This paper explores a mathematical model of game progress. We claim that a realistic model of the game progress during the in-game period is not linear but exponential. The second derivative value, i.e., acceleration in the sense of dynamics, is derived from the model and we propose to use the value as a measure of game refinement. This is because acceleration of game progress should be related to the emotional impact in our minds, as thrill or engagement in games. We also evaluate well known games using our theory like sport games, that would further be classified by the rule to finish the game. It is expected that the game refinement theory will be widely used as a tool to assess the quality of various types of games as a new game theory.
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