I'll reply to both of your responses in one go. As someone who's generally concerned about the existence of free will, I have understood the fundamentals of chaotically deterministic systems for a while. es, any multiplayer game, when you take into account the player actions, is an incredibly complex system. So is driving a car, or modelling the airflow over a 3D structure, or highly refined stress analysis on even a relatively simple structure. Yet me already have computer programs (in the case of the latter two) that perform those calculations, and an AI that can do the latter. We use computers to model chaotically deterministic systems already, and an AI to control the LoL bots would be no different. If LoL ever becomes the kind of phenomena that chess is, I would not at all be surprised if an AI was developed to test the ability of AI to beat humans. If the designers thereof wanted to make their job easier, they might make separate, autistic AI for each class. But ultimately combining them would be a relatively simple matter. It's just a question of economics and interest. Doing that would be a major effort of software engineering, cost shit tons of money, and require a whole lot of dedicated computer hardware.
Mathematical modeling is the best way to account for the interaction of champions and underlying game mechanics. What it wouldn't do is what the AI(s) described above would: model player choices. And this is fine, because - and I cannot stress this enough - balance has nothing to do with player choices. A champion is balanced based on what it brings to a game, the time frame in which the champion brings it, and how hard it scales off of input gold. Modeling how a champion best puts it's gold income to use allow one to tweak and shift that best practice to align with how one wants a champion to best utilize it's gold income. I'm not proposing Riot try to create an AI akin to Deep Blue; I'm proposing that Riot define a concrete, mathematical basis for their game so that they stop subjectively balancing their champions and instead say "It is balanced, y'all are just doin' it wrong. And here's the math to prove why we're right." They start be defining a value (I'll say gold value) for every champion statistic: max health, attack delay, the various types of CC (i.e. an Entangle effect is considered to bring X gold per second), etc. Then develop mathematical equations which model every mechanic in the game in their most finite form, i.e. a function to define a geometry-targeted, circle-AoE skillshot (think Eye of Destruction), with inputs of projectile speed, projectile trajectory, damage (if any), CC (if any), CD, Range from champion to AoE center, AoE radius, visual indicator (if any), etc. Each of these inputs would, in turn, have a defined, concrete value. Rather than use "id est" again I'll just put the elaboration in it's own sentence. Every type of visual indicator would have an equation to model how it contributed to spell's gold value, *but this equation, and the value derived therefrom, would be independent of the spells it might be used on. To properly balance a game, one defines each aspect of that game which the developer has control over (and this does not include player action) abstract from every other aspect, but in a consistent manner. Then you combine them. That's how one model's any system.