[The Romans] do not begin to use their weapons first in time of war, nor do they then put their hands first into motion, while they avoided so to do in times of peace; but as if their weapons did always cling to them, they have never any truce from warlike exercises; . . . nor would he be mistaken that should call those their exercises unbloody battles, and their battles bloody exercises.— Flav...

Received 30 October 2016 Accepted 15 December 2017 Abstract—Geometric Brownian motion with decision boundaries is used in modelling combat effects such as probability of winning a battle and duration of a battle. We verify that it is possible to construct a model and analytical mathematical formulas for these quantities. Variables of the model are force sizes at the beginning and at end of a ba...