9 cities for cultural victory...or?

[Thrar]

To achieve a cultural victory on a standard size map, many people consider it the optimal case to get 9 cities up, to be able to spread any religion they may get to all of them, and thus be able to build cathedrals in each of the culture cities.

I'm wondering, why is everyone so sure that 9 cities is the best number for that? It's obvious that you can't get by with less, but how about more?
I've taken a look at the optimal case, that all 7 religions are available to the player. The idea is basically the same with less, you still need 9+ cities, but probabilities change.

Some easy maths on that: 6*9=63, you need 63 missionaries to spread everything (minus the automatically spreads, at most one per city). In your culture cities you need all 7 each, so that's 3*7=21, leaves 42 religions to be distributed over the remaining cities. With 6 more cities (9 total), that's obviously 7 each. With 7 more cities, you're down to 6 in each one (missing a different one everywhere).
Now what's the point in that? Why would it be worth squeezing in a junk city somewhere just to spread those religions a little thinner?

I'm not sure if there is a point, but I also don't want to take for granted that there is none. That's why I'd like to hear some opinions of other players about this.
A settler costs 100 hammers at standard speed. A missionary is 40 a piece. By building a 10th city, you invest 100 hammers. However, as we know, it becomes incrementally harder to spread a new religion to a city, depending on how many there are already present.
For completeness, you technically get one more "free" spread with an extra city. Saves a missionary, but since you probably don't want to wait for that auto-spread, I'll disregard it here. With that 10th city (which could be in the middle of a desert, right between two other cities on an unused tile, on a 1-tile island), you save those 6 most difficult 6-spreads (spreading a religion with 6 present already), and instead get one more of the 1-5-spreads each.
As a result you'll get less failures in spreading those religions. Saves missionaries, which in turn saves hammers. But how many? Depends on the exact chances for each spread, which I don't know where to find. If it saves 3 missionaries on average, it's worth the extra city, given a crap tile somewhere to found it. I'm pretty sure you'll save those 3 and several more, but don't have the data to prove it.

Do people usually get to universal suffrage when going for culture? If so, where to found that last city doesn't matter at all, since you can always buy the temples. Otherwise, you'd have to consider finding a place that allows building them over time, or has food for poprushing.

It's a pretty weak incentive to found an extra city, but I think it should allow to get your cultural victory a few turns earlier, since you save time/hammers on the missionary work and thus building the cathedrals.
How are your experiences, how difficult is it actually to get that 7th (or 5th, 6th) religion spread in a city? How many missionaries does it take?

 

[SS-18 ICBM]

9 cities to spread religion (for cathedrals=+50% culture in a city), because religions become more difficult to spread with more religions in a city. You don't need to spread all the religions to every city, and building more cities you can't defend properly (cultural builds) only costs you money and may have you fighting a war with a neighbor.

No, uni suff is not a good civic and use representation instead.

 

[MrCynical]

There is also a significant issue that you may not have 5+ religions available at all. Unless you found all them yourself (impractical at higher difficulty levels) you may well not have access to that many religions, since your only alternative ways of acquiring it are:

1)Natural spread - extremely unlikely if you already have multiple religions in your empire since it can only occur to cities with no religion.

2)Foregin Missionaries - highly dependent on which AI leaders you get. Some will happily spam missionaries, but many will do nothing to spread religion.

3)Conquer a city with the religion - not really fitting with the cultural victory approach.

It is extremely difficult to get the 6th and 7th religions into a city, but the odds of you having this many religions in a normal game are low. Founding additional cities to save a few missionaries you lose to failures up to religion 5 isn't a very good trade off.

 

[Zophos]

Since this sort of post always makes me want to figure out the numbers, I looked in the SDK. The probability of spreading a new religion is calculated in CvUnit::spread (CvUnit.cpp:4045):

iSpreadProb = ((pCity->getTeam() == getTeam()) ? 40 : 20); // XXX mod
iSpreadProb += (((GC.getNumReligionInfos() - pCity->getReligionCount()) * (100 - iSpreadProb)) / GC.getNumReligionInfos());

In English, Prob=Base + (1-Base)*(Rel_NOT_in_city/Total_Rel), where Base is 40% in your cities (or teammates') and 20% in other civs' cities.

