Can Real-Time Strategy games be ever solved?
It looks like there are elements of (pseudo)randomness in StarCraft.

Of course, this does not seem like a major property and you can ask for solving the game without this feature. Then you end up with a very deep game tree that probably does not have any nice mathematical property or symmetry that would help you to effectively handle it. This is where it differs from the trees that arise from mathematical games.

You can use game theory to play StarCraft well (Monte Carlo, maybe?), but unless there is some strong form of rush that would quickly cut complexity of the tree, I am skeptical about solving it.