I mentioned that while listening to Foner, I've been trying to beat Civilization on "King." I managed a culture victory with Ghandi on "Prince" last week, with three cities. I built The Great Wall, Stonehenge, and a few other Wonders, and basically fought all wars on defense until I won. That isn't working so well on King. One commenter suggests:
I find being aggressive militarily early is the easiest way to beat Civilization on the harder levels. You just can't compete with the biases the AI gets in production and science, so you need to kick some of their asses before they can consolidate their advantages.