There are two basic reasons to connect your cities by roads: for Trade Route income, and for Unit movement
Connecting for Trade Routes
Warning! These calculations are now suspect because of new info found about how road maintenance works. I will update this with any changes needed once we have verified numbers for road maintenance costs.
Summary: only build trade routes to cities with 6 population or more. If you care for the math, then continue reading...
Now that Oak has solved the Trade Route formula for us, we know that normal trade income is very close to 1.25 * population of the connected city. (not the capital)
So, suppose you have your capital and one city, they are separated by 6 hexes. You'll be paying to maintain each of those roads, costing you 6g. So, at a population of 3, you would make 3.75g, be spending 6g, and be losing money overall. Your worker time is EASILY spent doing something else. Of course, if your cities are closer together, the calculations look better. Finally, I believe that Harbors cost 2g to maintain. Realizing that you only pay for your capital harbor once, sea routes effectively only cost 2g to maintain.
Population | Income | Net Income with...| Harbor/ |
| | 6 Roads | 4 Roads | 2 Roads |
3 | 3.75g | -2.25g | -.25g | 1.75g |
4 | 5.00g | -1.00g | 1.00g | 3.00g |
5 | 6.25g | 0.25g | 2.25g | 4.25g |
6 | 7.50g | 1.50g | 3.50g | 5.50g |
I would like to propose a rule of thumb. You can pick whichever population number seems best to you, but I believe my worker can do better than even a 4g improvement by working other tiles in the time it would have taken him to build that road. Thus:
Only build trade routes to cities with 6 population or more.
If you follow this rule of thumb, you will, at the least, never lose money on a trade route. Further, if you start working on the trade route when the city is size 6 already, there's a good chance it will have grown to 7 at least by the time you finish, and you can actually start making enough money for that worker time to be worth it.
Final note on trade routes: Arabia gets a flat +1 to trade route income. (AFTER the multiplier, so simply add 1 to every gold number on the chart.) So feel free connect Arabian cities at population 5 or more, if you like.
Connecting for Unit Movement
We don't have nearly as good of data on this, but from my Civilization experiences, roads are VERY worth building if you are producing units and sending them to war. You get your best units at the front for longer before they are obsolete, and you'll have more units at the front at any given time.
If you're not moving units for war, roads may also be worth building to quickly move defenders in the event of being attacked, by barbarians or another Civ. I think you can just ask yourself:
- Am I likely to be attacked in that city?
- Is the attack likely to beat the city?
- Do you HAVE units that could get there by the road to defend?
If any of those it no, the road is not worth it, cause it won't help.
And if you're not at war, and not defending, I doubt you want to build roads just to move units, because you don't sound like you're moving units around much at all!
Best Answer
As of Brave New World, Culture works differently: beyond the Monument, each Culture building provides a trivial +1 Culture, plus slots to hold Great Works. Don't think of an Amphitheater as providing "+1 Culture." Think of it as providing "+3 culture and +2 Tourism once it's full."
The point of Amphitheaters in Civilization 5 is to hold Great Works of Writing. There is no other building that can be built in every city to hold them. The other buildings that can hold Great Works of Writing are the National Epic, Heroic Epic, and Oxford University, for a total of four slots. If you're quick, you can also put some Writings in the Great Library and Globe Theatre, but in my experience the Great Library is always built – very quickly – by one of my opponents. (I usually play on King or Emperor, and the head start that the AI gets is enough to get one of them to Writing several turns ahead of me.)
As with other Culture buildings, it's worthwhile if you want to achieve a Culture victory, but also if you want to unlock social policies faster. If you use a Great Writer to write a political treatise instead of a Great Work of Writing, Great Writers generate about 8 turns' worth of your current Culture output. If you don't care for a Culture victory, then you can measure the Culture generated by a Great Work until the end of the game versus 8 times your current Culture output to see which one will get you more Culture.
Of course, building Opera Houses and Museums requires you to have an Amphitheater first. You won't always fill up your Amphitheaters, but once you get Archaeologists, it's very easy to fill up Museums with artifacts. Skipping Amphitheaters implies that you don't care about culture at all, which means you will have fewer Social Policies available to you. (And if you have only one high-Culture enemy, that enemy will win a Cultural Victory relatively quickly!) I find Social Policies to be so useful that I wouldn't consider ignoring them.