In the fundamental stochastic duels, the interfiring time means the sum of the time to load and the time to aim. However, in realistic stochastic duels, the interfiring time is related to the time of supplying ammunition. In this article we study the effect of ammunition supplying times on the stochastic duels. Suppose that the ammunition supplying time is negative exponential and the other conditions are the same as those in the fundamental stochastic duel. The marksman firing at a passive target is considered and the characteristic function of the time to a hit is developed. The effect of ammunition supplying times is analyzed by solving the stochastic duel with the situation where one duelist has negative exponential supplying times while the other has unlimited ammunition. The winning probability of the given side is derived and some interesting results are obtained.