In principle, it is comparable to the game of heads or tails. ... The game has caused such addiction that it had to be forbidden by the authorities. It precipitated most serious disturbances. ...
It is a simple game, without refinements or continuity. ... ...the symbolic and encyclopedic richness of the emblems is comparable to that of the capitals of Roman columns; at least it fulfills an analogous function. ... Above all, the ravages provoked by the passion for gambling, sometimes reaching disastrous proportions, must be stressed.
...
A striking example is furnished by the success of the "Chinese charade" (Rifa Chifá) in Cuba. This lottery, described by Lydia[149]
Cabrera as "an incurable cancer of the economy," is played by means of a Chinese figure divided into thirty-six parts, to which are assigned an equal number of symbols... The banker places a corresponding series of designs in a carton or box. One of these is drawn by lot, wrapped in a piece of cloth, and shown to the players. The operation is called "hanging the animal." Next, he proceeds to sell tickets, each of which bears the Chinese character standing for one or another figurine. Meanwhile, his confederates go through the streets taking bets. At a designated time, the emblem is unwrapped, and the winners receive thirty times what they have wagered. The banker gives ten per cent of his profits to his agents.
...while in roulette all numerical combinations are possible, the symbols of Rifa Chiffá are assembled according to mysterious affinities. In effect, each possesses or does not possess one or more companions and valets. Thus, the horse has the precious stone for a companion and the peacock for a servant;... Naturally, it is necessary to play the chosen symbol, his companion, and his valet at the same time.
... At the beginning
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of each game, after having "hung the animal," the banker announces a charade (charada) intended to guide (or mislead) the participants. What is involved is an intentionally ambiguous statement such as the following: "A man on horseback is riding very slowly. He is not stupid, but drunk, and he and his companion make a lot of money," As a result, the player imagines that he ought to play the drunkard or cavalier series. He can also bet on the animal commanded by one or the other. However, there is no doubt another, less clearly expressed word which provides the clue to the charade.
... The game is Chinese in origin. In China, an enigmatic allusion to the traditional texts takes the place of the charade. A scholar, after the drawing, was charged with justifying the true solution, supported by citations. In Cuba, a comprehensive knowledge of Negro beliefs is needed for the correct interpretation of the charades. ...
...
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...
A complicated and fantastic system of dream interpretation is also of help in guessing the lucky number. Its combinations are infinite. The facts of experience are assigned prophetic numbers. These go up to 100, thanks to a book kept at the Charade bank, which can be consulted by telephone. This repertory of orthodox concordances gives rise to a symbolic language considered "very valuable for penetrating life's mysteries." In any case, the result is that the image frequently replaces the number. ...
The Chinese Charade is widely diffused, even though forbidden by Article 355 of the Cuban Penal Code. Since 1879, numerous protests against its evils have been made. Above all, there are workers who risk not only what little money they have but also what is needed to feed their families. Of necessity, they do not play much, but persistently, since they hang "the animal" four to six times daily. It is a game in which fraud is relatively easy. ...
In any event, whether honestly or dishonestly, the bankers rapidly grow rich. ...
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...
...
In Brazil, the Jogo do Bicho or animal game has the same characteristics as the Chinese Charade in Cuba. ...[153]
...
...
Jogo do Bicho not only favors the usual arithmetic exercises but also encourages superstition. In fact, it is bound to a system of forecasting the future through dream interpretation, with its own code, classics, and expert interpreters. ...the animal of which one has dreamt is not always the one to play. ... Whoever dreams of a flying cow must play the eagle, not the cow. If one dreams of a cat falling off a roof, he must bet on the butterfly (because a real cat does not fall off a roof). ... Sometimes the relationship is obscure,... The more conscientious are not content with a mechanical correspondence. ...
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...
Theoretically the game of animals is forbidden in all the states of Brazil. In fact it is more or less tolerated according to the mood of the governor of the state or the caprice and policies of local officials,... ... public opinion, though continuously obsessed with the game, nevertheless seems to regard it as a sin... Politicians often organize, exploit, or profit from the game, and yet do not fail to fulminate against it in their speeches. ...
