For fixed accuracy functions, let Gnm be a discrete-fire (silent, noisy, or silent-noisy) duel in which the amounts of ammunition available to the two players are n and m, respectively. As n and m both become large, a class of ‘ε -optimal' pure strategies (with support (anm , 1)) is derived. If vnm denotes the value of Gnm , the asymptotic relationships among the quantities n, m, vnm , and anm are investigated.