Focus Fire Stage 2: Playing with Fire

Now, to define a mathematical strategy for the Focus Fire game... As defined last time, there will only be two types of units in this game, and there will be nine units total per team. Since its an odd number, that means my team will be dominated by one type of unit--let's say Fire for the sake of discussion, because the exact inverse discussion would hold true if it was Ice.

Intuitively, I know all the Fire units will be most optimal attacking the same target. I also know that target should be an Ice unit (if any exist), because Fire has an attack bonus against Ice and Ice has an attack bonus against Fire. In other words, Ice opponents are both the most vulnerable and the most threatening. (This would be a little more complicated using the Paper-Rock-Scissors architecture where vulnerability and threat were divided between different units; perhaps I'll run that scenario for the next game.)

So, with the majority of the team--the Fire units--properly assigned, the only open question is: what do the minority? Do the remaining Ice units assist the Fire units so that the team maximizes its focus, or do they attack their own counterparts (enemy Fire units) so they gain their attack bonus and the team maximizes its gross damage? It's a simple binary decision, but I can't see a definite advantage to one or the other. Which has the best effectiveness? Does that depend upon team makeup at all?

Since it is only a binary decision and since it could possibly vary across teams, I'm going to make strategies for both options. Then, I'll program computer algorithms to play each option against the other across several different team permutations and see what happens. Hopefully, that should answer some questions!