Optimum number of cities for Culture Victory

[padlock]

I've read somewhere that each new city adds 30% to the cost of social policies. If we assume that new cities can produce roughly the same amount of culture as existing cities, then the following shows the relative cost of acquiring social polices based on number of cities.

Cities ----- Cost of social policies/number of culture produced
1 --------- 100%
2 --------- 65%
3 --------- 56%
4 --------- 55%
5 --------- 57%
6 --------- 62%
7 --------- 69%
8 --------- 78%
9 --------- 91%
10 -------- 106%

As can be seen from the above table, 4 is the optimial amount of cities to posess in terms of social policy cost per culture generated. Clearly there are other advantages to having more cities (extra science, gold, resources, etc.) so a player going for a culture victory will need to weigh those against the increased amount of culture required.

 

[SeptimusOctopus]

Thanks for that.

Did you calculate the 30% increase as cost(n+1) = cost(n)*1.3, and does it work this way in the game or is it similar to civ4's bonuses from buildings (ie % increase to some base cost rather than the current cost).

I think I'll try a cultural turtle with the French when I get home tonight.

 

[Dhaeman]

I originally thought the same thing. If you hover over the culture counter at the top of the menu it says there is a 30% add on to social policy cost for new cities. So assuming that all cities produce culture equally the payoff is at 4 cities as stated since you would gain 33% more culture from the new city vs. a 30% loss due to size.

However, I just annexed a city and my required culture for a social policy upgrade went from 1990 to 2265 which is only a ~14% increase. I believe this took me from 5 to 6 cities so the math makes sense. So I'm pretty sure Civ 5 math calculates this and all percentage bonuses off of the base rate and not exponentially.

So in actuality if all of your culture producing cities are equal it will always benefit you to have more cities. On the other hand, it will benefit you more if your puppet states produce culture buildings as you get the culture without the increase in social policy. It would be a good strat if the puppet state AI wasn't so idiotic and produced useless buildings that ate up maintenance cost.

 

[padlock]

I calculated culture cost as:

x + .3x^(y-1)

where:
x is the base social policy cost with 1 city
y is the number of cities you have

I calculated culture generated as:

y * z

where:
y = number of cities you have
z = amount of culture generated by 1 city

so cost of social policies per culture generated for 1 city is:

x / z

For 2 citites, it is:

(x + .3x) / 2z

or 65% of what it is for 1 city

For 3 cities it is:

(x + .3x^2) / 3z

or 56% of what it is for 1 city.

etc.

 

[Celevin]

I'm going to be unbelievably snarky and say it's 1, with a whole bunch of puppets, and a bit of good luck.

 

[padlock]

I originally thought the same thing. If you hover over the culture counter at the top of the menu it says there is a 30% add on to social policy cost for new cities. So assuming that all cities produce culture equally the payoff is at 4 cities as stated since you would gain 33% more culture from the new city vs. a 30% loss due to size.

However, I just annexed a city and my required culture for a social policy upgrade went from 1990 to 2265 which is only a ~14% increase. I believe this took me from 5 to 6 cities so the math makes sense. So I'm pretty sure Civ 5 math calculates this and all percentage bonuses off of the base rate and not exponentially.

So in actuality if all of your culture producing cities are equal it will always benefit you to have more cities. On the other hand, it will benefit you more if your puppet states produce culture buildings as you get the culture without the increase in social policy. It would be a good strat if the puppet state AI wasn't so idiotic and produced useless buildings that ate up maintenance cost.

Interesting. If that's true and new social policies only add 30% of the base cost for each new city, then you're right and each additional city will actually reduce the cost of acquiring new social policies as long as it produces as much culture as the average of your previous cities.

The reduction becomes negligible after a very few cities though.

Here's the new table:

Cities ---- Cost of social policies per culture generated
1 -------- 100%
2 -------- 65%
3 -------- 53%
4 -------- 48%
5 -------- 44%
6 -------- 42%
7 -------- 40%
8 -------- 39%
9 -------- 38%
10 ------- 37%
25 ------- 33%
100 ------ 31%
500 ------ 30%

Note that this changes if you have any puppet cities since if you do, the percentage of extra culture you get for each new city might be less then the social policy cost increase.

As an asside, I think puppet cities not counting towards social policy costs is a bug which can be exploited and make cultural victories far too easy. I hope a future patch fixes this behaviour.

 

[rekenner]

Puppet state cities *don't* add to the cost you need to get for policies. You get their culture (what of it exists), but it doesn't increase the cost. Though, they act amazingly dumb anyway and go towards way too many buildings you don't need.

 

[padlock]

Puppet state cities *don't* add to the cost you need to get for policies. You get their culture (what of it exists), but it doesn't increase the cost. Though, they act amazingly dumb anyway and go towards way too many buildings you don't need.

I know, and I think that they absolutely should count. The current behaviour is either a terrible design decision, or a bug.

