I'm thinking there should be a saying, "it wouldn't be a Civ forum if every other post wasn't bashing the AI". Warning, long post.
So what about Civ, connectionist sounds pretty good, why not do that here? Well let's see. We'd need about, oh say 100k to 500k full games as training data to start, let's just generate data from AI vs AI games. Then we'd need to define the network, what's the cost function? In other words how do you define the 'value' of a move? Well that's a great question, like what's the numerical value (from 0-100) of making a builder? It needs to be a formula, how would you express that? Be careful and don't turn it into a classical system by putting too much thought into it, if it's complicated it probably won't work. But what about the hundreds of other things you could do at any moment of the game? What's the cost function for that? Finally, what are the input neurons and output? Given the number of orthogonal actions at any point it kind of seems like the network would be bigger than what even our modern CPUs/GPUs could handle. Brrrrr .... I'd love to get some time to look into this, but at first glance it's not an obvious solution.