Thanks guys. So splitting your workers is a bad idea for the first ten to twenty moves. Makes sense to me.
Right. I'd say it's a bad idea to split your workers in your capitol as long as you are at 2 pop and furthermore even after you get to 3 pop you should still focus two of your workers to the same task. Want to grow? Put them both on growth. Need a tech now? Put them both on science. Need archers? Put them both on trees.
If you like to play the Greeks, you can even take things a step further because your courthouse ideally will give you up to four grasslands, four trees and hopefully more than four trade tiles to work so you can really specialize. Pick a task and get it done quickly, then manage your workers to some other tasks. Athens with three grasslands can grow from 2 pop to 4 pop in just ten turns! This will leverage into a huge advantage later in the game.
As you begin to have more cities, then it starts to make more sense to split up your workers because their combined efforts are distributed across your empire. For example, if you have 5 cities and each of them has one worker on science (kind of a weak example, but it'll serve), you'll get a 20 beaker tech in two turns and a 30 beaker tech in three. That's way better than having one city with one worker on science and having to spend ten turns getting a 20 beaker tech.
So what do you guys think of splitting your workers into science/food after you have your first 2/3 warriors and are done producing for a reasonable amount of turns? Usually after i hit the 3rd warrior, i switch to food and science, one food square and 2 science. My three warriors usually get my 100$ leading to a free settler, at which point i would rush a library in my capital and settle down between me and an AI cap at a location that provides good growth and science, with maybe one production square. At that point its a toss up on whether or not i go for a 3rd city quickly, or library rush my 2nd city and go for a 3rd city slowly, maybe even capturing an AI capital while my 3rd settler is still finding a good location to settle down at. Any obvious problems im making at this point in the game?
Be careful about rushing a library in your capitol right away like that. How many trade tiles does your capitol have? How big an advantage are you really getting for your 80 gold? If you are, for example, the Russians (a civ with no trade advantage) and have just two sea tiles by your cap, that library isn't really going to get you very much. It'll turn your 4 beakers per turn into 8. That's not very impressive. It's better to focus on units and settlers.
Some other civs, like the Greeks or the Egyptians (especially if you have the Colossus) can benefit more from the early library.
In general, libraries should go in cities that will be able to produce a lot of trade and another rule of thumb is that settlers are often better than buildings in the early game. You can expand quite a lot before getting to Republic. Grow your city to 3 population, then you can put two workers on trees and one on grass and get a settler in 5 turns. The food you've accumulated in this period will restore your city to 2 population as ericball describes above.
The other way to do it is put two workers on grasslands and one on trees for just two turns and then rush the settler for 32 gold. Again you'll have accumulated enough food to grow back up to 2 pop (and can start growing again now). This method is faster, but costs you the 32 gold. A better use of that gold than a library, in my view.
A good game will see you get to about 10 cities by 0 AD, which is also when you should be able to reach the industrial era. If you do this, the AI will be pretty confounded by you and be easy to beat in SP and you'll be competative with many of the better players online.