Agree, I think countries already run their simulations, and when they believe they are on the winning side, they invade. Doesn't matter if the simulation is rolling a dice.

If you don't invade, you haven't taken control.

Or putting it from other perspective, you could run the simulation between 2 parties, be the winner and "impose" your will. But I don't think that the other side will now leave their houses and leave their own city voluntarily, at that point you need to invade anyways.