The upshot is that the probability starts at 100% (for a city with no religion) and drops by a fixed percentage for each religion that is present. The drop is steeper in enemy cities than in your own or teammates' cities.

The actual probabilities (to the nearest percent) are:

#Rel	Team	Non-Team
0	100%	100%
1	91%	89%
2	83%	77%
3	74%	66%
4	66%	54%
5	57%	43%
6	49%	31%

In particular, note that you'll blow over 1-in-6 attempts on your own cities with 2 religions, 1-in-4 with 3 religions, 1-in-3 with 4 religions, and 1-in-2 with 6 religions. I haven't made enough attempts to spread religion to heavily-multireligious cities to know if this matches experience.

 

[Nares]

EDIT: Nvm, you're looking to build nine cities regardless, and just cram as many religions in each one as possible. In practice, it seems worse than a 50% success rate, in general, for that last missionary.

Either way probably blows a lot of hammers, and you'd be better off with fewer religions and more cities.

Five religions and six cities is probably the best way to build extreme Culture mutipliers. Four religions in all six cities, the fifth in three others.

Five religions is also a fairly streamline tech/Wonder/Great Person progression. Six religions is pushing it (at the cost of Liberalism, which I suppose could be used to backtrack and grab Islam), and seven religions requires extreme circumstances (like Spain-on-a-lake).

EDIT: Nvm, there's really no ideal combination beyond nine cities and three or four religions. If you were to try all seven, fifteen cities would be much much easier spreading.

 

[armstrong]

To achieve a cultural victory on a standard size map, many people consider it the optimal case to get 9 cities up, to be able to spread any religion they may get to all of them, and thus be able to build cathedrals in each of the culture cities.

Some folks actually prefer 6-7 cities for "fast" cultural victories, especially if it's relatively peaceful and you don't need to build up a huge army of cavalry to protect yourself.

I'm wondering, why is everyone so sure that 9 cities is the best number for that? It's obvious that you can't get by with less, but how about more?
I've taken a look at the optimal case, that all 7 religions are available to the player. The idea is basically the same with less, you still need 9+ cities, but probabilities change.

You're right - having extra cities is helpful for spreading religions. In particular, it's can be really annoying to spread more than three religions to a city. Getting even one extra city can really help if you're going for more than 3 religions per city, and I generally like to have 7 or 10 cities. However... there are two trade offs:

1) You often don't want more than 3-4 religions. The return on multiple big religious building decreases pretty quickly. With three religions, you get you 3.5 culture (and 4.5 in one city) per commerce. Adding an extra .5 is probably not worth the 1000-2000 hammers to get the infrastructure in place. It's not just the missionaries you have to pay for, but the big religious buildings in your cultural cities (which will slow your culture rate, either if you build them manually or rush buy them.) If you were dead set on 5+ religions, there might be good reasons to be bigger, but that's rarely optimal.

2) Ideally, you're running 100% culture, which means you want the entire cost of your empire to be paid for by shrines, diplomacy, specialists, and building wealth. As you don't want to dilute your artist pool, you need to be very careful about running merchant specialists. The upkeep on 15 cities is much, much higher than 9 (or even 6, which is why is one reason it's sometimes preferable to go with only 2 shrines/religion.)

Do people usually get to universal suffrage when going for culture? If so, where to found that last city doesn't matter at all, since you can always buy the temples. Otherwise, you'd have to consider finding a place that allows building them over time, or has food for poprushing.

Absolutely! It's generally standard to not only run Universal Suffrage once you've finished teching up to rush-buy all of the temples/cathedrals you still need, but also to do anything and everything to build/acquire the Pyramids so you don't need to research Constitution->Democracy.

How are your experiences, how difficult is it actually to get that 7th (or 5th, 6th) religion spread in a city? How many missionaries does it take?

My experience is the fourth is hit or miss. Fifth and beyond is ridiculously hard. (Oh, I just saw someone posted the actual numbers! Thanks Zophos! )

That all being said, it's not a kiss of death to have a larger empire when going for cultural victories. In the event you do have tons of cities, then it probably is a good idea to spread more religions, it's just that the added cost of upkeep & time it took to acquire the cities/religions/temples/cathedrals will not usually be worth the gain.

