Maximum number of cities

[NuclearElephant]

And this is closer than any of the above garbly goo. If you couldnt then what would be the point. They said you arent going to be able to city spam. You just have to let your cities grow a bit before you think about putting more down.

We weren't talking about physical maximum for cities, just how many you could possibly sustain without going bankrupt. I agree, it would be rediculous to really care about something like this, but it sure is fun to speculate. Gives us something to do until the game comes out, heh.

However if the rates are low enough (1-100%) exponential is very close to simple addition.

With a lot of cities, it adds up even with a small rate. With a rate of say 2% per city, when you get up around 20 cities that's still going to raise your costs in each city by almost 50%

But like you both said, we have no idea how its really calculated, so I guess no one should get into a fit over it *Thinks of certain someones on another thread*.

-NE

 

[KrikkitTwo]

You can have 8749874098740987321409832450987+ cities on a map if you really wanted to...

Actually that would be impossible unless the game allows
800000000000000x1000000000000000 maps which I seriously doubt it does. (I'm almost certain there is a limit of one city per square)

With a lot of cities, it adds up even with a small rate. With a rate of say 2% per city, when you get up around 20 cities that's still going to raise your costs in each city by almost 50%

Although that is pretty close to the 40% you get by adding 20 2% increases.


The way I could see the maintenance for cities working
for any Given City
D=Distance (this city)
N=City Number (this City)
T=Total number of cities in Empire
lower case=constants (possibly based on civics+mapsize)

a*f^(N)*g^(T)+bN+cT+eD

Integrating to maintenance cost for an empire

[a*g(T)*(f^T-1)/(f-1)]+[bT(T+1)/2]+[cT*T]+(Distance factor)

Just because they seem to have a system that was designed to replace corruption, it is probably similar to the corruption formula, so probably no exponential term (although because exponential would be similar to additive I could see them doing it... but because it is similar there isn't much point...and additive is simpler)

In any case it simplifies to

City Number= City Income/(rate of increase =c + b/2))

 

[gruther4]

And this is closer than any of the above garbly goo. If you couldnt then what would be the point. They said you arent going to be able to city spam. You just have to let your cities grow a bit before you think about putting more down.

Actually, I would guess that this is way off. Most programs use 32 bits to represent 'typical' numbers, putting a practical limit on the size of numbers programs can easily manage. This limit is around 4 billion. So you are probably limited to around 4 billion cities, regardless of city cost, etc, unless, of course, the civ programmers took extreme measures to get beyond this limit...



Math is fun!

 

[vbraun]

Actually that would be impossible unless the game allows
800000000000000x1000000000000000 maps which I seriously doubt it does. (I'm almost certain there is a limit of one city per square)

I was assuming that the map was bigger then that, in other words as big as I want it/need it.

 

[gruther4]

Actually, I would guess that this is way off. Most programs use 32 bits to represent 'typical' numbers, putting a practical limit on the size of numbers programs can easily manage. This limit is around 4 billion. So you are probably limited to around 4 billion cities, regardless of city cost, etc, unless, of course, the civ programmers took extreme measures to get beyond this limit...



Math is fun!

By the way:

Assuming that it takes an averate of 2 seconds to create a settler, route the settler, build the city, etc, it would take 272 years to get to 2^32 cities, and Civ 5 will probably be out by then, so I wouldn't recommend testing this limit.

 

[NuclearElephant]

By the way:

Assuming that it takes an averate of 2 seconds to create a settler, route the settler, build the city, etc, it would take 272 years to get to 2^32 cities, and Civ 5 will probably be out by then, so I wouldn't recommend testing this limit.

Hehe. Wow. I should be doing my homework.

 

[gruther4]

I thought I read in the other thread "Empire Building: still possible?" That maintanence (or corruption) in each city was subject to an exponential increase depending on the number of cities you owned, minus the capitol.

You must mean quadratic, not exponential. Quadratic means something like N^2, while exponential means something like 2^N. An example of exponential increase would be if total maintenance cost doubles each time you add a city, which would soon get ridiculous (unless it was only a 5% increase or something like someone else mentioned, but I don't think this sort of growth is what we are looking at)

I'm pretty sure as people have described it, the relationship between total maintenance and number of cities is quadratic. That is, maintenance will be A * N^2 + B * N + C, for some values of A, B, and C. This covers situations where each city has a maintenance equal to the number of cities minus the capitol (N * (N - 1) or N^2 - N (A = 1, B = 1, C = 0), or if each city has a mainainence equal to the order in which it was built (city one = 0, city 2 = 1, city 3 = 2 becomes 0 + 1+ 2 + 3 + ... ) becomes N / 2 * (N - 1) or 1/2 * N^2 - 1/2 * N (A = 1/2, B = -1/2, C = 0).

The shape is significant because when you subtract this from a constant income per city, you get a different quadratic. Say we have the second situation:

Income = D * N
Maintenance = 1/2 * N^2 - 1/2 * N
Net Income = -1/2 * N^2 + (D - 1/2) * N

From this we can solve for two things: The optimal net income and the point at which your income becomes zero.

