City Growth

I have been inquiring into the system of city growth in civ IV. Sufficient results have been obtained to warrant posting and discussion.

A note about our topic: the fundamental dynamic at work in civ is the acquisition of rights to work game tiles. Aside from the food management issue, working such tiles yields commerce points and hammer points, and on this all else depends. Hammers are developed into units and resource multipliers (buildings); commerce generates trading options with other AI civs and, most obviously, beakers for the acquisition of techs. Managing the rate at which new tiles can be acquired is accordingly central to strategic play. This suffices as a defense regarding the significance of the topic.

I will proceed to list the findings of interest point-by-point. All numerical values are applicable for the correct game speed (epic speed). I have not inquired into how the system works at other speeds.

(1) Growth Requirements

A city of size 1 requires acquisition of 33F to grow to size 2. A city of
size 2 requires 36F, size 3 39F, size 4 42F, and so forth (temporarily
setting aside the effects of a granary). So far as I can determine this
system of +3 storage required per size > 1 continues indefinitely. A
size 20 city requires 90F stored to grow to size 21, which is in
accordance with the basic pattern. The core point to note here is that
there exists no “cut-off” point beyond which further growth becomes
abnormally more difficult than it was before (I mean this with
respect to storage requirements only. Obviously the availability of
health, happiness, and so forth can present interacting factors that
make further growth not possible).

(2) Food surpluses wrap after growth

When scanning over the food bar in the city screen we might see a value
of something like 42/48. What this means is that 42F surplus has been
stored, with 48 required for the current growth cycle to complete.
Suppose that we have a 10F surplus at this time. The city will
grow at the conclusion of the present turn. On the next turn the city will
show 4/51 – meaning that the extra 4F not needed for the cycle
has “wrapped” over into the next cycle. This alleviates the potential
need for obnoxious micro-management. Without it we would want to
remove citizens from food-tiles towards the end of a cycle so as to avoid accumulating resources that will be lost. Fortunately matters do not
work this way.

(3) Granaries, Part 1

The granary stores 50% of the needed food in one cycle for use in the
next. What this would mean in our previous example is that when the
42/48 city grows, the food bar will show 28F on the next subsequent
turn. 50% of 48 = 24, plus the extra 4F which “wraps” after growth =
28F total. If we were running a food surplus of 6F in that example (thus
matching the needed amount exactly), 24F would appear on the
immediate following turn via the granary effect alone. Note that the next
cycle would require 51F for growth, so we would see 24/51 on the
next cycle. This is slightly less than 50% of what is required for the next
growth increase. In practice the difference is negligible, but it is
noteworthy for understanding how the system

(4) Population and whipping (slavery civic)

The program straightforwardly eliminates X population when whipping
without doing anything else. What I mean by this: suppose we have a
size 6 city with 26/48 in the food bar and we whip 2 citizens. After
whipping we will show size 4, 26/42. The 26F present before
the whipping operation remains. This produces outcomes that can
appear weird in certain situations when not paying attention. Suppose we
have a size 6 city with 46/48 and we whip two citizens. After the
whipping operation we will have 46/42 with growth in 1 turn. On the next turn the city is size 5 and it appears that we whipped only 1
citizen. If we had NOT whipped the citizens, the city would have grown
to size 7 on the relevant turn (assuming at least 2 food surplus). Since
we DID whip the citizens, the city is size 5 on the following turn – a difference of 2 citizens, as advertised. It is a matter of understanding
that only the population has been eliminated, not the stored F-values
that have been accumulated.

(5) Calculating the food surplus

Suppose we have a size 3 city working tiles (1) a farmed flood plain, (2) a
mined grassland hill, and (3) another mined grassland hill. Each citizen
requires 2F support. The farmed flood plain provides 4F, the mined hills 1
F a piece – yielding 6F total. Since we have 3 citizens needing 2F each,
we have met the requirements and it would appear that the city should
be stagnant. But it isn’t. A related way of thinking about these tiles
holds that the flood plain is “supporting” the mines squares. This way of
thinking has its uses but it misses the point. Regarding the first
observation: the city is effectively given a “0-citizen” tile to work. This
is the city’s base (home) tile – usually 2F 1P 1C. This “free” tiles gives a
+2 food surplus if all the other tiles come out even (with respect to
surplus). The above calculation is skipping the base city square – the
city will have a +2F surplus because of the “free” tile. Regarding the“way of thinking” mentioned above: The art of city food maintenance is
the art of managing the rate at which new tiles can be worked. This is
directly tied to the city’s food surplus at any given time, which in turn is
the only value that matters. It is true that tiles (1), (2), and (3)
will be neutral with respect to food surplus. In this sense the flood plain
is “supporting” the mined squares. We don’t want to manage city growth
though via the roundabout method of balancing which squares
are “supporting” others. Doing so constitutes a mistake in understanding what the fundamental driving factor is in managing city
growth: the food surplus value, which determines the rate at which new
tiles can be worked over time The two points to note here are (1) the
effect of the free “0-citizen” tile in calculating the food surplus
value (it usually adds +2) and (2) understanding that the core value
which matters is the food-surplus number.

