What is the optimum number of cities to have in the early game if I`m relying on a SE (small map)? Does this ratio and the distance maintenance cost change when I play on a larger map? Just how important is the distance to the capital?
Many questions, I know
I`m trying to step up to monarch and overexpanding in the early game seems to be one of my biggest problems
Cheers
Mischief
These are quite difficult, nearly impossible questions to answer. There is no optimal number of cities. As you expand, your older cities are developing and soon they reach a state where they're that profitable that you can support even more cities. Almost every crappy city can and will eventually produce more commerce than its city upkeep + civic upkeep. Some cities will do this sooner, some later. If your capital or second city has a few gold mines, then you can expand faster because your commerce yield is big enough to pay for the maintenance of many cities.
Fast expansion is good for acquiring resources. With many resources, you can let your cities grow bigger and more profitable without health or happiness problems.
If you however expand too fast, all of those small new cities won't produce any commerce and thus will cost you instead of benefit you. So build enough workers to improve the new cities with commerce terrain improvements (and other improvements). And when your older, better developed cities reach a certain commerce yield, it might become very profitable to build a library or marketplace there than to build another new small city.
Note also that if you expand at a rate so that your science production never really increases, then it might take too long to reach crucial economical technologies like pottery (cottages), currency (more trade routes and the market), code of laws (courthouses) and calendar (the availability of new resources will let your cities grow and become more profitable).
At the start of the game, your science production will typicaly be 9, 10 or maybe 11 (palace + center tile + maybe some commerce from another tile) (check it in the F2 menu, the financial advisor). Then you start improving the terrain around this city and commerce and science will go up. It will go down a little when you build the second city. You can easily see that happen by looking at the gold per turn just before and just after settling the city. You keep improving the two cities and commerce and science will go up again. And you keep expanding which will reduce the science rate. If after checking the science rate after an expansion, you think that it went down a bit hard, then stop expanding a bit or at least give it less priority.
Just regularly check your maximum science rate (without losing money) and check the gold per turn before and after settling a city to get a feeling for the costs of expansion.
I regularly will see my science rate go down to something as low as 20-30%. That's not strictly a sign that I'm expanding too fast. 20-30% of a huge amount of commerce is still a lot. Check the real science rate in your F2 menu (financial advisor) to know if it is going better or worse than a few turns ago.
The commerce graph in the F9 menu can also be a help, but it's not perfect. It doensn't take into account the influence of buildings like libraries and marketplaces.
On big maps, the costs for expanding are lower. The number of cities upkeep and city distance upkeep are smaller. But you need to build more cities to have a competitive empire and the resources are typically further away from the capital
The distance to the capital is important enough to want a centrally located capital in most games. It's not a must, but it is not so great to build your second and third cities at 10-15 tiles from the capital. Of course, it takes too long to walk that way and thus it is less interesting, but the costs also make it a less attractive option. But if you see a great settling spot a little further away, then you should still go for it. The costs are certainly not crippling.
It is far more interesting to build a courthouse in cities that are far from the capital than in cities that are close to the capital.