I'd like to see some discussion about the math of the game. Do you think that way? For instance, three tanks can deliver six points of hurt, while an invaded territory might be getting $4 guerrila. -or- how many units should be the minimum in an invasion? Do you think in terms of shield points that have to be withstood? I don't see the battles talked about in math terms. I'll bet that you can predict a stagnat line outcome, lets say seven lightfoots vs two tanks and a bot, plus $2 per round.

Do you think in math terms in this game, or is there a better way to see how things will go?

you can do the maths, but it will be different all the time, different layout, terrain etc..

Well, this is a math intensive game, and some calculations are necessary (like how many units you need to keep a newly invaded territory for example), but like Donut said there are way too many considerations that can't be solved just by looking at the math of it. It takes strategic sense, and looking ahead. Consideration of terrain, possible secret allies, how soon you can bring in reinforcements, how to bring a new front to the opponent, etc.

One rule of thumb I go by in the invasion question (what to invade with): I count up the damage output of all the enemy units within striking range of my invasion force, then I add the cash value of how much they get in Guerrilla to this damage total (because Tanks, Mortars, and LAVs give one damage per $). If I don't have more hitpoints worth of invading forces, I don't invade. Then you have to consider how you will keep the invasion past the first turn, though, how you'll keep reinforcements streaming in so they can't drive you out again with that much more advantage.

It's like chess, you'll learn to recognise certain positions and know how they're going to turn out. Often I buy units just because it "feels" right, and it invariably turns out to be the right decision.