Maximum number of cities

remconius · Oct 20, 2005

Lets try to find Nmax using math and some assumptions

Assumptions:
->for the largest number of cities possible Income minus Maintenance is zero.
->Without distance from capital maintenance (state property civic), all cities will pay the same maintenance based on number of cities.
->If all cities pay the same maintenance, the highest everage income per city decides the max maintenance it can afford.
->Each city pays 1 gold for every city, except the capital. At 31 cities each city pays 30 gold maintenance for number of cities.
->For Nmax lets assume you need to run 100% tax rate. And you built all relevant improvements in all towns.
->city income consists of trade income and income from worked tiles.

At Nmax:
Income - Maintenance = 0

Income = Maintenance

That means:
(city income)*income enhancers = (N * maintenance per city) * maintenance reducers

city income* +25% (grocer)* +25% (market) * +50% (bank) = (N * 1) * -50% (courthouse) * -50% police station

City income * 234% = N * 25%

Nmax = (City income * 234%) / 25%
Nmax = City income * (234%/25%)

Nmax = City income * 9.4

So if cities on average have a base income from worked tiles (with towns, etc) and trade routes of 50 gold. You could have 470 cities.

Of course maintenance costs per city was estimated at 1. To factor this in:

N = City income * 9.4 / maintenance per city

So if city maintenance is 2, you could build 235 cities at 50 income per city.

But cities should be able to make more money than 50 -> 75-100. Allowing for 1.5-2 times more cities.

Other costs like unit maintenance are not factored in.

Let me know if the calculations needs to be changed or based on different assumptions.

gruther4 · Oct 20, 2005

remconius said:
Lets try to find Nmax using math and some assumptions

Assumptions:
->for the largest number of cities possible Income minus Maintenance is zero.
->Without distance from capital maintenance (state property civic), all cities will pay the same maintenance based on number of cities.
->If all cities pay the same maintenance, the highest everage income per city decides the max maintenance it can afford.
->Each city pays 1 gold for every city, except the capital. At 31 cities each city pays 30 gold maintenance for number of cities.
->For Nmax lets assume you need to run 100% tax rate. And you built all relevant improvements in all towns.
->city income consists of trade income and income from worked tiles.

At Nmax:
Income - Maintenance = 0

Income = Maintenance

That means:
(city income)*income enhancers = (N * maintenance per city) * maintenance reducers

city income* +25% (grocer)* +25% (market) * +50% (bank) = (N * 1) * -50% (courthouse) * -50% police station

City income * 234% = N * 25%

Nmax = (City income * 234%) / 25%
Nmax = City income * (234%/25%)

Nmax = City income * 9.4

So if cities on average have a base income from worked tiles (with towns, etc) and trade routes of 50 gold. You could have 470 cities.

Of course maintenance costs per city was estimated at 1. To factor this in:

N = City income * 9.4 / maintenance per city

So if city maintenance is 2, you could build 235 cities at 50 income per city.

But cities should be able to make more money than 50 -> 75-100. Allowing for 1.5-2 times more cities.

Other costs like unit maintenance are not factored in.

Let me know if the calculations needs to be changed or based on different assumptions.

Questions:

Do the effects of grocers, banks, etc. compound? If a city makes 10 gold unassised, and you have on thing that gives you a bonus of 50%, get get 15 gold. Does a second 50% improvement give you 20 gold or 22.5 gold? If the former, the number should be 2 instead of 2.34. I always assumed that this was how it worked in civ3, but I could be wrong.

And it seems like you have per city income on the left and total maintainence on the right (N * maintanence per city) * multipliers. I think you mean mainanence increase per city, making it:

N * city income * income multipliers = N * maint per city * maint multipliers
or
city income * income mulitpliers = maint per city * maint multipliers

with:
(maint per city) = ((N-1) * maint increase per city)
(income multpilers) = 2
(maint multipliers) = 0.25

city income * 2 = ((N-1) * maint increase per city) * 0.25
N-1 = city income * 8 / maint increase per city
N = (city income * 8 / maint increase per city) + 1

of course, if the income multipliers do compound, just use 9.375 insted of 8.

A pretty large number, regardless

Grant

Shillen · Oct 20, 2005

I thought the maintenance per city increased with each city you had?

Darwin420 · Oct 20, 2005

Maintenance per city increases, but there's no artificial limit imposed on the map (unlike civ3). It was said you could build as many cities as your hear desired - but that probably won't be a winning strategy. Personally, I'm looking forward to building a small, tightly knit nation that surpasses the AI by leaps and bounds in all areas.

remconius · Oct 20, 2005

Maintenance per city is equal I believe, but you have to pay for all cities in every city.

So if maintenance is 2 per city in each city.

with 5 city maintenance is 5*2 = 10 per city => 50 in total
7*2=14 => 98 in total
10 *2=20 => 200 total

In this case going from 5 to 10 cities doubles maintenance twice.

civchu · Oct 20, 2005

Darwin420 said:
Maintenance per city increases, but there's no artificial limit imposed on the map (unlike civ3). It was said you could build as many cities as your hear desired - but that probably won't be a winning strategy. Personally, I'm looking forward to building a small, tightly knit nation that surpasses the AI by leaps and bounds in all areas.

sounds like a really bad bad multiplayer strategy...u probably more a single player

Darwin420 · Oct 20, 2005

@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).

