A mathematical model of game refinement was proposed based on uncertainty of game outcome. This model has been shown to be useful in measuring the entertainment element in the domains such as boardgames and sport games. However, game refinement theory has not been able to explain the correlation between the popularity of a game and the game refinement value. This paper introduces another aspect in the study of game entertainment, the concept of “attractiveness” to reasonably explain the sophistication-population paradox of game refinement theory.