(6) City-Growth Table

At certain stages in the game we review our cities while they are in
various stages of their growth cycles. When they are midway or further
in a growth cycle, changing worked tiles (and thus the food-surplus
value) changes the number of turns remaining in the cycle by a
considerable factor – often by 3-5 turns. City growth management
however is ultimately a long-term project. We are interested in managing
the number of turns required to move from size 5 to size 10, 15, and
beyond. To understand the factors involved in this long-term project, we need to understand the cumulative effect of average food-surplus values over an extended period of time. The following chart is a
tool I have put together for this purpose.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 33 36/20 39/21 42/23 45/24 48/26 51/27 54/29 57/30 60/32 63/33 66/35 69/36 72/38 75/39
2 17 18/10 20/11 21/12 23/12 24/13 26/14 27/15 29/15 30/16 32/17 33/18 35/18 36/19 38/20
3 11 12/7 13/7 14/8 15/8 16/9 17/9 18/10 19/10 20/11 21/11 22/12 23/12 24/13 25/13
4 9 9/5 10/6 11/6 12/6 12/7 13/7 14/8 15/8 15/8 16/9 17/9 18/9 18/10 19/10
5 7 8/4 8/5 9/5 9/5 10/6 11/6 11/6 12/6 12/7 13/7 14/7 14/8 15/8 15/8
6 6 6/4 7/4 7/4 8/4 8/5 9/5 9/5 10/5 10/6 11/6 11/6 12/6 12/7 12/7
7 5 6/3 6/3 6/4 7/4 8/4 8/5 9/5 9/5 9/5 10/5 10/6 10/6 10/6 11/6
8 5 5/3 5/3 6/3 6/3 6/4 7/4 7/4 8/4 8/4 8/5 9/5 9/5 9/5 10/5
9 4 4/3 5/3 5/3 5/3 6/3 6/3 6/4 7/4 7/4 7/4 8/4 8/4 8/5 9/5
10 4 4/2 4/3 5/3 5/3 5/3 6/3 6/3 6/3 6/4 7/4 7/4 7/4 8/4 8/4
11 3 4/2 4/2 4/3 5/3 5/3 5/3 5/3 6/3 6/3 6/3 6/4 7/4 7/4 7/4
12 3 3/2 4/2 4/2 4/2 4/3 5/3 5/3 5/3 5/3 6/3 6/3 6/3 6/4 7/4

The rows are food-surplus values, while the columns indicate current city
size. Each cell consists of two numbers. The first number gives the
number of turns required for city growth if the city does not have a
granary. The second number provides the number of turns required
if the city does have a granary (and it was functional during the previous
growth cycle). The table does not take into account the food-wrap
issue discussed above. What this means is that sometimes we will save a
turn from the provided number. For example suppose we are running a 10
-surplus city at size 4. 42F is required to advance. On the 5th turn the
city will grow, resulting in 8/45 at the start of the next cycle. With 8
food stored, we will need 4 turns to reach 48/45 and thus to grow again.
The chart however indicates 5 turns (not 4) since that is the number of
turns that would be required if we had zero food at the start of the
relevant cycle. Note what happens here though. We will move from
48/45 to 3/48 at size 6. Here 5 turns will be required, as indicated in the
chart. In short, the food-wrapping effect intermittently permits us to
save one turn. In the long-term however the number of saved
turns is largely the same regardless of which row (and thus which
average food-surplus is being used). This permits us to ignore the effect
for relative comparisons.

(7) Observations from the City-Growth table

The key feature to note from the table is the significance of running a 5-food surplus (with a granary) or a 6-food surplus (without a granary).
Running a surplus of 4 or less comes with a very significant cost in long-term growth. Running a surplus higher than 5 or 6 does bring distinct
advantages. These advantages however are considerably more
incremental in character than they are at the lower values. Beyond a
food-surplus value of around 6, working a zero-food citizen (mined plains
tile, specialist, etc.) is considerably more palatable than it is at lower
surplus values [note: the decision to work a zero-food citizen is
significant since the cost of doing so lowers the food-surplus value by 2,
as opposed to lowering only by 1 working a mined grassland hills or
maintaining the current surplus by working a grassland pot (cottage)].

