Site searching spells - AI select likely province?

[thejeff]

No, it will not go crazy. Or at least I've never seen it.

The algorithm is pretty well understood now and I've never seen it go wrong.

The only bit not mentioned here already is that when a mage is site searching monthly, he picks his new target before battles take place, so he doesn't consider newly won provinces. He could also target a province you lost that turn.
That might be the source of your "refusing to check certain provinces", but he won't actually cast on your capital (unless it has less than 2 sites and hasn't been searched already), he'll just go the "defend" if he can't find a valid province.