A Mathematical Model of Game Refinement

Abstract

This paper explores a mathematical model of game progress and game refinement. 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 support the effectiveness of the proposed theory while showing some data from well-known games. © Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2014.