...
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...
The player would have no recourse against the dishonest Bichero, if he did not find him there, but that does not occur. It is astonishing and admirable to find more honesty in this equivocal game in which tempting sums continuously pass through so many poor hands than in other domains... the reason for this is obvious. Without trust, this kind of traffic would absolutely fail to survive. ... ...good faith is no longer a luxury, but a necessity.
...
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...
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APPENDIX II
Psychological and Mathematical
Approaches
The world of games is so varied and complex that there are numerous ways of studying it. Psychology, sociology, anecdotage, pedagogy, and mathematics so divide its domain that the unity of the subject is no longer perceptible. ...
...
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...
...
1. Psychological Approaches Schiller is surely one of the first, if not the first, to stress the exceptional importance of play for the history of culture. In the fifteenth of his "Aesthetical Letters and Essays" he writes:
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"For, to speak out once for all, man only plays when in the full meaning of the word he is a man, and he is only completely a man when he plays." Even more significantly, further on in the same text, he even suspects that it may be possible to deduce the character of different cultures from their play. He holds that in comparing "the race tracks of London, the bull fights in Madrid, the exhibitions in Paris, the regattas in Venice, the animal fights in Vienna, and the revelry on the Roman Corso," it ought not be difficult to determine "the various nuances of taste among these different nations."
We would do better to say, actually, that it ought to be difficult to determine this; it very well ought to involve a lot more elbow grease than does mere comparison; it ought not be so elementary to reduce cultures to taste .
... According to Spencer, "Play is a dramatization of adult activity." Wundt, decidedly and emphatically in error, states, "Play is the child of work. There is no form of play that is not modeled upon some form of serious employment, which naturally precedes it in time." This view was very influential. Misled by it, ethnographers and historians devoted themselves, with varying degrees of success, to showing that various religious practices or obsolete magic rituals had survived in children's games.
The idea of free and spontaneous play was taken up by Karl Groos in his work, The Play of Animals. The writer distinguishes play as joy of being from play as motive for culture. ...he defines it as pure activity, without past or future, and freed of worldly pressures and constraints. ...
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...because Groos first studied animals (although he was already thinking of man), he was led, several years later, when he studied human play (The Play of Man), to insist upon its instinctive and spontaneous aspects, and neglect its purely intellectual possibilities,...
Moreover, he too conceived of the games of a young animal as a kind of joyous training for its adult life. Groos came to see in play the guarantor of youth: "Animals also do not play because they are young; they are young because they have to play." Accordingly, he tried to show how play activity assures young animals greater skill in hunting their prey or escaping their enemies and accustoms them to fighting among themselves,...
...
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...
After reading the works of Karl Groos, it is possible to go on ignoring or minimizing the fact that play frequently, perhaps necessarily, involves rules and even rules of a very special kind—arbitrary, imperious, and valid for a time and space determined in advance. One is reminded that Huizinga's special merit was to have stressed this last characteristic and to have shown how exceptionally fruitful it is for the development of culture. Jean Piaget before him, in two lectures delivered in 1930 at the Jean-Jacques Rousseau Institute in Geneva, had strongly emphasized the opposition of imaginary and regulated games in the child. One is also reminded of the significance he very properly attributed to regulated play for the moral development of the child.
Can this purported
significance
be squared with the previous vignette on Bicho, whereby wide participation and wide moral condemnation exist side by side?
Relatedly, it is curious to recall here that in Bicho,
good faith is no longer a luxury, but a necessity,
for
Without trust, this kind of traffic would absolutely fail to survive .
Thus the more interesting questions about the
moral development
of children:
are such rules as exist are made and imposed by the adults or by the children themselves?
also,
what (if anything) has the play-morality to do with the life-morality?
The Bicho vignette is not about children or development, but nonetheless it smuggles in some skeptical answers to these questions. Here honesty arises out of necessity. Yet true necessity would seem to be anathema to any kind of "play." Play may be "necessary" in some broader sense, but it is because of this and not in spite of it that no specific form of play can claim the same necessity, at least not when there clearly are so many to choose from. (This paradox deserves academic branding and deployment, if it has not already received them.)
