This is the lesson that makes you dangerous. We know a battle compares the attacker's total attack points (call it A) against the defender's total defence points (call it D). Now we learn precisely what happens to each side, because there are exactly three outcomes and each has a clear, fair rule. Once you can picture all three, you can plan any attack down to the last surviving soldier. Let me walk you through them with real numbers, using a town defended by 5000 defence points as our example throughout.
Outcome one: the attack falls short (A less than D)
Suppose you send five Assault troops, each worth 500 attack, for a total of 2500 attack points against that 5000-point wall. Your 2500 is less than their 5000, so your assault fails. Every one of your attacking soldiers dies - remember, there is no retreat - and the defender loses troops worth your attack total in defence points. Your 2500 attack wiped out 2500 of their 5000 defence, so the defender is left standing but has lost half their wall. You achieved nothing but softening them up, at the cost of your entire force. This is the fate of every under-strength attack, and it is why you always check the wall first.
Outcome two: a perfect tie (A equals D)
Now suppose you send five Spec Ops, each worth 1000 attack, for a total of exactly 5000 attack points against the 5000-point wall. The two numbers are equal, and the result is mutual annihilation: both armies are completely destroyed. Every attacker dies and every defender dies. If the defender was an occupier holding someone else's town, the town goes free because the garrison is gone; if it was a town defending its own ground, that town is simply left with no soldiers at all. A tie leaves nothing standing on either side - dramatic, total, and occasionally exactly what you want if your goal was to break a garrison rather than hold the town.
Winning survivors occupy - by the dearest first
When you win, your losses are counted in attack points, and the game spends your most expensive troops first to pay that bill. So your cheap Assault soldiers tend to be the survivors who stay and occupy, while your priciest Spec Ops are the first to fall. It sounds harsh, but it means the soldiers left holding your new town are your most affordable ones - a small mercy built into the maths.
Outcome three: the attack breaks through (A greater than D)
Finally, suppose you send six Spec Ops, each worth 1000 attack, for a total of 6000 attack points against the 5000-point wall. Your 6000 beats their 5000, so you win the field. The defender is wiped out entirely. But you do not escape free: you lose attacking troops worth the defender's total in attack points. Their wall was worth 5000, so 5000 attack points of your force die - that is five of your six Spec Ops. The one surviving Spec Op marches into the town and holds it. You have captured the town with a single soldier left standing, and that soldier is now your occupying garrison. This is the textbook conquest: send more than enough, accept that the wall will cost you dearly, and leave whatever survives to hold the ground.
Sit with those three examples, because they contain the entire art of attacking. Too little (2500 against 5000) and you lose everything for nothing. Exactly enough (5000 against 5000) and both sides die. More than enough (6000 against 5000) and you win, but the wall still takes a heavy toll on the way down. Notice the tension the system creates: you want to send enough to win comfortably, but every extra soldier over the line is one you might have kept for the next campaign. Overwhelming force wins cleanly but wastefully; a narrow win leaves few survivors to hold the town. Threading that needle is what separates a good commander from a lucky one.
Winning the field is not always holding the town
There is one more subtlety worth knowing. If your attack points beat the wall but the losses leave no survivors - for instance a tie, or a win where the whole force is spent paying the defender's toll - then you crushed the defenders but have nobody left to occupy. The town is not captured; it simply ends up free again. To actually hold a town you must win AND have at least one soldier survive. Always send a margin beyond the bare minimum if occupation is your goal.
That is the combat engine in full, and it never changes no matter how large the armies grow. Attack total against defence total; fall short and you are wiped while chipping their wall; tie and both sides die; break through and you win but pay the wall's worth in attackers, with your dearest troops falling first and the cheap survivors staying to occupy. Everything else in this chapter - marching, occupation, liberation - is built on top of this one clean rule. Master it, and you will never again send an army to a fight you did not already understand.