Some people have said that the AI factions go north first becasue that is where the original Latium province is (Gotland). In RTW original game the goal for every faction was to take latium. I wonder if relocating Latium would have an effect? Maybe put it as Byzantion or some other centrally located province.
Furthermore, with the Hai they have war with a neighbour who is poorer than them and allied withg a superpower. Its an easy choice. Having said that though, in every one of my most recent games after I increased default movement points the Hai have united the caucasus region as well as kabalaka. And only one of those games have they gone north, admittedly with a vengence. Maybe the AS just get there before they do? try modding around some files a bit.
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