(G&K) Optimal number of cities for culture victory?

[Gort]

With religion giving lots of avenues for gaining culture, I thought I'd revisit the idea of a culture victory. But it appears that in Gods and Kings it's become less crippling to add extra cities to your empire - you only add 15% (or 10% with the appropriate Liberty social policy) to the cost of social policies per city. I'm going to assume that we have the cost reducer from Liberty because it seems a no-brainer for this kind of victory.

Now, I've read that the social policy cost increase is additive, so it's:

100% with one city
110% with two cities
120% with three cities

and so on.

Now, given that you should be able to get a similar amount of culture out of each city (although a wonder-spamming hermitage-type city might throw this out somewhat) expanding seems to be a no-brainer - you only have to make ten percent more culture as a result of the new city for it to be worth it.

Based on this, it would seem that a sprawling empire with a focus on the culture buildings would be ideal for a culture victory. Perhaps Napoleon, taking Liberty and Piety as his social policies, and exploiting the heck out of the +33% culture on a wonder social policy from Piety would be the fastest cultural victory?

 

[NukeAJS]

Social policy costs compound from the number of cities. They don't simply add another 10% per city. I don't know the exact formula, but it's definitely not linear. Here's an outdated chart to give you an idea but not the exact numbers: http://civilization.wikia.com/wiki/Mathematics_of_Civilization_V#Formula_for_Social_Policies

To answer your question, I think the rule of thumb is still as few as possible cities in most situations. Yes there are some instances where getting more cities will get you SPs faster in the short game (especially with religion added), but in the long run, they will slow you down.

Instead, think about how to use those religious policies for your small empire regarding culture the best you can. An easy example would be getting monasteries if you have lots of wine/incense around, or similarly -- cathedrals. Another example would be the +1 faith and culture from gold and silver if you're loaded with those.

 

[Hambil]

One. Assuming you have a good start.

 

[Gort]

Social policy costs compound from the number of cities. They don't simply add another 10% per city. I don't know the exact formula, but it's definitely not linear. Here's an outdated chart to give you an idea but not the exact numbers: http://civilization.wikia.com/wiki/Mathematics_of_Civilization_V#Formula_for_Social_Policies

To answer your question, I think the rule of thumb is still as few as possible cities in most situations. Yes there are some instances where getting more cities will get you SPs faster in the short game (especially with religion added), but in the long run, they will slow you down.

Even in the maths in that link you can see that there are cases where expanding will speed you up (playing France, or Songhai using Mud Pyramid Mosques), and they've basically halved the cost of adding extra cities, so I'm sure there will be more "corner cases" such as these.

First I need to get my head around the maths, though - finding it kinda impenetrable.

 

[Xile]

Social policy costs compound from the number of cities. They don't simply add another 10% per city. I don't know the exact formula, but it's definitely not linear. Here's an outdated chart to give you an idea but not the exact numbers: http://civilization.wikia.com/wiki/Mathematics_of_Civilization_V#Formula_for_Social_Policies

No, it is linear, if the the formula there is right.


pb(k) = pspd(25 + (6k)^1.7)

n = nr. of cities.

p(n,k) = pb(k)(1 + pm(n − 1)) rounded to the next multiple of 5.


The only part that's not linear about that is pb(k), which has nothing to do with the city count. Without any policies the increase is about 30% so you can just do 68.45*(100+30(n-1)) and compare them to the corresponding numbers in the table and you should come very close to them. When you add Representation and Religious Tolerance the increase of social policy cost per city drops down to about 10%.

 

[somerandomdude]

Regardless of the formula, the problem with adding more cities isn't the social policy cost. It's pretty clear that with enough culture buildings in each city you can overcome that.

The problem is that, with a large sprawling empire, you need a large sprawling army to protect it. This (a) costs money, that needs to be used for the maintenance of all the culture buildings you have, and (b) costs time, that would normally be used building infrastructure and researching the top half of the tech tree.

The smaller the empire, the easier it is to defend. The exception would be small conquests that result in puppets (which don't add to the social policy cost).

 

[Syntax Error]

From the Tradition article in the War Academy, the best would probably be four cities settled as quickly as possible, then get all culture buildings before Acoustics. Once Acoustics gets researched, pop the SP for free culture buildings in your first four cities. This gets you Opera Houses on all cities for free, and gives you the choice to build an Hermitage (I think?) quite early!

 

[Xile]

From the Tradition article in the War Academy, the best would probably be four cities settled as quickly as possible, then get all culture buildings before Acoustics. Once Acoustics gets researched, pop the SP for free culture buildings in your first four cities. This gets you Opera Houses on all cities for free, and gives you the choice to build an Hermitage (I think?) quite early!

You don't have to wait for acoustics to get legalism, you can get it as soon as you your amphitheaters are built.

Also, having fewer cities reduces the chance of getting DoW'd, because you have less land for AIs to covet. As already pointed out maintenance costs, large empire being harder to defend and the happiness issues, makes going wide is not worth it. 3 or 4 cities seems a good way to go and that mostly depends on whether or not you have 4 good city spots.

