I'm trying out the Mayans because they seem pretty good from a science/cultural standpoint and I was wondering what you guys had for a early/mid game strategy for them. Thanks in advance.
Train a Scout and at least one Atlatlist while researching Pottery. The Pyramid is one of the best unique buildings in the game, and building it in your cities will allow you to found a pantheon and a religion early on while also giving you a boost to science. Messenger of the Gods is probably the best pantheon to choose, since the Maya can develop science and religion concurrently.
Rush Theology so you can activate The Long Count as quickly as possible, using Warriors and Atlatlists to defend yourself. (You should have at least three cities by the time you finish researching Theology.) Upgrade your Atlatlists to Archers once you research Archery and have some extra cash, then keep growing the population of your cities while developing them for science and faith and trying to keep your empire's economy strong. The Maya can easily play a defensive game while working toward a science victory, but if you need to eliminate a militaristic or aggressively expansionist neighbor, you can get a free Great General from The Long Count and then wage war to wipe out the threat.
When choosing social policies, fill out the Tradition tree first and Piety second. Rationalism is a must once you reach the Renaissance Era. Try to build the Hanging Gardens (for the extra food) and the Porcelain Tower (for the free Great Scientist and extra Great Scientist points) as they become available, and remember that you can effectively build a free wonder with the Great Engineer from The Long Count. Save as much faith as you can to buy Great People in the Industrial Era and beyond - depending on which ideology you adopt, Great Scientists and/or Great Engineers will be extremely useful.
Hope this helps. Have fun with the Maya - they're one of my favorite civs in Civ5 and its expansions! :)
What do you think?