i'd make culture flips critical to gaming strategy, by ...
1) eliminate razing and abandoning
2) make culture flip chances independent of size, so starving cities does no good
3) deceased civs can still get favorable culture flips
4) make culture flips common enough that it is impossible to hold on to large numbers of foreign cities without a favorable culture ratio. granted that sweeps through enemy territory may still be made to destroy all those culture buildings.
then, culture might actually become an important aspect of the game.
Civ3 Vanilla actually doesn't have abandoning. But the AI doesn't use it anyway.
I feel culture is important enough. You don't want it to be the most powerful force in the game. Try conquering a culturally adept neighbor as a backwater, uncouth civilization. You get a lot of culture flip problems. At some point it becomes worth it to build up your own culture just to stop the incessant revolts.
Having played Rhye's and Fall of Civilization for Civ4, I'm not sure I like the concept of deceased civilizations being able to come back at all. It really didn't seem to add to the fun of the game when I played with it in RFC. It added a bit of extra balancing to do, but it wasn't necessarily what I'd consider fun.
I also object to point #4. Do you really have to have the superior culture to be victorious? Sure, it helps (and Civ3 recognizes this), but it's certainly not mandatory. Look at the fall of the Roman Empire. Did the barbarians have some sort of cultural superiority? Maybe a less decadent, corrupt society, but I wouldn't say more cultured. Did culture help the Japanese control China in the 1930's? Definitely not! But the barbarians overcame Rome and came to rule its former empire, and the Japanese were able to stay in China quite awhile despite the cultural canyon.
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I'd like to see the AI sensibly use armies. As it is now, they're just a huge advantage for the human. Would the AI use them well (in Vanilla and PTW they use them poorly, in Conquests not at all), they'd actually be an interesting part of the game and it wouldn't feel cheap using them.