A Monte Carlo Model of Lanchester's Square Law

F. W. Lanchester published, in 1916, the book entitled Aircraft in Warfare, the Dawn of the Fourth Arm (Lanchester, F. W. 1916. Aircraft in Warfare, the Dawn of the Fourth Arm. Constable, London.). In the course of the development of this work. Lanchester suggested equations, based upon probability analyses, that express various types of tactical situations. In the simplest form as proposed by Lanchester the theory, theorem, or law for a multiple-element engagement states “The over-all effectiveness of a given force equals the average effectiveness of the individual units multiplied by the square of the number of units engaged”. By multiple-element engagement is meant a situation in which each element of one force can fire on any or all elements of the other, as distinguished from a series of individual duels such as were experienced in early sword to shield warfare.