I was thinking specifically of how a lot of strategy games have a triangle of infantry-cavalry-archers, where infantry armed with polearms beat cavalry, cavalry beat archers, and archers beat infantry. However, this can also be applied to the warrior-thief-mage trio, where the warrior's armor protects them from the thief's blows, the thief is able to get the jump on the mage and take them out before they can cast a spell, and the mage's spells can blast a warrior before they get close.

It kind of surprises me we don't really see more of this in D&D, considering it started as a modified wargame where you control a single soldier instead of whole armies. I'd like to see a lot more stuff like this. I think it works best when it's an emergent property of the mechanics, rather than specifically giving bonuses or penalties to certain characters. For example, cavalry are typically an emergent counter to archers simply because their faster speed lets them get into melee range to butcher the archers, especially when the archers are mechanically represented as glass cannons. But often pikemen have to be given special bonuses that specifically target cavalry instead of it being emergent based on more general traits that they have.

I was thinking about this specifically in the context of D&D 5e, possibly for a homebrew project, but as I was reading through the TV Tropes page on this subject I saw this blurb:
Quote Originally Posted by TV Tropes
Nonmagical combat in 3rd Edition has a subtle version of this. Most Uberchargers (characters who rely on massive speed and damage) lose to Lockdown tactics (combining long-reach weapons with Counter Attacks that halt movement), which in turn has little defense against ranged combat. Other combat styles have less consistent properties, but are generally weaker.
My knowledge of 3e is fairly sparse, but I'm intrigued that there seems to have been shades of this rock-paper-scissors arrangement, and specifically one that matched pretty well with the infantry-cavalry-archer triangle. 5e seems like it has some of the pieces to recreate this, but a lot of it is locked behind feats (PAM and Sentinel for the Lockdown characters, GWM and maybe Mounted Combatant for advantage for the Ubercharger, and so on).

I think I mostly just want to explore this topic and see how it might be handled in other systems and what sorts of tweaks one could make to D&D 5e to make this a bigger part of the game. And again, I'm more interested in when these tactical counters arise as emergent aspects of the rules; X doesn't get a bonus against Y specifically, it's just that X gets a bonus that happens to make them particularly effective against Y. For some good examples of what I'm talking about, you can look at the Slayer class (forum thread, homebrew doc) that I wrote up a while back (still WIP); the Demon Slayer gets zero bonuses against demons or fiends, the Dragon Slayer gets zero bonuses against dragons, and the Goblin Slayer gets zero bonuses against goblins (the Witch Slayer is admitted a bit more targeted specifically to spellcasters). But look at the bonuses they do get, and why those bonuses might make them more effective at fighting their chosen prey. (You can probably skip reading the base class and go straight to the subclasses if you just want to see how they counter those types of enemies.)

I'm not saying it has to be just like that, but that's one example where the character being good at fighting a specific type of monster is more of an emergent property of the bonuses they get, instead of getting a bonus specifically against that monster. Charging into a line of pikes is still a bad idea even if you're on foot, it just so happens that it does a particularly good job of countering cavalry whose whole strategy is to run up to enemies really fast and stomp them.