KrikkitTwo · Oct 20, 2005

Well the formula probably is more complicated than that (It sounds like the maintenance per city Does vary for each city, so city 10 costs X and city 12 costs Y...since distance is a factor.)

but in general it sounds like the way to determine city maintenance is effectively N*N/X Where N is number of cities and X depends on civics, map size, and may vary a bit based on number of cities.

(because if is City 1 costs 1 and city 2 costs 2, then the result is still About N*N/2)

So basically Nmax=~Income*8/X

Where X is (how much a new city adds to all city's costs)+(how much more that city costs than the last city/2)

Willem · Oct 20, 2005

So where are you getting all these figures from? How do you know that a Grocer will increase your citiy's revenue by 25%. It all seems like so much conjecture if we don't even know for sure what these improvements will do.
Besides, there's also civics/techs/improvements that are supposed to reduce the maintenance costs. Not including those tosses your calculations right out the window.

remconius · Oct 20, 2005

since distance is a factor.)

I am assuming you are running state property which eliminates distance factor.

So where are you getting all these figures from? How do you know that a Grocer will increase your citiy's revenue by 25%. It all seems like so much conjecture if we don't even know for sure what these improvements will do.
Besides, there's also civics/techs/improvements that are supposed to reduce the maintenance costs. Not including those tosses your calculations right out the window.

Information is gathered by civfanatics site, see the pre-release info.

Civics can only increase the max city number. More income there, less maintenance here. Or choose something neutral.

It's fun speculation to prove the max number of cities is large enough to allow huge epic builder / warmonger games are viable.

elderotter · Oct 20, 2005

you guys think too much lol

Willem · Oct 20, 2005

remconius said:
I am assuming you are running state property which eliminates distance factor.

Do we know for certain that it eliminates it or does it just reduce it?

Civics can only increase the max city number. More income there, less maintenance here. Or choose something neutral.

Yes I'm aware of that. I'm just pointing out that your figures are purely conjecture at this point since we don't have all the information yet to make an accurate calculation.

It's fun speculation to prove the max number of cities is large enough to allow huge epic builder / warmonger games are viable.

Well the numbers are certainly high enough to satisfy me, I like large empires myself. At least we won't have to deal with a hardcoded limit on the number of cities anymore. It might be interesting playing on a map size of 516 X 512. That would make each square equivalent to about 50 miles in real life.

PS: Anyone know the dimensions of the Earth? I believe the circumference at the equater is 25,800 miles. From pole to pole it's slightly less than that.

NuclearElephant · Oct 20, 2005

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. Also, I thought maintainance was based off of improvements in the city? So here's my alternate assumption: instead of paying 1 gold for every other city, there is a basic cost of all the improvements (the cost of the maintainance reducers and income enhancers, assuming you build only these improvements in every city), and there is a percentage increase in city maintanence costs for every city you add after the capitol. If that was true, along with your other assumptions, then the maintainence function should be something like C(n)=[(n)(k)(c)^(n-1)][maintainance reducers] where n is the number of cities, k is the base cost of the infrastructure (Buildings) in every city, and c is the percentage increase in overall maintainence for an additional city/100 +1. Of course, if this is true we have no way to calculate the max number of cities unless we know c. k, on the other hand, should be *relatively* easy to find. :cool:

-NE

KrikkitTwo · Oct 20, 2005

remconius said:
Information is gathered by civfanatics site, see the pre-release info.

Civics can only increase the max city number. More income there, less maintenance here. Or choose something neutral.

It's fun speculation to prove the max number of cities is large enough to allow huge epic builder / warmonger games are viable.

Actually I believe the Civics chosen determine the city maintenance cost they are listed as High/Medium/Low Maintenance. (If that is a simple onetime cost it doesn't seem to affect much)

NuclearElephant said:
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.

I'm thinking exponential is used in the generic (really fast/increasing sense) If it really is exponential, then that does make the calculations Very Wierd.

making it Log(City Income*constant 1)/log(Constant 2)

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

Alistic · Oct 20, 2005

Its going to change as the city grows obviously that has been stated before. Without knowing by how much and the modifiers this is really just a stab in the dark. I doubt anyone comes even close to the actual calculation.

vbraun · Oct 20, 2005

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

Alistic · Oct 20, 2005

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

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.

Mujadaddy · Oct 20, 2005

elderotter said:
you guys think too much lol

Quoted for Redundancy

Just play the game and keep track of your most-cities game stat... THEN let us know

Tactician Zhao · Oct 20, 2005

Krikkitone said:
Actually I believe the Civics chosen determine the city maintenance cost they are listed as High/Medium/Low Maintenance. (If that is a simple onetime cost it doesn't seem to affect much)

does anyone know for sure if this is true? if it is, it will make the organized trait more appealing to me.. for some reason I was thinking that civics themselves had maintence costs.. but I had no basis for that belief that I know of, I just didn't think of the other possibilities

vbraun · Oct 20, 2005

Alistic said:
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.

I never said it was a good idea or actually possible without cheating. I was just saying that there is no limit.

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