Manovich (2001) defines the “algorithm” as the underlying structure of the videogame, the structure in which players strive to uncover in hope of mastering the game. The algorithm is not only the underlying code of how the game functions, but how this code reveals itself to the player, through the various worlds and puzzles it generates. In seeking to discover the algorithm, the player “gradually discovers the rules that operate in the universe constructed by the game” (Manovich, 2001). It is through this chapter that the concept of the ‘algorithm’ will be discussed by understanding the game as a paradigm. Through an analysis of the game as a paradigm, it can be seen how the game is constructed of various syntagmatic relationships. Syntagmatic relationships are defined by Chandler (2007) as “the various ways in which elements within the same text may be related to each other”. By discussing videogames in this way, it is possible to see how various syntagms of play can arise within the game world. Each syntagm can be related to one another but consist of various motivations by the player. It is through defining these motivations that two types of play are defined, that of ‘purposeful play’ as intended by the game designer, in contrast to ‘appropriated play’, created by those players seeking to decode the algorithm in a different way to which it was originally intended. These new play types rework and build upon Caillois’ (1958) definitions of ruled and free form play, or “ludus” and “paidia”, thus renewing their uses within videogame environments. Finally, this discussion recognises that videogames are played within a social setting, an idea I will term the ‘cultural logic’ of the game. In understanding how players are part of a wider gaming culture, both in single player and multiplayer gaming scenarios, the motivations for various types of play and their outcomes become situated within the wider context of game play itself.