In the model of the OK Corral formulated by Williams and McIlroy
lines of gunmen face each other, there being initially m on one side, n on the other.
Each person involved is a hopeless shot, but keeps firing at the enemy until either he
himself is killed or there is no one left on the other side.’ They are interested in the
number S of survivors when the shooting ceases, and the surprising result, for which
they give both numerical and heuristic evidence, is that when m=n,
as m→∞ (where E denotes expectation).
It is the occurrence of this curious power of m, rather than any application to real
gunfights, which makes the Williams–McIlroy process of interest. The purpose of this
paper is to give an essentially elementary proof of the fact that if m and n are not too
different, then S/m3/4 has a simple asymptotic distribution that leads at once to (1.1).