 

[Gort]

I appreciate all the gut advice people are handing out, but what I really want to do is work out what the new formula is for social policy costs.

p(n,k) = pb(k)(1 + pm(n − 1)) rounded to the next multiple of 5

was what the formula was before.

What would help now is if we could construct a table of values for how much a specific policy costs at a specific number of cities. We could then work out if adding cities would speed or slow your policy acquisition.

It seems obvious to me that the best social policies for this strategy are:

1. Representation (reduces the increase of social policy costs per city to 10%)
2. Religious freedom (reduces the cost of social policies by 10%)

 

[budweiser]

Regardless of the formula, the problem with adding more cities isn't the social policy cost. It's pretty clear that with enough culture buildings in each city you can overcome that.

The problem is that, with a large sprawling empire, you need a large sprawling army to protect it. This (a) costs money, that needs to be used for the maintenance of all the culture buildings you have, and (b) costs time, that would normally be used building infrastructure and researching the top half of the tech tree.

The smaller the empire, the easier it is to defend. The exception would be small conquests that result in puppets (which don't add to the social policy cost).

Not exactly. If you own your own continent, you are free to go wild on culture and load up on cities.

I just played a Dutch game where I had a good sized continent and it was only me Egypt and Polynesia, two cheeseballs. I went Liberty for 3 fast cities and build nothing but men. I had them both dead by 150AD and then I went wild filling up on cities. I had 11 by the end. At one point I was making 8 or 9 turn culture.

A case like that is a good candidate for wide culture.

 

[Gort]

I don't find defending myself against the AI to be that hard no matter the size of my empire. Playing as someone like Napoleon would make it even easier with his two great unique units.

 

[Zerrigan]

For anyone wanting to work on that table, I'm going to make a thread for it and we can compile our numbers there.

 

[Gort]

Sounds good, Zerrigan. Just be careful that difficulty, game speed and map size all seem to have a hand in policy cost.

 

[Hambil]

I can keep my turns to new policy under 10 with one city. So, though it might have been good fun I don't see much difference between my 1 and your 11 mentioned above. Both ended up with under 10 turns per new policy.

 

[budweiser]

I can keep my turns to new policy under 10 with one city. So, though it might have been good fun I don't see much difference between my 1 and your 11 mentioned above. Both ended up with under 10 turns per new policy.

Yeah, thats a curious point. When I was playing it, I felt to myself that I just had too many cities.

But there must be a benefit one way or the other. I dont think it would be a very good game design if it made zero difference between how many cites you had. Or would it?

 

[Gort]

Well, I think the design intent of the cultural victory is that it should be achievable by small, tall empires as well as wide ones. If it made zero difference how many cities you had, the wide empire would beat a tall one any day of the week - any idiot can make more culture with a hundred cities than with one.

The question is - when will adding new cities slow you down, and when will adding new cities speed you up? In vanilla on "normal" settings, you needed 79,940 culture in total to win the game. If you added a second city, you needed 103,950, which is 24,010 more. Therefore you would win faster if you could guarantee that the new city would make 24,010 culture before you won. 24,010 is roughly 30% of 79,940, which is the "30% increase per city" stat.

Now that they've changed it to only 15%, your new city only has to be half as good before it's speeding you up towards your victory. I want to know exactly how good it needs to be to be worth building.

 

[Calouste]

One. Assuming you have a good start.

And if you don't have a good start, Culture is probably not the most convenient victory condition.

 

[Tabarnak]

It's probably unchanged : 4 cities is probably optimal.

 

[Omniabsence]

On this, are additional cities better off being micro-managed to focus on culture or is it more efficient to make them in to production or gold cities? Or should I just focus all of my cities in to Culture?

 

[budweiser]

Well, I think the design intent of the cultural victory is that it should be achievable by small, tall empires as well as wide ones. If it made zero difference how many cities you had, the wide empire would beat a tall one any day of the week - any idiot can make more culture with a hundred cities than with one.

The question is - when will adding new cities slow you down, and when will adding new cities speed you up? In vanilla on "normal" settings, you needed 79,940 culture in total to win the game. If you added a second city, you needed 103,950, which is 24,010 more. Therefore you would win faster if you could guarantee that the new city would make 24,010 culture before you won. 24,010 is roughly 30% of 79,940, which is the "30% increase per city" stat.

Now that they've changed it to only 15%, your new city only has to be half as good before it's speeding you up towards your victory. I want to know exactly how good it needs to be to be worth building.

Yesterday I played a culture game as ethiopia with 4 cities. I had a wonder in every city, I had the liberty and Piety culture bonuses working.

Once I hit railroad, I made a 5th city so that I could build the new castle wonder in that city. I spent gold to purchase all the culture buildings including a radio tower and I very quickly had 82 CPT coming out of this city but did not have a wonder in place there yet.

How can you tell if that speeded me up or slowed me down?