Two armies in the field Assume two armies of unequal size are fighting, where each soldier on both sides is of equal ability. Assume that each soldier is capable of taking out an enemy soldier each [unit of time], and that the battle continues until one side is annihilated. How would you determine the size of the surviving army? There are no volleys, or distinct actions by either army -- consider a "fire at will" scenario. That is, how would you determine how many soldiers would a larger army have left after the lesser army is annihilated, all things being equal, and knowing only the size of each army?

You appear to be describing a situation modeled by Lanchaster's linear law, where the result is the larger force has the difference in numbers surviving. With firearms, this corresponds to the results of unaimed fire.

You should also be aware of Lanchester's square law, which applies when there is aimed fire.

In modern warfare, there is usually a mix of aimed and unaimed fire, so powers between $1$ and $2$ can be more accurate.