Having said that, the predictive power could largely come through the AI hacking into enemy communication networks, rather than running simulations, which I think is a lot more plausible.

You can also have a game system with random components, which an AI can predict. Even combat could work that way: you win if attack + (number of heads in five coin flips) > defense, and the AI can predict some of the flips.

<tangent> Hmm, I wonder if there could be an interesting way of turning this into a good game mechanic for a board game ... for example you have units (cards) with strength, and on each one you put a face-down token that may or may not have a "+1" on it. During a combat, reveal all tokens and apply their bonus, losers die/get damage as usual, survivors get new tokens. And of course some actions allow looking at tokens.