[gambler]

To the best of my knowledge, the only thing in SC2 that requires pixel-level precision is selecting units. Everything else can just as easily be represented as a fairly coarse grid with no loss of expressiveness. Buildings are explicitly snapped to a grid, and moving your units several pixels to either side simply doesn't matter. So calling SC2 "continuous" in terms of space is misleading.

I don't think there is anything that requires super-fast response times either, so you could conceivably get ~1 frame per second and not lose much information.

Well, IIRC, there are some visual indicators that rely on blinking, but I don't think they are crucial.

[smallnamespace]

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.

[gambler]

>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.