Optimum (zero crossing of derivative) -> -N + D - 1/2 = 0 -> N = D - 1/2 or D for large D. The interesting conclusion is that the optimal number of cities is pretty much equal to the average gross income per city. Any city past this limit will cost more than it produces. Now, the additional production/great people/map placement will probably offset these losses for some time, but a practical optimum still exists.

Absolute Maximum (zero crossing of function) -> -1/2 * N^2 + (D - 1/2) * N = 0 -> 1/2 * N = D - 1/2 -> N = 2D - 1 So if you build more cities than this then you wont be able to support them without other sources of income.

I agree with some posters that this sort of discussion is pretty useless until we figure out what the real rules are and the real numbers. But speculation is fun, and some people enjoy these sort of problems . And they also give us some insight into how the rules might play out. For instance, the optimal number of cities will increase as the income per city increases, and it is a linear relationship. So every time you get an advance/civic/building that increases your income by 50% you should attempt to get 50% more cities as the increase comes into effect to stay near the optimum.

Ok, I'm done now,
Grant

 

[Alistic]

If the number is set then this game is broken from the start. If you dont see why that must be true then I dont know what too say.

I think this is a flawed problem because your looking for a set number that can't exist. To much math and too little common sense.

Throw civics, religion, govt type, wonders, terrain bonus's, lux. Especially with random maps. Leaders, huts, barbs. Way to many factors. Wich is the beauty of civ.

You could probably get it down to percentages, under defined curcumstances. After countless hours of calculations. Maybe it could be your lifes work.

 

[remconius]

Also, I thought maintainance was based off of improvements in the city?

You're thinking in civ 4 terms. Improvement maintenance is taken out. Pretty sure I read that.

Also distance from the capital tax can be avoided with state property civic.

 

[gruther4]

If the number is finate then this game is broken from the start. If you dont see why that must be true then I dont know what too say.

I think this is a flawed problem because your looking for a finite number that can't exist. To much math and too little common sense.

Throw civics, religion, govt type, wonders, terrain bonus's, lux. Especially with random maps. Leaders, huts, barbs. Way to many factors. Wich is the beauty of civ.

You could probably get it down to percentages, under defined curcumstances. After countless hours of calculations. Maybe it could be your lifes work.

Oh, it is certainly finite. Computers don't handle infinity very well. Do you have an infinity GB hard drive? No, I didn't think so. So nothing in Civ can be infinite. If city names are only 20 characters, you would need 20 GB per billion citties just to store the names. Now, this is a bit ridiculous, since a thousand cities is effectively infinite for the purposes of civ (max ten thousand for really, really patient players).

So the question is: is there a practical limit based on the rules (ie, you could cheat to get more cities, or have more cities for a limited time, but without cheating it is impossible to do sustainably because the rules would prevent it). And the answer, if the relationship is quadratic, is yes. This is because the growth of a quadratic function will eventually exceed the growth of a linear function, no matter what. This is a change from Civ 3.

The thing is, we don't need to deal with exact numbers to state things like this. And I think you will agree that it is important to look at things this way, since according to your post, if the rules work like this the game will be 'broken from the start'.

I disagree, by the way. Being limited to some finite but large number of cities is fine in my books. I have trouble keeping track of more than 10 or so, anyways. My attention span is finite

Grant

 

[Alistic]

Sorry i used the wrong word its definatly finite. But its not a set number. No way will someone come up with a single number for an answer.

Someone could find out the probabilitys under set circumstances alot eaiser. Thats a realistic goal anyways.

 

[gruther4]

Sorry i used the wrong word its definatly finite. But its not a set number.

True Better wording.

Not set, but it can be approximated. And relationships can be established. Civ is much simpler than the real world, and we are always trying to establish formulas and relationships in the real world. Civ, and my posts in this thread, are really just an imitation of that. I didn't say you should build 42 cities; I said that as your income per city increases the number of cities you should have should also increase. That is a relationship, not a set number.

(Edited to complete idea)

 

[rilzic]

i didn't read through all that but if more cities becomes more expansive then if you want a empire with more cities then just lower main cost in a mod a little. the way it works (i think) is you can have fewwer cities that make more money or more cities that make less money. i don't think you would even need a real mod just use the editior you might be able to do this. as long as you DO make the extra cities then nothing will happen to gameplay besides their being more cities. or just do anything to increase wealth generation make hamlets and towns generate more money or anything. i wouldn't worry after a week or less there will be mods and such to change this, infact i bet someone will come out with a mod that says:

on a small map dl this for 10 - 20 cities in the first age

on a small map dl this for 20 - 30 cities and so on and so on.

have no fear the modding community is here!!

 

[NuclearElephant]

You're thinking in civ 4 terms. Improvement maintenance is taken out. Pretty sure I read that.

Also distance from the capital tax can be avoided with state property civic.

