Re: added value of additional cities.
What I will consider here is what I will call the economical value of a city. The criterion I will apply is if a city can cover the added maintenence while building wealth and running 100% gold slider.
I.e. for reaching the domination limit, grabbing essential resources or producing more units other considerations will apply. These are not considered here.
Calculating the maintenance of a city
As a reference I used this thread:
https://forums.civfanatics.com/threads/city-maintenance-costs-the-numbers.612888/. I am using the same convention for size/difficulty, namely Standard/Deity. For speed I will assume Standard.
The code for city maintenence is found in
CvCity::calculateBaseMaintenanceTimes100()
.
First lets consider number of cities maintenance. There is a cap of 8
/turn for deity. This is
iMaxNumCitiesMaintenance
in
Assest\XML\GameInfo\CIV4HandicapInfo.xml
. For a sufficiently large empire this will only be 8
/turn, flat. Sufficiently large means that even a size one city hits the cap. This is equivalent to 27 cities.
Obviously most cities will be bigger than size one, reducing the number of cities when the cap is hit.
This is important because below this cap building a new city increases the number of cities maintenance in all cities. This contribution is at most equal to the cap per city.
Thus above the cap an additional city adds 8
/turn in maintenance, but just below the cap that amount can nearly be
doubled.
Assuming a less homogenous empire will smear out this effect, making adding the most expensive additional city less expensive, but making more additional cities more expensive. In the limit of very high (equal) city count all empires will pay the same number of cities maintenance.
Note that for a size 12 city the cap is reached at about 17 cities.
Now distance maintenance has to be added, and since later built cities will tend to be further away from the capital (or FP, Versailles, I will call those centers for brevity) they will also tend to have higher distance maintenance. A size 12 city that is in the 16th ring of the nearest center will have distance maintenance of about 10
/turn.
So roughly adding a ~16th city on the fringes of an empire can drive up maintenance by about 20-25
/turn.
Now we have to consider Inflation. Inflation is handled in
CvPlayer::calculateInflationRate()
. In the early game (before turn ~200) it can be approximated reasonably well as 0.3*(turns-90). So by turn 170 (1100AD) it will be about 30%.
Adding that inflation will result the above example to have a post-inflation maintenance of 26-33
/turn.
If we assume that new city to be size one the added maintenance is still about 16-20
/turn.
The cost of a city
If we assume two trade routes at 3
each the city will still need at least 20
+
to not be a drain on the economy, and more if it is to pay back the investment of building settler and growing it. That corresponds to about 2 per tile for size 12 city.
This means that growing on coast is barely acceptable, and that non-river cottages take time (30 turns) to be better.
Note that due to the base values in the maintenance calculation growing a city reduces the maintenance per population. Furthermore, it means that on top of building a settler a new city will frequently incur a cost due to non-covered maintenance on small sizes. A settler will cost at least 100
, due to not producing wealth. Due to halting growth/whipping this will be significantly higher in most cases. Since this is a game of snowballing the actual investment is again higher.
The cost of the settler and uncovered maintenance will make up the cost of the city. That usually needs to be paid back before the next milestone to be worth it.
Conclusions
Having the GLH on with overseas foreign trade-routes will almost cover the costs. Similarly, on non-Pangaeas post-Astronomy and post-Corporation the trade routes will cover a lot. SP will get rid of distance maintenance and inflation on it, halving the cost and allowing to workshop, cutting the time to grow cottages into great tiles. If the next milestone comes after these building a new city pays back quicker and may speed said milestone up. IMHO this is the time to build mediocre cities.
The value of added population implies, again, that only a city that has enough food to grow in a reasonable time is worth it.
What I did not consider is colony expenses, which apply for cities not on the same continent as your capital. Obviously, they increase the cost of a city.
Edit: fixed last section