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?
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?