I didn't know that. Well that changes things quite a bit. Is it purely based off of number of cities and distance and then modified by civics, etc? Heck as far as we know it could be made up of some quadratic (such as the square of the distance from capitol) and an exponential function, one for each component, with modifiers. And to precede an argument here, yes if that was true we could estimate an exponential part by adding some percent per city, but for the sake of perfectionists everywhere I hope they didn't write that into the code

BTW, are these kinds of things possible to find out by looking at these sections of code we are supposed to be getting access to? Not that I would ever look...

Interesting point, Gruther, about the ideal number of cities. And Krikkitone so you are saying that maybe cost is calculated differently for different cities based partly on the order in which they were founded? I hadn't ever thought of it that way, but I guess it is possible.

 

[NuclearElephant]

have no fear the modding community is here!!

Are you a modder? If so, you aught to hook up with Aussie Lurker. Now there is someone with some good ideas for a mod.

 

[KrikkitTwo]

Interesting point, Gruther, about the ideal number of cities. And Krikkitone so you are saying that maybe cost is calculated differently for different cities based partly on the order in which they were founded? I hadn't ever thought of it that way, but I guess it is possible.

Well it wouldn't have to be the order that they were founded in, but that would work just as well (since... well I guess it does matter which city generates the maintenance because then it matters which city the courthouse is in)

Eg.
group of 2 cities (A and B) total maintenance=20
group of 3 cities (A, B, and C) total maintenance =40

It matters which city generates the maintenance because what happens if I add a courthouse to C only...
did C add 20 extra maintenance itself [so adding a courthousewould save you 10 gpt], or
did C's presence cause an increase in the maintenance of A+B [so adding a courthouse to C will save you less than 10 gpt because C doesn't have 20 maintenance cost]

Actually given that game mechanic, I can see why they said some is added based on the city and some based on the total # of cities, so
A=0
A=1, B=2
A=2, B=3, C=4
A=3, B=4, C=5, and D=6
(although that does seem a bit fast of an increase, I'm sure fractions and rounding will come in, as well as civics... And the reason I think Civics will affect the City maintenance cost is because otherwise, they Don't really matter for a civ with say 10 cities)

It probably would be easiest (in terms of balancing, and keeping track of things) to have all cities have the same 'city number' maintenance and have the distance be the only differentiating factor. That way you avoid bugs like the RCP from Civ3. (determining the order of cities)

OK, so on the argument from simplicity, here is my PROPOSED Maintenance formula for Civ 4

Maintenance to support a City=
(Civics Factor*Map Factor*Total Number of Cities+
Civic Distance Factor*Map Distance Factor*Distance)
/2^(Number of anti corruption buildings)

Where Distance is to either the Palace or Forbidden Palace, whatever is closer.

What I'm interested in is if Distance is the tile distance or the travel time distance, and if things like radio or electricity decrease it (given that they provide for rapid communication)

And as someone pointed out the number does exist [again depending on Civics, and assuming fully developed cities at a certain tech level], especially if the amount of terrain is fairly large, because once you have a fairly large amount of terrain your gold per TILE should be fairly close to the average, because you won't have any unusual spots in your empire (there will be enough of them that they aren't unusual)

It's just like for Civ3 Communism you could determine the number of cities that would give maximum production for your empire... if you had a reasonably large number of well spaced cities the Average production of a city was pretty much fixed (2 per tile +bonus grasland+hill+floodplain-Desert-Tundra+bonuses... the numbers of those bonuses and penalties per city would average out after a decent # of cities... Nuclear plants complicated things, but you can assume ~X% have access to a River, based on the map)

 

[hclass]

i didn't read through all that but if more cities becomes more expansive then if you want a empire with more cities then just lower main cost in a mod a little.

mod is one way, but one burning quetion remain:
Will conquest or building big empire in a long game still fun in Civ4 (without modifying)?

Why can't Firaxis make Building huge empire (especial then win with conquest) as important as other non-conqueror option?

Hint: Anything BIG like espionage system, huge and agressive game and so on which should be good selling points (if Firaxis has done them well) but absent from all previews mean something.

"I come, I see, I conquer" (Guess who say this)

For Civ4,
"I come, I can't see, I rather wait"

 

[civchu]

@civchu: it all depends how the new rules play out. Who knows, you might have a winning strategy with smaller, larger cities, if you know what you're doing (at least that's what I'm gathering from all the previews).

But, you're right, I don't usually play much multiplayer (just a few hotseat games with my wife and some friends).

but i see your point....i guess larger more efficient cities may be the way to go

and a few more razings on the way!

 

[Mr. Blonde]

My bet is that if you work your cities and tiles in a reasonable way and get the optimal civics for large empires, a domination victory will be possible in the middle of the industrial age, this is all that is needed for balanced winning options, really.
People out there are looking forward to a gamplay where you don´t have to expand like crazy and build a behemoth empire as fast as possible to have a good chance at winning. In civ4 there may finally be -gasp- several equally valid ways of winning the game.

 

[Martinus]

You have to also remember about civic costs. I may be wrong, but I would assume State Property is medium to high maintenance.