Food to Grow

[darrelljs]

Its very possible someone has done this already, but I haven't seen it. I was tired of not knowing the food to grow vs. city size equation, so I took data through size 8. Here is the result:

Darrell

 

[Spatzimaus]

You could always just look at the game's data files. In the GlobalDefines.xml file are the following values:

BASE_CITY_GROWTH_THRESHOLD = 15
CITY_GROWTH_MULTIPLIER = 6
CITY_GROWTH_EXPONENT = 1.8

5^1.8 is about 18.1. Your size 5 looks to be at about 50, so adding 15 isn't enough; that 6 has to come into it somehow.

8^1.8 is about 42, so the size 8 should require just over twice what the size 5 does, before that base threshold is included. Since your size 8 seems to be just under 100, this actually fits pretty well; the 1.8, at least, seems to be the correct exponent.

Now, these values presumably are also adjusted by game length, world size, difficulty, etc., so your data might not match. There could easily be a constant in there we don't see.

So what are your exact numbers? Say, for size 5 and size 8? And was this on normal difficulty, etc.?

(Other interesting things in that file? CIRCUMNAVIGATE_FREE_MOVES is currently set to 0. So the whole Magellan's Voyage logic isn't being used, apparently. You can also set the default difficulty, world size, etc. if you're tired of it always defaulting to Chieftan.)

 

[Nunya]

Nice. Could you also supply the data for sizes 2-8 in a chart and the formula used for projected?

 

[Bibor]

You also have to calculate in the Hospital and the Medical lab which change this curve substantially (up to 75% less food required for growth).

 

[KrikkitTwo]

15+6*(pop-1)+(pop-1)^1.8 ?

1 15
2 22
3 30.48220225
4 40.22467406
5 51.12573253
6 63.11949159
7 76.15777628
8 90.20293476
9 105.2242531
10 121.1959152
11 138.0957344
12 155.9043144
13 174.6044652
14 194.1807826
15 214.6193342
16 235.9074208
17 258.0333894
18 280.9864856


I would imagine this is then changed for game speed + difficulty level with a simple multiplier.

And Hospital/Med labs don't change the food needed for growth, they just make sure more food is available for growth.

 

[Spatzimaus]

15+6*(pop-1)+(pop-1)^1.8 ?

Looks like that's it. The (pop-1) hadn't occurred to me, but it does seem like that'd be necessary since you start at size 1.

The question is, when we say "it takes 50 food at size 5" does that mean to go from 4 to 5, or from 5 to 6?

 

[darrelljs]

My settings were Emperor/Normal speed/Standard size.

15+6*(pop-1)+(pop-1)^1.8 ?

It nicely matches the data I've taken . It also explains the discontinuity at size 3 to 4. The trend I was seeing is that the amount of food to grow increases by the city size + 6, but at 3 to 4 its city size + 7. You found out why, many thanks! Here is an updated chart to go with the table:

The bottom line is that sometime in the early teens there isn't much point to a food focus until Hospitals become available. The ROI on food just doesn't seem to justify the cost. This jives with what I've experienced in games.

Darrell

 

[darrelljs]

The question is, when we say "it takes 50 food at size 5" does that mean to go from 4 to 5, or from 5 to 6?

It takes 51 food to grow from size 5 to size 6.

Darrell

 

[Bibor]

You're correct, at size 13 its better to wait for hospitals, which then push you to 18-19 when it's time to get the Medical Labs (if you want them at all).

 

[darrelljs]

One last set of figures comparing civ 4 and civ 5 (civ 4 is 20 + 2*city size if memory serves). I ignore Granaries and Hospitals, which skews things quite a bit in civ 5's "favor".

So basically to get a size 30 city in civ 5 you need ~8000 food, vs. ~1500 in civ 4. Given the lower tile yields and lack of punch from the bonus resources, I posit that maritime city states are actually balanced for the job they need to do.

Darrell

 

[Roxlimn]

I'm finding Maritimes to be necessary in at least twos in order to grow a significant city. Of course, they also power up small cities marvelously well, but they do seem to be necessary for a decent size, as well.

I'm not sure I agree with such a design choice, since alternative building options for getting more food are not similarly powerful. Even Granary + Watermill only adds up to 4 food.

