In the emerging academic field of game studies, Roger Caillois' Les Jeux et les hommes has already received the status of an obligatory reference. It is honoured as one of the few classic texts in game theory, but some also argue that it is not useful for analysing digital games. Gaillois' book is of particular interest for cultural theorists, though, because it presents a theory of games and play while also addressing the meaning of play. After analysing more closely why Caillois' theory falls short when it is applied to digital games, we suggest a slight modification of its categories. Starting from the four game dimensions outlined by Caillois competition, chance, simulation and vertigo - and his two modes of playing, paidia and ludus, we build on his theory by distinguishing two additional game characteristics, called repens and repositio. Both deal with the internal, temporal organization of a game. Repens is a specific characteristic of games that appeals to the player's desire to discover, explore and get to know the surprises a game has in store and to make progress by learning from these surprises. Repositio denotes complementary experiences: having to retry, return, replay and repeat a certain action while getting better at it with every try. The balance, or unbalance, between repens and repositio, as characteristic elements of many digital games, determines to a large extent their attraction. Finally, repens and repositio are not only indicators of fun in the playing of digital games; they also hint at basic elements in learning theories and social theory. The study of the interplay between repens and repositio can help in clarifying the possibilities and limitations of digital games for learning purposes.