Is this thread about chess or Civ? I think that many of the AI problems are quite simple. You just introduce several layers.
For instance, how do I improve the terrain for a city? Well, develop all resources and try to get at least two food from each square. That may not be optimal, but is good enough. What improvements should I build? See which ones give you the best ratio between invested shields and output (hammers, money, culture, etc). Sometimes it is even simpler, you just have to build an aqueduct for your city to grow. The AI does these trivial things pretty well.
You can then introduce a higher level of decision making with higher priorities. Where should I build my wonders? How do I connect my cities? Again, not very hard.
Then comes, what should I research? Well, picking the cheapest usually is not a bad choice. The real AI is much more refined. But again this is easy.
The big decisions are how to interact with the others. What does it mean that I see forces on my border? Should I attack someone who is overexpanding and probably is vulnerable? The AI rarely does this. It is bad in assessing who is the greatest threat, and tends to deploy forces evenly, not taking into account that it might be better to have more either at a central location from which it could reinforce a sector under threat using inner lines, or having more units where the threat is the largest to begin with. In forming relations it usually rarely shows a strategy. To simplify a little, it just dislikes its neighbors.
While I am not saying that it is bad, it is not really very advanced either, and could be improved very easily by adopting a better tree of rules, or by optimizing the hierarchy of decision making. These things are not very hard! They just take a lot of time.
I am sure that rather than adopting a more fundamental approach to developing the system of rules for Civ4, it was mostly done by rules of tumb and trial and error. To use, for instance, neural networks or some other optimizing methods is too time consuming.
But the result isn't that bad!