 

[Spazzmaticus]

So basically to get a size 30 city in civ 5 you need ~8000 food, vs. ~1500 in civ 4. Given the lower tile yields and lack of punch from the bonus resources, I posit that maritime city states are actually balanced for the job they need to do.
Darrell

I disagree. They magically provide constant amount of food to all cities. So it means that all cities you plant can get more or less immediately to size 5, no matter the terrain.
That's broken and not fun.
Also it's really hard to believe that one city with mediocre land can supply 50 food per turn to your civilization (or more).
A better idea would be for them to provide fixed amount of food that is distributed equally to all your cities. So having one city, you'd get let's say 10 food, while having 5 cities, you'd get 2 food in each.
As it is now, it's very very strong to build masses of tiny cities which pay for themselves in terms of gold and happiness while adding to your research and production considerably. And you can build them anywhere, the only requirement is to have reasonable amount of hammers to build colloseum.

 

[darrelljs]

I said they were balanced for the job they need to do. Its my snide way of saying the food growth curves are way out of whack .

Darrell

 

[Spatzimaus]

Well, this whole thing begs for a bit of modding. Specifically, as has been pointed out, there's a point in the low teens (13ish) where you suddenly want Hospitals, and their 50% storage makes a HUGE difference at that point. To me, that's a big problem; it's not quite like in SMAC, where at sizes 7 and 13 you had to build a new building if you wanted the city to ever grow again, but it's close to that.

I'd prefer a more gradual progression. So what I'm putting in a mod is this:
Granary: 10% food storage
Hospital: 20% food storage, +2 research
Research Lab: 20% food storage, +5 research

And I'm adding a line of low-maintenance city buildings that are intended to offset some of the problems of growing too large:
Aqueduct: +1 happiness, 10% food storage (at Engineering)
Sewer System: +1 happiness, +2 food, 10% food storage (at a tech in the industrial era, I forget which), requires city size Medium
Recycling Center: +1 happiness, +3 production, 10% food storage (at Ecology), requires city size Large

With all six buildings, you'd be at +80% food storage plus some happiness (to offset the unhappiness for large populations) and a few other bonuses. But most importantly, the food storage would come in a more gradual way; as long as you were building these regularly, your growth rate would only slow down a little as you go. It'd actually slow a bit faster than you'd think, since obviously the high-yield tiles get worked first, so as you get into the teens you're starting to work the almost-unusable stuff or load up on specialists.

(And then in my future era, one last building along these lines, the Habitation Dome, adding another 10% to get you to 90% storage. Then it becomes more of "if the city has any excess food at all, you grow" thing.)

So the real question for this thread becomes, how do those curves change if you assume a Hospital will be built at size 12 and a Medical Lab at size 18, for instance?

 

[Nefelia]

I disagree. They magically provide constant amount of food to all cities. So it means that all cities you plant can get more or less immediately to size 5, no matter the terrain.
That's broken and not fun.
Also it's really hard to believe that one city with mediocre land can supply 50 food per turn to your civilization (or more).
A better idea would be for them to provide fixed amount of food that is distributed equally to all your cities. So having one city, you'd get let's say 10 food, while having 5 cities, you'd get 2 food in each.
As it is now, it's very very strong to build masses of tiny cities which pay for themselves in terms of gold and happiness while adding to your research and production considerably. And you can build them anywhere, the only requirement is to have reasonable amount of hammers to build colloseum.

...

Its basically a Civ IV corporation without the micromanagement. I would be interested in seeing more types of city states, as well as stronger competition from the AI in attaining alliances with these states. Also it is far from broken, as one is still limited by one's global happiness and economy.

And fun is subjective. For instance, I greatly enjoy the maritime city mechanic and know from these forums that I an not alone.

 

[Roxlimn]

Spatzimaus:

I'm not sure that's a good way to go about this. In the current environment, getting Hospitals and Medlabs is actually a strategic choice. You can do with smaller cities, or pay for bigger ones. It seems to just come a little late, is all.

By making larger cities more attractive, it becomes the only strat that works, and hospitals suddenly are required everywhere and is reduced to just more things you need to click.

 

[Nunya]

I'd rather not imagine what the extra food from the sewer system is supposed to represent.

 

[Spatzimaus]

I'd rather not imagine what the extra food from the sewer system is supposed to represent.

