First, a game is a closed formal system that subjectively represents a subset of reality. Let us examine each term of this statement carefully. By 'closed' I mean that the game is complete and self sufficient as a structure. The model world created by the game is internally complete; no reference need be made to agents outside of the game. Some badly designed games fail to meet this requirement. Such games produce disputes over the rules, for they allow situations to develop that the rules do not address. The players must then extend the rules to cover the situation in which they find themselves. This situation always produces arguments. A properly designed game precludes this possibility; it is closed because the rules cover all contingencies encountered in the game.
Formal
By formal I mean only that the game has explicit rules. There are informal games in which the rules are loosely stated or deliberately vague. Such games are far removed from the mainstream of game play.
System
The term 'system' is often misused, but in this case its application is quite appropriate. A game抯 collection of parts which interact with each other, often in complex ways. It is a system.
Subjectively Represents
Representation is a coin with two faces: an objective face and a subjective face. The two faces are not mutually exclusive, for the subjective reality springs from and feeds on objective reality. In a game, these two faces are intertwined, with emphasis on the subjective face. For example, when a player blasts hundreds of alien invaders, nobody believes that his recreation directly mirrors the objective world. However, the game may be a very real metaphor for the player抯 perception of his world. I do not wish to sully my arguments with pop psychological analyses of players giving vent to deep seated aggressions at the arcades. Clearly, though, something more than a simple blasting of alien monsters is going on in the mind of the player. We need not concern ourselves with its exact nature; for the moment it is entirely adequate to realize that the player does perceive the game to represent something from his private fantasy world. Thus, a game represents something from subjective reality, not objective. Games are objectively unreal in that they do not physically re create the situations they represent, yet they are subjectively real to the player. The agent that transforms an objectively unreal situation into a subjectively real one is human fantasy. Fantasy thus plays a vital role in any game situation. A game creates a fantasy representation, not a scientific model.