Game refinement is a unique theory that has been used as a reliable tool for measuring the attractiveness and sophistication of the games considered. A game refinement measure is derived from a game information progress model and has been applied in various games. In this paper, we aim to investigate the attractiveness of Pokemon, one of the most popular turn-based RPG games. We focus on catching Pokemons which are important components in the game. Then, we propose a new game refinement model with consideration on a prize cost and apply it to catching Pokemons. We analyze in every generation of the game. Experimental results show that a game refinement value of catching Pokemons which has been changed many times tries to reach to an appropriate range of game refinement value: 0.07 − 0.08 for which previous works have confirmed.