Some quick observations to help make this point. Suppose that we are
growing a size 3 city to size 4. Without a granary, this requires 14 turns
with a 3F surplus. It requires only 7 turns with a 6F surplus,
accomplishing the task 50% faster. A second case: suppose we are growing a city from size 3 to size 6 (without a granary). Using a 3F
surplus requires 42 turns; using a 5F surplus requires 26 turns. Again, the
difference is remarkable. On the other hand: we grow from size 3 to size
4 in 7 turns using a 6F surplus. If we increase our surplus to 9F, the
task will be accomplished in 5 turns instead of 7. Switching from a 3F-
surplus to 6F saves 7 turns. Switching from 6F to 9F saves only 2 turns.
Without a granary, a 6-F surplus is the maximally efficient number.

I will leave other observations to those who see them. The quick point
to note is the significance of the window between the 5F and 6F surplus
numbers. Running a surplus 4 or lower for any significant amount of time
will yield poor and sub-optimal returns. The 5F to 6F window is entirely
satisfactory and maximally efficient. Running a surplus beyond 6F will
yield accelerated development, but with a lowered incremental rate of
return. Beyond 6F the prospect of utilizing a zero-food citizen becomes
notably more reasonable.

(8) Obvious caveats

I mention this to ward off needing to say it at some future time. There
are obviously going to be situations in which other game factors are more
important than managing city growth. In the window before
calendar/hereditary rule, we are often running with a happiness limitation
to growth. In these circumstances running a surplus of 4 or lower is
entirely reasonable. If we’re in a military conflict, running with sub-optimal growth parameters may be advantageous and/or necessary. In
addition, when making a run for a world-wonder, emphasizing hammers in
exchange for growth can obviously be correct. The larger issue of
balancing the various intersecting factors in the game isn’t the point of
issue. We are isolating one segment of game-play to see what can be
discovered about it.

(9) Granaries, Part II

The long-term cumulative effect of granaries is quite striking. Suppose
we are growing a city from size 5 to size 15 with a steady 5F food
surplus. Without a granary the process will take 121 turns. With a
granary the process will take 66 turns. The city without the granary requires 55(!) more turns to complete the process. This constitutes a
steady delay in acquiring new tile resources, which in turn drives all other
aspects of play. The default plan for any normal city accordingly must
include building a granary at some point or another. The issue of when to
build it is open to context, and of course there will be exceptions for
cities that are geographically placed in growth-limited locations, or are
peculiar in some other such way. For any normal city though, there must
be some feature in the larger strategic context that overrides the default
plan to make skipping the granary completely a reasonably correct

(10) The State Property civic

Suppose that we are in the later stages of developing some particular
city. We have a 3F surplus, and we intend to “complete” the city by
growing onto 3 plains tiles with 1F a piece. When this is done the city
will be completed in its capacity to work the maximal number of tiles it
can, and will accordingly be stagnated. Growth may start up again way
later when we obtain the biology tech, but we can assume this will be a
long time in coming. The obvious problem which we face here is that
growing onto the last tiles will take an extremely large number of turns.

The 3F surplus is bad enough (especially when we are likely dealing with a
reasonably large city already, with extended food storage requirements).
Matters will only get worse though when the first cycle is completed,
leaving a 2F surplus followed by the snails-pace that will arrive for the
last tile with a 1F surplus. Reasonably speaking, growing onto the
last tiles will take such a long time that we are largely foregoing their
use. The State Property civic appears designed to assist with this. The
civic is quite popular for the maintenance bonus it gives (no distance-from-palace maintenance) but it’s effect on city growth strategy appears
to be overlooked. In many cases we will want to build windmills on plains-hills tiles and watermills on plains-river tiles. Doing so makes both of
them interchangeable at 1F 2P 1C, and they will improve later: +1P with
replaceable parts and +2 commerce with electricity. The State Property
civic gives a +1F bonus for windmills/watermills. What this means is that if/when we employ State Property, either as a long-term civic or as a
temporary 15-20 turn choice, we will very often be able to complete
cities that would otherwise take an inordinate number of turns. In the
above example, suppose we have 4 windmills/watermills being worked in
that city. When we adopt state property our food surplus will increase
by 4F. In the process of growing onto the last 3 intended tiles, we will
move from 7F to 6F to 5F in surpluses rather than from 3F to 2F to 1F.
The result is that the city can grow onto those last tiles in an entirely
reasonable number of turns. If/when we change out of state property
afterwards our food surplus will disappear and the city will be stagnant, but working the tiles that were planned for its employ. This is
often the only feasible way to enable tile utilization in the late stages of
city growth – unless we want to wait for Biology (which is typically an
unacceptable delay).

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