Some tricks to reduce the cost of extra cities once you move to 100% culture include: having a really good artist farm (so you can run merchants in all your other non-culture cities), whipping cities down to population 1 (saves civics costs and ensures your culture cities get all the best trade routes), replacing all cottages with mines/workshops (convert hammers into gold), or even giving them away to rival civs.

 

[GoodSarmatian]

Six cities are enough.
You will need no cathedrals in you capital because it is far ahead in culture anyway.

 

[SS-18 ICBM]

Six cities are enough.
You will need no cathedrals in you capital because it is far ahead in culture anyway.

What about your other cities? I had a recent cultural victory that was delayed because one city counldn't catch up fast enough. Like a poster here said, your cultural victory is only as fast as the slowest city.

 

[Gumbolt]

In my experience holy cities will spread religions to any city without a religion as long as the AI or person who started the religion is on your island or known. If one already exists in all your cities its unlikely one will be spread.

I think 4 religions is enough to make the cultural victory. You would have to be lucky to get 5+ religions on your island on Monarchy and above unless you plan to beeline Codes of law, islam etc but the first 3 are a lottery unless you have the right leader and are first in queue. Not sure about the 63 missionary figure as when more religions exist in a city adding a 4th or fifth becomes harder and often it may fail to add the religion to the city.

9 cities is probably optimal if you just assume the basics required to maximise cathedrals, temples and spread religions. Although i wouldnt want to leave a large civ nearby to attack me. Also if nearby AI have started religions its useful to steal holy cities and cripple their threat. Holy cities make good cultural cities and provide lots of commerce. The sea threat cant be ignored too. Someone might attack.

On many of my cultural victories i have relied on a dorment AI who sits back and doesnt attack. I could be relying on a army at times 1 million less than the AI come end game play if i had 10 or so cities.

I think given all this the difference in cultural output by 2-3 cultural cities it can be made up by great artists. On a good game you coul produce 10+ great artists thats 40,000 of 50k required. The question is how soon do you switch to the cultural slider. Do you wait for riflemen for defenders or stop as soon as possible. I like to have a good defender in case im attacked.

On the cost of settler debate you could weigh this against cost of an axeman rush at start. Might work out cheaper than 3-4 settlers and cost of the workers etc.

Done

 

[Araqiel]

What about your other cities? I had a recent cultural victory that was delayed because one city counldn't catch up fast enough. Like a poster here said, your cultural victory is only as fast as the slowest city.

If you have less than 9 cities the key is to prioritize building early culture producers. Temples, Libraries, Monastery, and even Obelisks. If you make a point of having those in your 2nd/3rd city very early they'll pile up culture and start to gain multipliers due to their antiquity.

 

[Bushface]

I suppose it isn't really in the spirit of the game, but if at the outset you are determined to go for a cultural victory then set your game up with "always peace" and "no barbarians". Hence you won't need any military units beyond the one-per-city to keep the citizens from demanding military protection even though there is no need for it, and can concentrate on building culture-producers and missionaries.
You need to have every possible religion present in your three key cities, so that you can build 'cathedrals' there, each giving +50% of base culture. Also, spread your Wonders among those cities to avoid having one lagging well behind.

 

[The Keeper]

1) You often don't want more than 3-4 religions. The return on multiple big religious building decreases pretty quickly. With three religions, you get you 3.5 culture (and 4.5 in one city) per commerce. Adding an extra .5 is probably not worth the 1000-2000 hammers to get the infrastructure in place. It's not just the missionaries you have to pay for, but the big religious buildings in your cultural cities (which will slow your culture rate, either if you build them manually or rush buy them.) If you were dead set on 5+ religions, there might be good reasons to be bigger, but that's rarely optimal.

I disagree. The more religions, the better. Spending the 40 for a missionary is great. In your last city, every bit of culture helps.