Health. In Civ4, unhealthiness (which things like sewers and aqueducts negated) just directly subtracted from your food if you got too much of it. So subtracting unhealthiness was the same as adding food once you got to the sizes we're talking about.

By making larger cities more attractive, it becomes the only strat that works,

If you look closely at the numbers I gave, you see that it actually makes larger cities LESS attractive, not more.

Currently, a player who reaches the right tech can build Hospitals and get 50% food storage for the cost of a few gold per turn. This makes them no-brainers for any decent-sized city that still has surplus food (or that can GET surplus food through Maritimes). But before then, cities grow VERY slowly since they don't have any kind of food storage at all. So they're a textbook definition of a no-brainer strategy.
And, while it's expensive, you can rush-build a Hospital in a small city and get full effect out of it, resulting in the ability to very quickly get a late-game city to decent size. (Especially useful if you've captured an enemy capital that was knocked down to size 3 in the process but that is full of Wonders and such.)
Given that large cities have such huge benefits, being able to get to those sizes for such little cost and effort leads to the obvious strategy.

Under the system I'm working on, you'll still hit 50% at Hospitals, were you to build one, but now it'll have required three other buildings along the way to reach that threshold (Granary, Aqueduct, Sewer), and several of the buildings in question require the city to be a certain size. Obviously, that'll be more expensive, and all the other benefits I've listed will only partially offset the cost difference. Plus, think about how much extra construction time it will have taken; now, if you want your city to grow big, you'd have to take time away from production of other things.
The end result is that cities in high-food areas might build the full set, but ones without a lot of surplus food might stop after the first couple buildings. THAT is the effect I'm going for.

To keep things balanced, I've been tweaking the equation a bit as well. Instead of 15 + 6*(size-1) + (size-1)^1.8, I might use a flatter curve like 20+8x+x^1.6. Still evaluating that, but the original values should still work.

 

[Roxlimn]

Spaztimaus:

I don't follow your goal.

Right now, the hospital is a "no-brainer" only if you want big cities. If you don't want big cities, then food curve assures that you won't get there if you didn't make hospitals. You don't always want big cities. Some strategies call for cities of only size 6 or only of size 14. This is particularly true if you're spamming cities under Communism.

 

[Spatzimaus]

Right now, the hospital is a "no-brainer" only if you want big cities.

Unless you're going for a very specific social policy, like the Communism case you mentioned, you DO want big cities. In part, this is because the base science output and base trade rate income are tied directly to population. If your choice is two size 6 cities or a single size 12, which is better? Both produce the same science and money, but the 12 has two less unhappiness, needs fewer road hexes to connect to a network, and produces things twice as fast. Also, you don't need to pay for two Factories, etc. to boost your production. (The +culture and +happiness buildings are a different story since their outputs effectively stack.) Then there's the whole Specialist angle; with a larger city, you can actually build up enough GPPs to generate a great person occasionally, while smaller cities would effectively waste their points.

The problem is that in the core game, Hospitals become an all-or-nothing thing. People playing a "normal" way (i.e. not basing their entire strategy around a select group of SPs) will find that all of their cities grow to the point where they'd need Hospitals and then stagnate as the growth curve begins to quickly outpace what they can produce (thanks to the x^1.8 term). But there's simply no intermediate steps along the way.
Again, I point to the SMAC-type Hab Complex scenario, where your cities would grow at the full rate until you hit size 7, at which point they'd grind to a halt until you built that structure. Then came Hab Domes at size 13(?), with a similar effect. So what you saw, in practice, was an empire that would stagnate for dozens of turns, suddenly research the right tech, and BOOM, population would shoot through the roof (especially if you could tweak Civics to get Growth up to +6 to set the Baby Boom condition in every city).

I'm seeing the same thing happen here, albeit not as explicitly. Populations bog down, you unlock Hospitals, and then suddenly, massive population explosion within your empire, especially if you abuse the Maritimes. (A similar effect is seen on the production side of things when you unlock Factories.) To me, this is a bad model for a game. A more gradual progression is far better, IMO; you build a Granary in the ancient era, and it makes things a little better, you build an Aqueduct in the classical era and it's even better, and so on, but you're really only pacing the ever-increasing growth requirements.