This paper deals a novel variation of the versatile stochastic duel game, which incorporates an energy fuel constraint in a two-player duel game. The energy fuel not only measures the vitality of players but also determines the power of the shooting projectile. The game requires players to carefully balance their energy usage while trying to outmaneuver their opponent. This unique theoretical framework of the stochastic game model provides a valuable method for understanding strategic behavior in competitive environments, particularly in decision-making scenarios with fluctuation processes. The proposed game provides players with the challenge of optimizing their energy fuel usage while managing the risk of losing the game. The unique rules and constraints of the game in this research are expected for contributing insights into the decision-making strategies and behaviors of players in a wide range of practical applications.