Lets suppose it takes 5 tries to get that 5th religion in your 3rd cultural city. you have spent 200 to get it. That is 200 that you didn't have to spend in your 3rd city to get 1 (with free religion)

But you get more than just that one. If you have 4 cathedrals + national epic running free speech that is

1 * 5.0 = 5 culture/turn. That is an excellent investment for 200 hammers.


Add a temple and that is even more bonus.


I won a game once because of that exact senerio. Late in the game, a city flipped to me that had islam in it. I didn't have Islam in my borders till then. I switched to Organized religion to build a few missionarys, and the second missionary successfully founded Islam in my 3rd culture city. It was a good thing too, because 2 turns after he was built, the UN changed the global civic to Free Religion (saved me the turn of anarchy even though I voted against it because I wasn't sure if he would succeed or not.)

 

[armstrong]

I disagree. The more religions, the better. Spending the 40 for a missionary is great. In your last city, every bit of culture helps.

Lets suppose it takes 5 tries to get that 5th religion in your 3rd cultural city. you have spent 200 to get it. That is 200 that you didn't have to spend in your 3rd city to get 1 (with free religion)

But you get more than just that one. If you have 4 cathedrals + national epic running free speech that is

1 * 5.0 = 5 culture/turn. That is an excellent investment for 200 hammers.


Add a temple and that is even more bonus.

Well, my original point was regarding building Cathedrals. I never mentioned simply spreading a religion to a city.

It's often worthwhile, but not always. If you're running 100% culture with a gold surplus and have extra hammers laying around, then absolutely go for it -there's no pain and all gain. But if you aren't, you're trading putting hammers into a missionary instead of building wealth that can be funneled back into your culture cities.

Using your numbers, you could have put turned those 200 hammers into 125 gold (100*1.25 for a market.) That gets directly pumped back into culture by being able to keep the culture slider at 100% longer. Each gold is worth 5 culture in one of your cities, and 4 in the others, so 4.33 culture. So, that missionary effectively costs 125*4.33 = 541 culture. At 5 culture/turn, it wouldn't be worth it unless you're more than 100 turns away from victory.

Likewise, building a temple has costs. If your culture city is not building a temple, it can be building culture. In your example, the 80 hammers for a temple could be turned into 40 base culture * 5 = 200 culture. It would take 40 turns after the completion of the temple for it to be worth the cost.

Add in a monastery, and what you have is simply a numbers-crunching game. Sometimes it's worth it, sometimes it's not

I won a game once because of that exact senerio. Late in the game, a city flipped to me that had islam in it. I didn't have Islam in my borders till then. I switched to Organized religion to build a few missionarys, and the second missionary successfully founded Islam in my 3rd culture city. It was a good thing too, because 2 turns after he was built, the UN changed the global civic to Free Religion (saved me the turn of anarchy even though I voted against it because I wasn't sure if he would succeed or not.)

How much culture did you lose in your city due to the anarchy? Were you running at 100% culture, or could the hammers have been used to build wealth? Was it worth delaying your remaining great artists a turn?

There are many situations where spreading religion to a culture city is a good move. But it's not cut and dry - it really depends on the game.

 

[KrikkitTwo]

Well basically in a Cultural Win, Neglecting the Cutural Cities, you need 42 Religions... which means you have two components

Now the Successful Missionaries are a fixed amount, the Failed Missionaries and Settlers are variables

For the different numbers
Failed Missionaries per city to reach a certain number of religions Religions (Team )... with Total
1-0-0
2-0.1-0.1
3-0.2-0.3
4-0.333-.63
5-0.5-1.13
6-0.75-1.88
7-1-2.88

So looking at the Cost per city (Settler+Failed Missionaries only)
1-100
2-104
3-112
4-124
5-145
6-175
7-215

The cost Per religion supported is
1=100
2=52
3=37
4=31
5=29
6=29
7=30

I rounded off a bit, but basically 5 or 6 religions per city is the best, so actually 7-8 extra cities is the ideal (for 10-11 cities total) However, 9 total is the minimum and given the fact that cities not only cost settlers but also money, and that the gains are minimal~75 Total production, when you probably have an 'extra city' that has nothing better to build. Basically past the basic nine, more cities should be added if they actually add some other benefit (ie will be profitable city), otherwise, not worth wasting time.