Okay so maybe I'm showing a little bit if ignorance here but my understanding is that the three core pillars of play in any RPG are generally combat, exploration, and social. Combat being the killing of things, exploration involving travel but also puzzles, traps, etc., and social being, well, social.

Most of the big name games prioritize combat, but there are also plenty of games with "social combat" systems and games with in-depth travel mechanics.

My main question is this: is there any game that actively attempts to treat each pillar with the same or relatively equal complexity and depth? There are, of course, plenty of rules light games where everything is resolved with a roll of the dice/flip of a coin, or no randomization at all and so I want to clarify that is not what I mean.

I'm specifically looking for games where eqalizing each pillar is a core philosphy of the game's design, whether explicitly or implicitly.

This is mostly out of curiosity.

I feel that Legends of the Wulin does one of the best jobs of this, and the way it manages it is a way that you wouldn't expect.

It works through the damage system.

Heroes of the Wulin don't have 'hit points' or 'life'. They're too awesome to do anything as mundane as die. How this is handled in game is that all consequences are through the application of conditions to a character, and the condition does not have to be the same as the way it was acquired.

As an example, say a PC loses a fight badly. They escape, but take a severe cut to the face. It heals but leaves them with a nasty scar that gives them penalties on social rolls in the future. Going the other way, another character is out-maneuvered socially and is shunned by the person they were courting. This strikes at their ego and them questioning their abilities means that they take penalties on combat rolls.

I think the 3 pillars thing was invented for D&D, possibly even as recently as 5th edition D&D.

That's actually really neat! Definitely adding this to my reading list.

Well, there's Exalted, for one. Only about a third of the Abilities are useful for combat (sort of. Martial arts exist that mess with this a little), and the 3e rules for social influence, Sorcerous Workings, investigation and fact introduction (those last three are intended to be used together [sort of]) are about as in-depth and have about as much impact on the world around you as the rules for combat. It helps that you're allowed to (and really should) make characters that are good at wildly-different things.

The best editions of Shadowrun (3 and 4/20a) do something similar. Actually, heist games are particularly good for this. Everyone steals, bur everyone needs to bring something unique to the table to make the heist work, including the option to shoot your way out uf things go badly.

The one ring. Has specific mechanics for each of those. Because travelling, combat and social meetings were also core components of the source material.

I don't think you're wrong, but it applies to, maybe not all, but certainly the majority of games, right? Like, say there's an ambiguous conflict. Tension. Some drama between the players and their ending goal.

How do you resolve that tension in a way that doesn't fall under oner of these categories? If there's an enemy, you fight them. If there's social pressure, you maneuver, make allies, participate in the art of persuasion. "Exploration" does often tend to be a catch-all for a few things that don't fall under these two, like deciding to sabotage the operations of an enemy without outright violence or conducting an investigation into the social pressures the players are facing, but they actual play of these things seems close enough, at least to me, to fall under the same category.

If you want to divide the world that way then obviously you'll manage to squeeze everything into those groups. The question is then why did you decide those groups were right in the first place?

Yes you can divide Call of Cthulhu into exploration mostly, social partly and combat a tiny bit. But it totally misrepresents the tone of the game to do so. Really you've got investigating and escaping and struggling.

Maybe there's really 5 pillars? Three is as arbitrary as the specifics of which three.

One Ring would also be my first thought.

Broken Empires by Trevor Duvall, has everything cover. It's a giant of a book with rules for almost everything. Combat, social interactions, travel. You name it.

Well, there's a lot of ways to do that. The most common is to have a universal resolution system that doesn't treat combat any differently from other activities. In Burning Wheel and derivatives like Mouse Guard (and other systems with universla resolution like QuestWorlds) there's several different "grades" of resolution - sometimes you just use a simple roll, sometimes you bring out the big, step-by-step "combat" system. This means that, when it seems appropriate, you can model a debate or a trial, or any activity, really, with the exact same level of depth and complexity as an important combat.

The other obvious option is to build separate minigames for different activities. The One Ring is a good example of a system that has somewhat elaborate travel mechanics to emphasise the physical and mental toll of travel that you see in the source material. Similarly, there's a subsystem for important negotiation scenes too.

That said, I think your premise might be slightly mistaken. A game having complex mechanics for something doesn't actually mean that the game "prioritizes" that thing - it just means that designers thought that modeling that particular thing with complex mechanics is more fun. Universal resolution systems like Burning Wheel are interesting, but in practice, most players find that modeling a debate or a sea journey, say, with the same level of mechanical detail as a combat encounter isn't very fun: it feels cumbersome and the connection between the fiction and mechanics begins to unravel. So a lot of RPGs have very simple mechanics for social roleplay, but that doesn't mean that it's out of focus in actual play. It's just that social roleplay, for instance, is often more fun and exciting when you don't use a complex subsystem to handle resolution.

>my understanding is that the three core pillars of play in any RPG are generally combat, exploration, and social.

No. Some RPGs, yes, but not all, not "any".

As far as games that have systems for all of that, Traveller, but combat is quite dangerous in most versions.

I confirm that there was no mention of the three pillars in 3e and 4e D&D, they were invented in 5e.

Lupus in Tabula is a simple competitive role-playing game, far removed from your vision. Those pillars aren't generic; there are games where you don't kill anyone who tries to steal from you, and the enemy doesn't want to kill you (like Lady Blackbird).
Try looking at the Free League games; they look similar but are very different. Look at Vaesen, but also Dragonbane, which is anything but a D&D clone.

What I can say is that many games allow for more of a focus on storytelling, and if combat happens, it is part of the storytelling instead of being its own game mode.

I wouldn't say that combat, exploration and social encounters are equally balanced because these games depend highly on what the players choose to do, which means having tight control over equal focus of those things is antithetical to the system.

For the record, I mainly run PbtA/FitD games, and also, sometimes, Dragonbane, Coriolis, Spire, Otherscape, and Savage Worlds (SWADE).