The greatest problem with this RPS idea is that, for the progenitor of pike-horse-bow, it... does not work like that. At all.

Spoiler: How it does work
Show

All of the infantry, ranged and cavalry can have equal armor, and did have equal armor historically. Whether or not a particular individual had full plate was the question of whether or not he could afford it, not some restriction on archers not being able to function in full plate. At worst, archers opted to go without visors, but so did infantry.



Which means that defensively, they are all equal, unless we're concerned with early and high medieval periods, where archers can't use shields as well as other two. But even then, they can still opt to use them. The mostly didn't do so because they didn't need the shields.

The thing is, archers and infantry are deployed together. First two to four ranks of a shield wall are melee troops, the rest are archers, and archers can then fire between the heads of their friends and be covered from return fire by the meat and shield wall in front of them. This was a formation so effective, it was used at least from early medieval all the way to late, where it was replaced with other formation models that still combined melee infantry, archers and gunners.

This combined arms infantry block is almost impervious to frontal cavalry charge - the very heaviest cavalry will probably break it, but suffer horrendous losses, anything less will get torn to pieces. The role of cavalry is therefore twofold: 1) look for infantry that is badly equipped, out of formation and/or has low morale and frontal charge them to rout them, or 2) wait until the enemy infantry is engaged and then charge their flanks or rear. The third role is an emergent one from the enemy having their own cavalry - find said cavalry and kill it.

The only time you see archers operate separately from melee troops is when they have constructed some sort of fortification that will make it difficult to get to them (e.g. flanking archers at Agincourt and Crecy), because that small advantage is all they need. These archers are, after all, armored as heavily as anyone else, and sword is as good as a pollaxe when you are fighting three on one.

So, cavalry beats everyone, but only barely and often with losses that are too bad, and archer+infantry block wins in theory if their nerve and equipment is good enough and they don't get flanked.


So, if you want to have a game that has some sort of verisimilitude, you either have to assign arbitrary bonuses, or set up mechanics very specifically (and risk them falling apart). The tank triangle is a tad better, but you need to make it into a mobility-power-defense-cost-training time pentagon. You can have a soldier that has great attack power, excellent defense and good mobility, but the costs for his training and time required will be horrendous - because we're talking about European knights, or Mongol Keshiks at that point.

What all of this means is that, if you're running a game that tries to be somewhat realistic, you need to forget about RPS units, and start to think about RPS tactics and strategies. If your enemy rolls up and starts to capture your cities, you can try attacking their foraging parties, but it will leave you open because your troops are now dispersed, but if you have strong enough castles that may not be a problem because you have a month until you need to relieve that siege, and can make that month suck for the besiegers by starving them.

DnD is pretty good at doing this with caster-like classes (Tome of Battle is technically not casters, but...), you select your spells and can never have all of them ready, and if you do (sorcerers), there is some other drawback to it. If you are geared to fight things immune to fire, you can be badly surprised if one of them summons something that is immune to ice, if you have setup your spells to counter magical defenses, you will be far less effective against brute force opponents.

Where frustration happens is with builds that can't change their tactics well enough. If you have someone optimized to do bucketloads of fire damage and are confronted with a fire elemental, you may be out of options and resort to being far less effective. This is both a bug and a feature, a bug because it can be intensely frustrating, a feature because it makes the build you use matter more. Well, in theory. That also means you tend to see this less in DnD (outside of fairly highly optimized builds) because it requires your players to actively make a heavily specialized build for it to be apparent.