Help with some complex math: Optimal # of cities for France opening

[joncnunn]

So what would your conclusion be in terms of when, or even if, to stop building/annexing cities with France?

If there's no reasonable possibility of getting a world wonder built on it (by any means)

Late in the game, the outside culture should be very high. (Ally status with every cultural city state on the map) In addition the capital will be working a lot of Holy Sites & Landmarks (and have Freedom finisher)

At which point to have a decent shot (in addition to all cultural buildings and all artist slots worked) every city to continue paying for itself will need:

1. You to have adopted the Liberty policy decreasing per city cultural cost
2. You to have adopted the Piety policy giving 33% culture to every city with a wonder
3. You to have built a world wonder.

The good news is that even after the late game increase in outside & capital cultural it's very possible for a city missing a world wonder to come close to paying for itself.

 

[futurehermit]

If there's no reasonable possibility of getting a world wonder built on it (by any means)

Late in the game, the outside culture should be very high. (Ally status with every cultural city state on the map) In addition the capital will be working a lot of Holy Sites & Landmarks (and have Freedom finisher)

At which point to have a decent shot (in addition to all cultural buildings and all artist slots worked) every city to continue paying for itself will need:

1. You to have adopted the Liberty policy decreasing per city cultural cost
2. You to have adopted the Piety policy giving 33% culture to every city with a wonder
3. You to have built a world wonder.

The good news is that even after the late game increase in outside & capital cultural it's very possible for a city missing a world wonder to come close to paying for itself.

How about if you don't go down the Piety tree (e.g., if playing for domination, but still want to push culture for policies)? Anything different from the 9-10 city conclusion reached earlier?

 

[sanabas]

Eh good call, solution is indeed cpt_N/(N+9). I didn't have the time yesterday to quickly solve it and Sanabas had done a random obvious mistake on post#23 so I just figured it was one of those formulas lying around on the forums that people improperly use or adapt over time.

No, I did just quickly solve it.

What random obvious mistake? *Heads off to look...*

 

[sanabas]

Said x = 10 cities, then said that x+9 = 11. Yep, definite obvious mistake in the example I used.

It's really only the BONUS culture that is creating a breakpoint.

Yes. Which you'll also find explained already in the thread.

 

[BWS]

With that said, amphitheaters and staffing them should not alter the value of an additionnal city if you assume you will build the amphitheater AND staff it as well in your additionnal city. Neither is outside the realm of what your BASE city could be. Obviously since you can't instantly grow it enough to staff a rush purchased amphitheater, it's not as straight forward but pretend you do some warmongering and takeover cities of the appropriate size, annexing it could still be optimal. It's really only the BONUS culture that is creating a breakpoint.

When talking about the practical factors that determine how many cities you should found, it doesn't make much sense to ignore the practical factors and the new city. There's more than one breakpoint, and the one you're talking about – whether a basic city can ever pull its weight for culture – generally only comes into play for Culture Victory, not the kind of game we're talking about here. The new city breakpoint is more interesting for Domination games, and you can't just ignore things like unstaffed culture buildings for that case.

 

[BWS]

How about if you don't go down the Piety tree (e.g., if playing for domination, but still want to push culture for policies)? Anything different from the 9-10 city conclusion reached earlier?

My earlier conclusions were based on the assumption that you did not open Piety.

 

[joncnunn]

How about if you don't go down the Piety tree (e.g., if playing for domination, but still want to push culture for policies)? Anything different from the 9-10 city conclusion reached earlier?

No, if your not pushing culture in capital / outside pressure hard, then more cities is better up to that 9-10 limit as described above assuming you have new cities build whatever cultural improvements you build in the capital. (If your not filling artist slots in the capital, then you don't need to fill them in the other cities; but if you are, you should fill those in the outer cities.)

 

[Deau]

So what would your conclusion be in terms of when, or even if, to stop building/annexing cities with France?

Purely in terms of culture victory, I wouldn't really deffer from my confort zone CV strat with other civs. Generally occ-4cities depending on, sadly enough, expected neighbor warmongering, availible outstanding city settling grounds and whatnot.

For right about every other strategy, early ICS is really strong with france. I wouldn't really alter my general pattern of annex vs puppet as the UA works on puppets as well so the puppets should increase your policy rate faster than annexing (unless you rush culture buildings which you generally won't outside CV)

Annexing a potential puppet actuall plays both ways since you gotta consider their current CPT into the "bonus" culture of your empire for Sanabas' formula.


Then @Sanabas, I'm sorry if the way I wrote up why I had overlooked your answers was insulting. It was really not the intention, I apologize. It was indeed the obvious case of X=10 and X+9 = 11. Had there been a link to your detailed post I would gladly have read it all before doing any write-up. I have just happened to come accross people copy/pasting formulas left and right as if their sources were always absolutely 100% right. I had to argue over various soft and hard caps through the (far too many) years of WoW to idiots taking wowwiki as an absolute source of knowledge while it was barely getting updated anymore 2-3 years into the game. I've seen the same here a lot when the first major overhaul patch came in vanilla. So I just naturally always remain skeptical of up front formulas. Probably excepted Vexing's and the few other players' I had built confidence in when I was actually active.

 

[Deau]

When talking about the practical factors that determine how many cities you should found, it doesn't make much sense to ignore the practical factors and the new city. There's more than one breakpoint, and the one you're talking about – whether a basic city can ever pull its weight for culture – generally only comes into play for Culture Victory, not the kind of game we're talking about here. The new city breakpoint is more interesting for Domination games, and you can't just ignore things like unstaffed culture buildings for that case.

Agreed in general. I am a somewhat stubborn player who still nearly only plays Deity with way out dated knowledge of game mechanics and appropriate strategies -_-.

In general though, on deity, I almost never build culture buildings past monuments until at least rationalism is unlocked and also obviously have close to no world wonder built. There always seem to be needs for units or more relevant buildings. I also pretty much never run culture specialists outside CV - maybe if it pushes a few turns off for the rationalism 2 free techs.

So the part that I don't agree with is the consideration for culture staffing for non CV games. In most case scenarios, you won't/shouldn't have any culture staff for non CV games. More than anything to avoid the additionnal micromanagement of not looping over and getting a great artist -_-.

 

[futurehermit]

Gotta say all the discussion in this thread has been great and I'm loving the 9-10 city rule -- it's working awesome and I'm dominating those games

 

[BWS]

Oh good, I'm glad that it's working out in practice. Plans don't always survive contact with the enemy.

 

[tommynt]

totaly impossible to do "math" on this, as factors in the equation change every turn.

Early midgame CS will be most of your culture f.e. so in an equation more cities d hurt at this point - at the point when all cities got 5 culture slots filled u think more cities d be great now - and when u finally finish freedom and got 10 landmarks planted - u think hey wtf all these cities - half of my cult comes from cap anyway

 

[T-hawk]

I played out a wide culture game with France, inspired by this thread. Here's my full writeup.

http://www.dos486.com/civ4/civ5gkfrance/

Summary: It wasn't full-blown ICS, but wide-ish, 11 native cities plus four puppets. I used Rationalism to reach Sydney Opera House fairly fast (T236), then turned around into Piety instead for the end game. Turn 280 culture victory.