rule systems
there are three different rule systems that govern how games work. these systems make up the formal structure of the game. this is not a strict framework and some games may not fit the system.
the first rule system is the operational rules. they are the basic rules that describe how the game works, e.g. the game's manual.
the second rule system is the constitutive rules. they describe the basic mathematical structure that governs the game. they exclusively the describe the math, are not usually described the game's manual.
the third rule system is the implicit rules. these are the unwritten rules of the game. often, they are related to the context and culture surrounding the game.