Social Policy Cost vs Number of Cities

[evanbgood]

The relation between over-expansion and social policies has bothered me since day one. What's best? Should I expand late to get earlier policies quickly? Are more cultural cities enough to offset the higher cost? So, to try to put a little sense into things, I ran a couple quick games and pumped out settlers and culture, then recorded the info of each. Here are my findings (hopefully it will show up as a legible chart)


__1___2___3___4___5___6___7__
1_25_________________________
2_45__55_____________________
3_90__110_130_145____________
4_160_190_???_255____________
5_245_295_???_395_440________
6_345_415_485_555_625_695_765

The numbers at the top are the number of cities, and the numbers at the side are the number of social policies IN PROGRESS (For example, it takes 25 culture to get your first SP with one city, it takes 130 culture to get your third social policy with 3 cities). ??? spaces are ones that I didn't run into over my two trial games.

This information is probably in some XML document, but I wasn't able to find it. I'm trying to figure out the exact formula that culture cost uses. In the game it says "30% more for each city", but 30% of what? Of an invisible base culture cost for that number of policies? Or for the previous amount? If you take a look at line 3, you'll see that the cost goes up b 20, 20, and 15. Not only is this not consistent, but what's 20 30% of? Also, there seems to be a lot of rounding to the nearest multiple of 5 going on.

Any thoughts, facts, opinions, or expanded research to this data would be greatly appriciated! I love knowing just how these little systems work!

EDIT: Added Show's data to first column. As at least one person noted, the map size does come into play here. I did my data on a "large" sized map.

 

[aryah]

but what's 20 30% of?

just to be obvious, 20/0.3=66.6666...

 

[Show]

Just to add some info, 245 and 345 are the missing values for the 1st column.

Played a bit on excel, it's rounded which makes it very difficult to tell the "real" values, especially since we don't know if it is rounded up down or to the nearest value.. Would need larger sample. As for a chart, hard to make one before tuner is released. We can tell between what 2 values the increment is but thats about it.

 

[allenciox]

From another thread, the effect is additive, not multiplicative, and is also based on world size, on tiny it is 30% and then scales downward as your world size increases. It also appears to round it to the nearest five from your data. It appears that for whatever world size you have recorded, the percentage is about .2. Thus:

45*1.2=54 (rounds to 55)
90*1.2=108 (rounds to 110)
160*1.2=192 (rounds to 190)
245*1.2=294 (rounds to 295)

and, continuing with your "4" column:
90*1.6=144 (rounds to 145)
160*1.6=256 (rounds to 255)
245*1.6=392 (sort of rounds to 395)
345*1.6=552 (sort of rounds to 555)

The last two are probably accounted for that the percentage isn't exactly .2 it is probalby .21 or .205 or something like that.

 

[pi-r8]

how many culture points do you need to get 25 SPs with just 1 city?

 

[Show]

From another thread, the effect is additive, not multiplicative, and is also based on world size, on tiny it is 30% and then scales downward as your world size increases. It also appears to round it to the nearest five from your data. It appears that for whatever world size you have recorded, the percentage is about .2. Thus:

45*1.2=54 (rounds to 55)
90*1.2=108 (rounds to 110)
160*1.2=192 (rounds to 190)
245*1.2=294 (rounds to 295)

and, continuing with your "4" column:
90*1.6=144 (rounds to 145)
160*1.6=256 (rounds to 255)
245*1.6=392 (sort of rounds to 395)
345*1.6=552 (sort of rounds to 555)

The last two are probably accounted for that the percentage isn't exactly .2 it is probalby .21 or .205 or something like that.

I have doubts the 1 city values aren't themselves rounded from another fixed base value.

If 1 city value is exact and it is rounded to nearest it would need to be higher than 0.208333333 but lower than 0.20410628, which is impossible.

 

[slobberinbear]

For France, more cities = more culture = more social policies, obviously. You could argue the same for Rome (build all the cultural buildings in Rome, then cheaply replicate them in other cities). For everyone else, it's one of those "oh well" things unless you are doing a One City Challenge kinda thing or grabbing a bunch of early wonders.

Delaying the land grab for social policy reasons is kinda like saying you don't want a raise because it'll push you into a higher tax bracket. The benefits to expansion are immediate and significant.

 

[cracked]

If you're trying to develop culture quickly, there's still something to be said for expanding at a more casual rate. Particularly if you want to build stonehenge early. But not expanding at all as the French is a bit lame and doesn't take advantage of their traits.

 

[KCMcG]

The base numbers (based on number of social policies unlocked) are based on the square of the number of policies unlocked I think.

10*1*1 = 10 (actually 25)
10*2*2 = 40 (actually 45)
10*3*3 = 90 (exactly 90)
10*4*4 = 160 (exactly 160)
10*5*5 = 250 (actually 245)
10*6*6 = 360 (actually 345)

It's not exact, but if you notice, 1 is 15 higher, 2 is 5 higher, 5 is 5 lower and 6 is 15 lower. Maybe the 7th policy is 30 lower, 8th is 50 lower, etc.

Unfortunately, if you follow this logic then it takes a total of 78,190 culture to complete 30 policies with one city. Over 400 turns, that's an average of 190 culture in one city. If someone could get information on the 7th, 8th and higher policies we should be able to figure out the formula.

