Is there an optimal city size to start building settlers?

Summary: Early game, build a settler basically as soon as you can. Continue to grow as quickly as you can defend your settlers, or until you hit your desired size for your long term strategy.

In terms of the early game, it is pretty easy to apply some science to this. Let's say that I'm in a typical starting situation. I build my first city on turn 1, and I start working a space that gives me two extra food. That means it will take 8 turns for my city to grow to population 2.

On turn 8, I start working another square that gives me 2 food. At this point I can start building a settler. It will take me 18 turns to complete that settler. On turn 30, I have completed the settler, and moved him to a new location to build a city. So far I have accumulated (8*4)+(22*5)=142 science, and I am now working 5 tiles (3 population, plus 1 for each city) and gaining 6 science per turn. Both of my cities are 8 turns from growing.

After those 8 more turns, I have accumulated 134 +(8*7) = 190 science. I am now working 7 tiles and gaining 7 science per turn.

Let's say that instead I decided to just grow my capital. My capital grows to size 3 on turn 20. When turn 30 rolls around, I'm still at size 3. I have accumulated (8*4)+(12*5)+(10*6)=152 science, 10 more than scenario 1. I am now gaining 6 science per turn, but only working 4 tiles. My capital is 6 turns from growing.

Moving forward 8 more turns, I have accumulated 144 + (6*6) + (2*7) = 194 science, 4 more than scenario 1. But now I'm only working 5 tiles, and gaining 7 science per turn. As soon as my scenario 1 cities grow again the science advantage is gone, my capital is only 1 population larger, I'm working fewer tiles and gaining less science and money, not to mention having fewer resources in my borders.

There are a few other benefits to having a large capital, but I think they are far outweighed by the benefits of having multiple cities growing simultaneously. Even if you're going for a cultural victory, getting those first couple cities down quickly will put you way ahead later on.

This question is very opinionated so here is my experienced answer. I personally refuse to use my capitol to build settlers, I will either wait till i have 500 gold to buy a Settler or if im trying to expand quickly i will unlock the social policy Collective Rule under the Liberty Tree.

The thing to keep in mind when deciding how much you want to expand or how little is that there are very few disadvantages to expanding as little as possible compared to the disadvantages of expanding to your fullest capacity.

Small Empire:

Advantages

• Low Unhappiness*
• Low Building Upkeep
• Less Ground to Defend equals less military cost
• Less Chance of you Upsetting your Opponents and Causing an Early War*
• Less Culture/Science needed to gain more Policies/Research (this kinda goes in hand with Low building upkeep)*
• Less Workers for Improving the land

Disadvantages

• Possibly missing out on some resources*
• Not having enough cities to build an army up in a hurry

Now when it comes to having small empires you should usually have 3-4 cities altogether, and make sure these cities are increasing their population as fast as you can get them to without burning through your happiness since there is nothing more slowing to an empire then the effects of unhappiness. Now keep in mind that more importantly then growth is making sure you build every scientific and cultural building available to you as if you are more advanced then your opponent they will more likely fear you then attack you.

Alright so i got a few of these listed out for you and i starred a couple of the important ones. Some may disagree with the importance of some of these but having an opponent mad at you and whether you overrun him or just keep him from defeating you, this will cause you to suffer on your culture and science if you are against more then one opponent. Well you may say, I just destroy my enemies with large armies and im sure that works great on Cheiftain and Settler difficulties. The best army to have is the most advanced army and this happens by having the strongest science and culture gain. Science gives you more advanced units while Culture gives you the means to get them faster/have more of them. If you play on Prince or harder you will find that doesnt matter how many Cannons or Cavalry your empire has once your opponent has the power of Flight your armies will dwindle at a considerable rate.

Now missing out on some resources isnt a huge problem as if you play nice with the AI they will most likely trade with you. Not having a massive army at a moments notice shouldnt be an issue long as you have a few guys roaming your lands including the ones garrisoned at your cities. Knowing how to use the land and your cities to defend is better then any number of units that you can produce. But that is for a different question time to address large empires.

Large Empires

Advantages

• Massive armies
• A Surplus of luxuries and resources*
• Your opponents will most likely fear you/try to be your friend then fight you
• Your surplus of resources will allow you to trade if you happen to not have something within your empire.

Disadvantages

• Lots of building upkeep*
• uncontrollable growth sending your empire into unhappiness*
• upsetting your neighboring allies
• lots of land to defend equals more units to waste time building/waste gold on.
• harder to keep up with the higher science/cultural requirements*
• takes way more of your time up to control
• more workers needed to speed up improvement/road building

This usually consists of 5 cities and more. When it comes to larger empires I like to have a building strategy for each city set up. Whether i have all my cities build scientifically and one group of cities build for production/military while the another group builds for cultural and a smaller group of cities builds for growth and wonders. This helps me keep my building upkeep a bit lower then having all my cities build everything. I usually accomplish this by naming the city what group its in like GrowthI and GrowthII for example.

Now keep in mind that most of these disadvantages arent that important but the biggest disadvantage is low science and culture which will lead you into a battle with cannons verse artillery which always ends badly, specially since the only reason to have a large empire is to produce a massive army. i feel like im babbling on for to long so im gonna end it with that.

Anyone who can edit feel free to add to the advantages/disadvantages.