Even with the restrictions you put in place, SC2's state space is much larger than any board game.
A typical game might last 15 minutes = 54000 60fps frames and a typical map is larger than 10k x 10k in terms of 'coarse units'.
For any given frame of animation there are at least a million valid actions - if you have 10 units then you can move any subset of those units to any place on your screen.
>Even with the restrictions you put in place, SC2's state space is much larger than any board game.
That depends entirely on how you represent it. You're forgetting that there are plenty of AIs that actually play the game right now. They just don't use the same kind of "interface".
>For any given frame of animation there are at least a million valid actions
That's Google's marketing cool aid. "Actions" that produce the exact same result cannot be meaningfully counted as separate actions, especially when you're trying to compare them to board game moves.
A typical game might last 15 minutes = 54000 60fps frames and a typical map is larger than 10k x 10k in terms of 'coarse units'.
For any given frame of animation there are at least a million valid actions - if you have 10 units then you can move any subset of those units to any place on your screen.