 

[KrikkitTwo]

I think there is probably rounding going on, even in the base values.

 

[taltamir]

puppet cities increase your culture production but do not increase culture cost... (also give you research and gold... both of which can benefit a cultural victory)...
i think the solution is to conquer a lot and puppet everything.

 

[iop]

I agree, aside from the first policy, costs seem to follow a square law (I rounded the factors 4 and 9 to integers; the agreement would be better with fractional numbers). If you plot the square of the policy cost vs the number of policies, you get a straight line with the exception of policy #1, which is comparatively too expensive.

[cost of n-th policy] = (4*n + 9*n^2) * (1+0.2*(nCities-1))

For 1 city
13 - 25
44 - 45
93 - 90
160 - 160
245 - 245
348 - 345

For 2 cities
15.6 - ? (30?)
52.8 - 55
111.6 - 110
192 - 190
294 - 245
417.6 - 415

For 1 city, the total number of culture needed is ~51k to unlock 5 full trees, though that doesn't take into account Cristo Redentor, for example.

 

[KCMcG]

For 1 city, the total number of culture needed is ~51k to unlock 5 full trees, though that doesn't take into account Cristo Redentor, for example.

51k is to unlock 25 SPs. To get a cultural victory you have to unlock 30 SPs because it costs 1 SP to activate each tree and then 5 SPs to fill out the tree. By this formula it would cost ~87k culture. Even with the SP that cuts costs 25% and Cristo Redentor, you're looking at ~36.7k or 92 culture per turn for a cultural victory. I haven't tried for one yet, but is that a realistic per turn culture?

 

[Ecori]

92 culture/turn is very easy to obtain. In my last game I was producing 500 culture/turn with Askia by 1900ad. I had 4 cities, 6-7 puppets and 4-5 CS allies.
Cultured CS is really key to obtain high culture/turn.

 

[saraid]

When I tried out cultural victory, I had a lot of cities (didn't realize it increased cost of SPs), and was making 700 CPT or so despite that. Granted, I was also spamming great artist landmarks, but still.

I have yet to try out a larger map or a harder difficulty (kind of feeling like a newb, me), but 92 CPT sounds really really easy as long as you aim to make it happen. Especially now that I know about the increased SP cost, I'd probably use Tradition rather than Liberty and stay small.

 

[CrimsonEdge]

51k is to unlock 25 SPs. To get a cultural victory you have to unlock 30 SPs because it costs 1 SP to activate each tree and then 5 SPs to fill out the tree. By this formula it would cost ~87k culture. Even with the SP that cuts costs 25% and Cristo Redentor, you're looking at ~36.7k or 92 culture per turn for a cultural victory. I haven't tried for one yet, but is that a realistic per turn culture?

From my experience, yes.

There's an achievement for getting 100 culture a turn in one city.

I won a cultural victory as India with my main city having about 125 culture a turn and my other having about 75.

 

[Alexfrog]

You dont really need to hit 30 of them, because free ones do not increase the cost to get to the next one. So you can get one free from Oracle, two free from the Piety policy, and then we are down to 27 needed for example.

 

[MaXimillionZero]

Even with the SP that cuts costs 25% and Cristo Redentor, you're looking at ~36.7k or 92 culture per turn for a cultural victory. I haven't tried for one yet, but is that a realistic per turn culture?

In my current game (turn 255, King, standard speed), my capital is producing 50+ culture per turn without temple/monastery/opera house/museum/broadcast tower, and I'm making 140 culture/turn from city states. So 90 is really not much of a challenge.

 

[evanbgood]

Some great ideas here! It sounds like the actual formula hasn't been pinned down yet. The post with [cost of n-th policy] = (4*n + 9*n^2) * (1+0.2*(nCities-1)) sounds promising, but I'm still wondering if other variables come into play like map size.

Would love to hear more tactics, as well. Has anyone been successful with large numbers of cultural cities? Have puppet states helped or hurt? In theory, it would make sense if two highly cultured cities end up being better than one, while one cultured city would be better than one cultured and one not. However, without a good grasp on the data, it's hard to tell if a "one-city challenge" is the fastest way to cultural victory or not (not taking other factors like happiness and such into account, of course).

 

[taltamir]

Some great ideas here! It sounds like the actual formula hasn't been pinned down yet. The post with [cost of n-th policy] = (4*n + 9*n^2) * (1+0.2*(nCities-1)) sounds promising, but I'm still wondering if other variables come into play like map size.

Good question... I think the in game speed setting mentioned that it affects culture... so epic vs standard you get different culture amounts. I wonder which one is best for culture.

Would love to hear more tactics, as well. Has anyone been successful with large numbers of cultural cities? Have puppet states helped or hurt? In theory, it would make sense if two highly cultured cities end up being better than one, while one cultured city would be better than one cultured and one not. However, without a good grasp on the data, it's hard to tell if a "one-city challenge" is the fastest way to cultural victory or not (not taking other factors like happiness and such into account, of course).

I noticed that it only recalculates values on turn end... so you don't see differences immediately.
I noticed that puppet cities produce culture for you.
I noticed that annexing a bunch of puppets in one turn sent my cost for next culture up to 10x what it was before.

Thats all the info I have. Anyone else that knows anything please share.
I really wish we had more concrete data. With concrete data we could mathematically calculate the best approach.