So, there is no "necessity" to play Bicho, not in any abstract sense; yet in a world where Bicho IS played, and where it enjoys fanatical participation, there emerges (I assume this is the point?) a kind of "necessity" which is no less powerfully felt than the kind that might attach to, say, child-rearing or subsistence.
What to make of this play-honesty, then, vis-a-vis "moral development?" Clearly it is "real," but it is also absurd; it is lived and experienced, but also highly compartmentalized. This honesty's ladder is leaning on the wrong wall. Also, it is borne of "necessity," which means it really represents no "moral development" per se aside from the "developments" of circumstance. Or at least that is where the above account places it: at the end of a process rather than the beginning or middle.
Given only this account, one could be forgiven for imagining that people are not nearly so honest in their dealings outside of Bicho as they are within it. Conversely, the phrase moral development of the child precisely implies a carryover effect. It implies that some moral value is not merely compartmentalized to the play situation. Again, the Bicho vignette is not about children. Still, it points up a certain absurdity in ascribing something as lofty as "moral development" to (literally) child's play, and meanwhile the adults, of whom we can at least say here are "playing for real," are idle at best, degenerate at worst, and yet also, concurrently but not integrally, demonstrating rare "honesty."
There is more to be unpacked here than the mere petty hypocrisy of moralists, though that is certainly detectable and it could lead to some conclusions with broader applicability, i.e. to the social standing of all kinds of activities that seem not to be particularly productive.
Speculatively at least, I think it's fair to wonder if the
significance
of
regulated play for the moral
development of the child
is just one more sociological answer in search of a question; if alongside "development" there is an "emergence" of something determined; if rather than (or alongside) games teaching honesty, honest people play games. They are able to play competitive games (agon) in fact because, as Caillois emphasizes several times, this kind of play disintegrates in absence of agreed-upon boundaries. Finding no cheaters where they were expecting many, breathless arrivistes can opine that there must be some "moral development" inherent in competitive play. If I'm in no position to render any kind of informed judgment on such a broad question, that's because it's easy to find writers merely asserting one or the other thesis but more difficult to find (perhaps also to understand) good science on the question. What little I've stumbled on seems rather blatantly to run afoul of Taleb's "silent evidence" problem.
To wit, it could be also that the cheaters and deadbeats have already been kicked out by the time the sociologists show up; a confounding factor in the chicken-or-egg question, certainly, but hardly one which argues for a "development" and against an "emergence." I suspect Taleb is useful here too, in calling out social scientists for abusing the notion of "anecdotal" evidence. Self-policing cannot be dismissed as anecdotal, because it's the only way any social institution manages to function at all. Without it there would be nothing to study.
Also p. 166 below—"play is a test rather than an exercise"
This is the direction I would lean.
Then again, neither Piaget nor Huizinga leaves any room for games of chance,... It is understandable that games of chance are almost fated to be sidetracked, for they are certainly not encouraged by educators. ...[166]
...marbles are especially peculiar in that they are both medium of exchange and game. ...
... In deliberately ignoring games of chance, it begs an important question, i.e. whether the child is or is not aware of the lure of chance, or whether he seldom plays games of chance in school because such games are not tolerated there. I believe that there is little doubt as to the answer. The child becomes aware of chance very early. It remains to be determined at what age he does so, and how he accommodates the verdict of chance, which is unjust in principle, to his very positive and stern sense of justice.
Chateau's aim is genetic and pedagogic at the same time. ...he has no trouble in demonstrating, contrary to Karl Groos, how play is a test rather than an exercise . The child does not train himself for a definite task. Thanks to play, he acquires a more extensive capacity to surmount obstacles or face up to difficulties. ...
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...
In a general way, play is like education of the body, character, or mind, without the goal's being predetermined . From this viewpoint, the further removed play is from reality, the greater is its educational value. For it does not teach facts, but rather develops aptitudes.
