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http://onlyagame.typepad.com/only_a_game/2006/04/thecomplexity.html

In 1958, the eclectic French intellectual Roger Caillois identified four patterns of play - Agon (competition), [Alea]? (chance), [Mimicry]? (simulation), and [Ilinx]? (vertigo), about which I have written previously at some length. Caillois' model for play also includes an axis of distinction, between the anarchy of spontaneous play called Paidia, and the more formal, rule-focused state he refers to as ludus. He describes ludus as follows:

A primary power of improvisation and joy, which I call paidia, is allied to the taste for gratuitous difficulty that i propose to call ludus, in order to encompass the various games to which, without exaggeration, a civilising quality can be attributed…

In general, the first manifestations of paidia have no name and could not have any, precisely because they are not part of any order, distinctive symbolism, or clearly differentiated life that would permit a vocabulary to consecrate their autonomy with a specific term. But as soon as conventions, techniques, and utensils emerge, the first games as such arise with them: e.g. leapfrog, hide and seek, kite-flying, teetotum, sliding, blindman's buff, and doll-play. At this point, the contradictory roads of agon, alea, mimicry and ilinx begin to bifurcate. At the same time, the pleasure experienced in solving a problem arbitrarily designed for this purpose also intervenes, so that reaching a solution has no other goal than personal satisfaction for its own sake. 

This condition, which is ludus proper, is also reflected in different kinds of games, except for those which wholly depend upon the cast of a die. It is complementary to and a refinement of Paidia, which it disciplines and enriches. It provides an occasion for training and normally leads to the acquisition of a special skill, a particular mastery of the operation of one or another contraption or the discovery of a satisfactory solution to problems of a more conventional type.

At this point we must pause and clarify that in talking about ludus here we are talking specifically of Caillios’ ludus; the term can and is applied by other people, and therefore like all words has diverse meanings and definitions. Here we are talking solely about what Caillois meant when he said ludus (or what we suppose that he meant), and looking at what this means in the context of the modern games industry. 

A few key phrases are worth repeating, in order to understand what it was that Callois was speaking of: