Combat mechanics are GM fiat, that is the bottom line. Even if they are equations, those equations are designed by the GM with their own particular brand of bias and blindness, and (as far as I've seen) only serve enshrine and magnify logical problems rather than alleviate burden.
Chief's description is basically the standard, adjusted in exact flavor by individual DMs. For me, I write up a cheatsheet of the advantages and disadvantages each side has in a conflict. Given that, I can write a skeleton of how those advantages and disadvantages between sides interact that defines the scope of the battle. Given that skeleton, I can then put more flesh on the bones as needed for narrative and descriptive purpose.
In the example you've given, it's really crucially important to note that most AR games are not scoped at that level. Most ARs take the position that a front is big enough, reinforcements are good enough, and enough battles take place that every battlefield situation will occur simultaneously. Two evenly matched sides do not get halved at the end of the day, they skirmish back and forth over ground, the turn of chance creating vicious defeats and hard-won victories on both sides. In the end it's net zero, no territory lost or gained, but it's a much more bitter net zero than just burying everyone with odd numbered both years.
Now, there are some ARs that do use finite numbers of units fighting finite numbers of units. I'd strongly advise against using the GalactiRace system for doing so unless you're dead certain, have meditated long on the issue, and have struck a deal with one of the dead Godflesh aggregates who wait within the dreamveil and whose names structure the void between voids. I'd strongly advise against the spires system of infantry combat, period.
In GR ground combat, you can have roughly the situation you described above. However, in most cases, units will never be lost. It's important to remember that war is NOT a competition to kill the most people, it is a conquest to take the most COWS ground from your enemy. Your main goal, as with most ARs, is to gain territory. If the advantages your troops have outweigh and/or cancel the enemy advantages to a sufficient degree, then you gain territory and the enemy is pushed back. Thematically, this involves some of them dying, but from a mechanical standpoint these numbers are small as an intelligent commander will pick their battles and pull back before being crushed. Massive casualties in GR combat only occur when one side decides they have to hold ground at all costs, or a side decides to push a campaign at gale speed.
In GR space combat, things are much different. The numbers of units are small, and you can get into exactly the situation you described above. Teams make tactical decision on what to do with their units, but at the end of the day it's loadout pitched against loadout, but even then you have to consider what the units actually are. Two perfectly matched forces butting heads generally won't end up with 50% mutual losses. If they're individual humans with the ability to retreat, then you might have minimal or no losses. They value their own lives, and without the opportunity for a decisive victory will not just slug it out to X point and then politely agree to stop. Tanks, however, in the same situation may inflict heavy mutual casualties, beyond 50%, as the game is very much who gets to shoot who first. If the two sides aren't allowed retreat, then consider the fact that evenly matched forces will turn into a meatgrinder. It's not 50% losses you're looking at, but a no survivors or wounded only scenario.
The boildown of this is you just can't boil down the fighting with a few simple axioms. It depends on what kind of mechanics you're using (finite units, infinite fronts, or a combination), what units are actually involved in combat, and the base nature of the game.