 

[KrikkitTwo]

I thought you didn't get Puppet culture
(and the idea of a puppet state is that it builds worthless buildings...Puppets drain your Gold, Annexes drain your happiness)

 

[Dhaeman]

I know, and I think that they absolutely should count. The current behaviour is either a terrible design decision, or a bug.

I disagree. There are only 2 advantages a puppet state has over an annexed city:

1) No unhappiness from occupation without a courthouse
2) No increase in social policy cost

If you annex a city and build a courthouse and social policy costs went up either way then the obvious strat would always be puppet state until you have enough happiness to withstand building a courthouse. As is it is now you have to think which is more important to you.

 

[Grotius]

So, padlock, now you're saying that there's no need to limit expansion even if one's pursuing a culture win?

I know your second table assumes that each new city has about the same amount of culture as its predecessors. In practice it may not work out that way, as culture buildings are pricey, and later cities may lag behind in producing them.

My first attempt at a culture win has been a dismal failure. For a long while I had only 5 cities, though recently I expanded to 8. I have completed only two social policy trees, and it's 1970 (at Prince level). Fun to try, though.

 

[weregamer]

The 1 + (n-1)*.3 cost formula makes a lot more sense anyway as a game design decision. Larger empires are more costly, and as Grotius pointed out making all of your cities cultural powerhouses will be expensive, so adding an artificial exponential increase on policy cost would be ruinous.

This suggests that Rome might be a good choice for an expansive approach to cultural victory, since you get a big discount on construction of all those duplicate buildings. You'd definitely want to aim for Socialism before you got too big, too.

 

[padlock]

So, padlock, now you're saying that there's no need to limit expansion even if one's pursuing a culture win?

I know your second table assumes that each new city has about the same amount of culture as its predecessors. In practice it may not work out that way, as culture buildings are pricey, and later cities may lag behind in producing them.

My first attempt at a culture win has been a dismal failure. For a long while I had only 5 cities, though recently I expanded to 8. I have completed only two social policy trees, and it's 1970 (at Prince level). Fun to try, though.

Now that I think about it, the assumption that each new city produces as much culture as the ones before isn't a very good one. First of all, only one city can have the national wonder that doubles culture, and also the culture provided by city states, which could make up a substantial chunk of the culture generated, is not affected by the number of cities you own.

Perhaps less cities are better after all.

 

[AlienFromBeyond]

I think there's a reason the Bollywood achievement says max 3 cities .

 

[qyll]

Hmmm... but wouldn't 5 or 6 cities be better than 4 just from the fact that the 5th/6th city will bring in extra research so that you can get to wonder techs faster?

 

[Shillen]

I think there's a reason the Bollywood achievement says max 3 cities .

I did the bollywood achievement. I think it would have been easier if I had more cities and teched to broadcast towers and cristo redentor faster.

 

[DalekDavros]

As an asside, I think puppet cities not counting towards social policy costs is a bug which can be exploited and make cultural victories far too easy. I hope a future patch fixes this behaviour.

Not a bug. It's a documented feature mentioned on the description of what making a puppet state does. It's also historically accurate: think conquered people paying for palaces in the capitals of their conquerors, artists moving from conquered cities to core cities, etc.

Now that I think about it, the assumption that each new city produces as much culture as the ones before isn't a very good one. First of all, only one city can have the national wonder that doubles culture, and also the culture provided by city states, which could make up a substantial chunk of the culture generated, is not affected by the number of cities you own.

Perhaps less cities are better after all.

In my experience, over 50% of early game culture comes from city-states and another 25% comes from Stonehenge. Eventually, the cities end up approximately equal, but early on fewer cities is definitely better. If you're going for puppet-culture, that's probably true later on as well. And having fewer non-puppet cities is good for getting out the national wonders too.

Empirically, I'm finding 3-4 to be best: not so many that you can't keep up on culture buildings, but enough to guarantee that you get the early strat resources (and a few lux) and to enable you to have the capacity to put military units out even when you really need to be building a wonder/culture building too.

 

[tiels]

Having very many cities is not necessarily a bad thing - at least in this thread the computer wins a cultural victory with approximately 30 cities.

Civ 5 Playthru -How to Conquer the World...

On page 19 you can see the world map and on page 20 the cultural win. The difficulty was 'normal' (prince) so the computer should play the same game as we do (at least as far as I remember).

 

[Meneer Popken]

Having very many cities is not necessarily a bad thing - at least in this thread the computer wins a cultural victory with approximately 30 cities.

Civ 5 Playthru -How to Conquer the World...

On page 19 you can see the world map and on page 20 the cultural win. The difficulty was 'normal' (prince) so the computer should play the same game as we do (at least as far as I remember).

All of those are puppet cities, so no culture cost increase.

 

[tiels]

I believe you, but does the knowledge come from the fact that the AI always plays like this or can you see it from a save game?