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Just on Civ, if you like it I'd highly recommend checking out any of Paradox's grand strategy games like Hearts of Iron or Europa Universalis. The AI is generally pretty good, although you might see some questionable behaviour from time to time. Balance is another matter though, for the most part the games try to at least start with some historic accuracy so you'll find some nations are just straight up hard to play.…
Thanks - Hearts of Iron is definitely on my list. Europa Universalis appeals a bit less, though that's mostly because of my perceptions of the interface and cognitive burden. I could be totally wrong about those. I definitely don't mind bad balance if the game isn't trying for it; Rome: Total War did something very similar with certain nations starting in terrible positions.
EU is a different beast though, and I know exactly what you mean about the UI. EU4 has made some improvements but once you add in even just a few of the bigger expansions/DLC then it can really get a bit overwhelming.