However, pure games of chance do not develop any physical or mental aptitude in the player, since he remains essentially passive. Their moral consequences are also quite formidable, because they detract from work and effort in creating hope of sudden and considerable wealth. That—if so desired—is a reason for banning them from school (but not from a classification system).
Well okay, he sides with the moralizers in the end. But there is a bit too much of both consequentialism and projection in this assessment.
%%
I sometimes ask myself whether logic has not been pushed to an extreme. Play is not exercise, it is not even a test or activity, except by accretion. The faculties developed by it surely benefit from this supplemental training, which in addition is free, intense, pleasing, inventive, and protected. However, the proper function of play is never to develop capacities. Play is an end in itself. For the rest, the aptitudes it exercises are the very same as are used for study and serious adult activities. If these capacities are dormant or feeble, the child can neither study nor play, for he is then unable to adapt to a new situation, concentrate. Or apply himself to study. ...[168]
...
There is scarcely any doubt that the desire to freely respect an agreed-upon rule is essential. ...
... Playing laundress, grocer, or soldier is always an improvisation. To make believe that one is a sick patient, a baker, aviator, or cowboy involves continuous inventiveness. To play prisoner's base or tag, to say nothing of football, checkers, or chess, presupposes, on the contrary, respect for precise rules that allow the winner to be decided. ...
...
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...
...games of vertigo are no better analyzed by psychologists than are games of chance. Huizinga, who studied adult games, pays no attention to them. He no doubt holds them in disdain, because it seems impossible to attribute a cultural or educational value to games of vertigo. Huizinga derives civilization, to whatever degree necessary, from invention, respect for rules, and fair competition, just as does Chateau for the essential qualities needed by man for building his personality. The ethical creativity of limited and regulated conflict and the cultural creativity of magical games are doubted by no one. However, the pursuit of vertigo and chance is of ill repute. These games seem sterile—if not fatal—marks of some obscure and contagious malediction.
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They are regarded as destructive to the mores. According to a popular view, culture ought to defend itself against seduction by them, rather than profit from their controversial revenues.
2. Mathematical Approaches Games of vertigo and games of chance have been implicitly boycotted by sociologists and educators. The study of vertigo has been left to physicians and the computation of chance to mathematicians. ...
...
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...
Paralleling their work on games of chance, mathematicians have for a long time been conducting research of a very different kind. They applied themselves to the calculus of numbers in which chance plays no part, but which can be made part of a complete, generalized theory. ... Certain traditional games such as sliding-part puzzles or ring puzzles are also based upon problems or combinations of the same kind,... Recently, by combining the calculus of probabilities with topology, mathematicians have founded a new science, with many varied applications—the theory of strategic games.
Here the point is for players who are adversaries to defend themselves; i.e. in successive situations they are required to make a rational choice and appropriate decisions. ... It originates out of the desire to find a necessary, scientific solution beyond empirical dispute but at least approximately quantifiable. ... Psychological elements such as ruse and bluff enter into the calculations. ...
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...
Nevertheless doubt remains with regard to the practical implications of such speculation, and even as to its utility outside of pure mathematics. These calculations are based upon two postulates that are indispensable for rigorous deduction, and which, by definition, are never encountered in the continuous and infinite universe of reality. The first is the possibility of total information , using all the relevant data. The second is the competition between adversaries who always take the initiative with full knowledge of causes, in anticipation of an exact result , and are supposed to choose the better solution . In reality, however, on the one hand, the relevant data cannot be enumerated a priori, and on the other hand, the role of error, caprice, dumb luck, arbitrary and inexplicable decisions, preposterous superstition, and even a deliberate desire to lose, on the part of the enemy, cannot be eliminated. There is no motive that can absolutely be excluded from the absurd human universe. Mathematically, these anomalies do not engender new difficulties; they merely lead back to a prior case, already resolved. Humanly, however, for the concrete player, it is not the same, because the entire interest of the game lies precisely in this inextricable concatenation of possibilities.
