I need help with how I can deepen my understanding of analyzing game complexity. Is there an official topic I need to look into that I'm describing:
Tic Tac Toe is really simple game. It has 5,478 legal state spaces mapped out. A priori, I would say this is the simplest sort of game people tend to play and I'd use it as a measuring stick to say "if a game is as complex as Tic Tac Toe, it's not really complex at all".
Jumping into video games - the original Pokemon game is in its most competitive format a 6 vs 6 battle. There are 151 Pokemon to choose from, with 4 available moves per Pokemon and a finite number of stat configurations - you only have 9 decisions to make at any given moment during battle. You could write a combinatoric formula to represent this game's "state space". I don't need to write it out to know it would generate a number faaaaaar larger than 5,478. Yet, I would make the case this game is not that much more complicated than Tic Tac Toe. If you play a few hundred games of Pokemon against a large enough group of humans, you will eventually uncover "patterns of play" much like you will in Tic Tac Toe. These "patterns of play" (pokemon used, moves used, turns when players switch out) make the game simple enough you can anticipate exactly what your opponent will do. But my point is, Pokemon still has a large state space (It might be as large as 10^20 or 10^40.), even if you measure some heuristic for each decision made and prune all the decisions which are decidedly "unwinnable", you will still have millions of potential states.
Then, to launch into even more arbitrary game types - you might have a game like Path of Exile, which has 1100+ passive skill tree nodes, an incredibly diverse equipment pool and monster variety - but the goal of the game is incredibly 'simple' if hard to define ('get the best items' or maybe 'clear an area the fastest for the highest item drop quality+quantity'). If you were to try to map the state space of this game, it would be enormous, to the point of dwarfing the state spaces of Chess and Go combined, games which we would consider "rich" and "complex" and "enduring".
My question is: How do you simplify the definition of complexity to the point where you can accurately put Pokemon and Path of Exile on a sliding scale between "not complex" (Tic Tac Toe) and "really complex" (Go). Is there a mathematical principle to refining "meaningful choice"? I would argue in Pokemon or Path of Exile, many decisions you make are meaningless because A) there are lots of decisions of equal heuristic value and B) there are lots of decisions where this only one immediate right answer, even in the 'long term'.
But I still don't think even if you did that exercise of pruning fruitless state spaces, you would get a number that approaches 5,478, or even smaller than the state space of a 19x19 Go board. My rambling's conclusion is: There's no "scalar concept of complexity".
Or is there?
Surprisingly, Go has the same number of states as we think there are atoms in our entire universe (10^80), this makes trying to understand complexity very difficult for me (is 10^80 even that impressive?). Is there anything more I can do to understand it better?