This post wasn't well thought out or explored.
After reflecting on this more I have reformulated this information into a new post:
Describing With Set Theory:
We can attempt to describe a game of tic-tac-toe by abstracting various properties of a game and using what we know about the branching complexity of the game.
The total possible state space for a game is 9!
Here we describe the GameBoard with 9 possible locations:
set of coordinates: (x,y) => 2
set of players: (X,O) => 2
set of 'places': (00,01,02,10,11,12,20,21,22) => 9
set of game-ending-moves: (5,6,7,8,9) => 5 [halting states]
We also assume:
The median number of moves in a game => 7
Vector size of a: game-action: (1,2,3,4,5,6,7,8,9) => 9
NOTE: ^ each move has probability of affecting 1 of 9 places on the board
Applying Big O theory
If we can assume the computational complexity of a game has Big O of 2^N
Tic-tac-toe has a Game-Tree Complexity of '5'
So we use N=5
9! / 2^5 = 2 * 2 * 9 * 5 * 7 * 9
Read about Computational Complexity here: https://en.wikipedia.org/wiki/Game_complexity#Computational_complexity
UPDATE: thinking more about this
The total permutations of games is 9! - which makes the assumption that every game will have 9 Total moves (not 7 as in the above example)
I'm not really sure how to correct this - the calculation of the total 'degrees of freedom' when combining factor-sets still seems like a good aproach, but perhaps there is some redundant information resulting from the choice of factors.