Theoretically , in a pistol duel, where both adversaries are walking toward each other, if one knows the range and accuracy of the weapons, the distance, visibility, relative skill of the duelists and their degree of calm or nervousness, and provided it is possible to quantify these varied elements, it can be calculated at what moment it is best for each of them to squeeze the trigger. It is a matter even for aleatory speculation, in that the facts are outside of agreed-upon limits. However, in practice , it is clear that calculus is impossible, because what is needed is the complete analysis of an inexhaustible situation. One of the adversaries may be nearsighted or suffer from astigmatism. He may be distraught or neurotic; a wasp may sting him; he may stumble over a root. Finally, he may want to die. Analysis is
[173]
never adequate, except for the bare bones of the problem. Reasoning becomes fallacious as soon as the problem's original complexity is discovered.
In some American stores, during sales, the articles are sold the first day at 20 per cent off list, 30 per cent the second, and 50 per cent off the third day. The longer the customer waits, the more he saves on his purchase. But at the same time his possibility of choice is diminishing, and the desired commodity may no longer be available. In principle, if the facts to be taken into account are limited, it is possible to calculate on what day it is better to buy such and such an article in terms of its relative desirability. However, it is likely that each customer makes his purchase consistent with his character—without waiting, it he regards obtaining the desired object as primary, and at the last moment, if he is trying to spend as little as possible.
Herein lies the irreducible element in play, inaccessible to mathematics. For one does not play to win as a sure thing. The pleasure of the game is inseparable from the risk of losing. Whenever calculation arrives at a scientific theory of the game, the interest of the player disappears together with the uncertainty of the outcome. All variables are known, as are conceivable consequences. In card-playing, the game ends as soon as there is no longer any uncertainty about the cards dealt. In chess, the player gives up as soon as he becomes aware that the outcome is inevitable. In the games that they are addicted to, African Negroes calculate events as carefully as von Neuman and Morgenstern calculate structures requiring a peculiarly more complex mathematical system.In the Sudan the game of Bolotoudou, analogous to tipcat, is very popular. It is played with twelve little sticks and twelve pebbles, which each player places in turn on thirty boxes arranged in five rows, six to each row. ... Champions have their own equipment, which as part of the family inheritance is transmitted from father to son. The initial disposition of the pieces is of great importance.
[174]
The possible combinations are not infinite. Furthermore, an experienced player frequently stops the game whenever he recognizes that he is virtually beaten, before his defeat is apparent to the uninitiated. ... No one takes much pleasure in profiting from the inexperience of a mediocre player. On the contrary, he is eager to teach him the winning maneuver, if he does not know it. For the game is above all a demonstration of the superiority and pleasure derived from testing one's powers. There must be a feeling of danger.
Mathematical theories that seek to determine with certainty, in all possible situations, which piece to move or which card to put down, are not promoting the spirit of the game but rather are destroying its reason for being. ...
It is not probable, but it is possible and perhaps theoretically necessary that there should be such a thing as an absolute chess game, i.e. one in which from the first move to the last no stratagem should work, since the best possible move is automatically neutralized. It is not too farfetched to suppose that an electronic computer, having exhausted all conceivable combinations, could construct this ideal game. However, one would no longer be playing chess . The first move alone would determine the winner or perhaps the loser of the game.
The mathematical analysis of games thus turns out to be a game in itself which has only an incidental relationship to the games analyzed. It would exist even if there were no games to analyze. It can and must develop independently, gratuitously inventing ever more complex situations and rules. It does not
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have the least effect upon the nature of the game itself. In effect, mathematical analysis either ends in certainty, and the game loses interest, or it establishes a coefficient of probability which merely leads to a more rational appreciation of the risks assumed or not assumed by the player, depending upon his prudence or temerity.
Play is a total activity. It involves a totality of human behavior and interests. Various approaches—from psychology to mathematics and, in passing, history and sociology—by reason of their special biases have been unable to contribute anything too fruitful to the study of play. Whatever the theoretical or practical value of the results obtained by each of these perspectives, these results are still without true meaning or impact, unless they are interpreted within the context of the central problem posed by the indivisibility of the world of play. This is the primary basis for interest in games.
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