India Total Peaceful Photojournal

[YukiN]

Interesting how you chose to use the rivers as defence rather than settling on them. I wonder if this means waterwheel should come earlier in the tech tree.

 

[crdvis16]

Count the number of scientists in your games. This sounds right on paper, because long term, Progress would eventually beat Tradition in everything (except GWAM), but games are usually ending before your 8th city has any great scientists.

This is correct- at some point, adding more cities with scientist slots will not result in an extra great scientist being born within the time frame of a game.

Also, even if every new city quickly comes up to speed in population/infrastructure, at some point adding new cities cannot mathematically overcome the tech cost penalty. If the tech cost increase is 7% then I think the soft limit on cities is 14 (and that's assuming the city is instantly producing the average science of all cities right from the turn it is settled). In practice, the actual soft limit is probably much lower, like 9 or 10 I would guess, as it takes a while for a city to get up to speed and dig you out of the hole of settling it.

 

[Minh Le]

Interesting how you chose to use the rivers as defence rather than settling on them. I wonder if this means waterwheel should come earlier in the tech tree.

If I plan to kill Korea early, I will settle on river, but Im planning to just defend myself so definitely no. Settle on river means enemies ranged can shot my city from 2 tiles away and my troops must cross the river to get them, and Hwacha is no joke.

Also, even if every new city quickly comes up to speed in population/infrastructure, at some point adding new cities cannot mathematically overcome the tech cost penalty. If the tech cost increase is 7% then I think the soft limit on cities is 14 (and that's assuming the city is instantly producing the average science of all cities right from the turn it is settled). In practice, the actual soft limit is probably much lower, like 9 or 10 I would guess, as it takes a while for a city to get up to speed and dig you out of the hole of settling it.

Assuming each addition city produce average total amount of yield equal to 50% of your capital and increase cost by 7%, we have total cost is 1.07^N, and total yield is 0.5N where N is number of new cities. Solve the equation: 1.07^N=0.5N we have N=46. So the break even point is 46, less than that number any addition city bring benefit

 

[Tzar Sasha]

Total peace? Does that mean game over if another civilization declares war on you? Cause in my book, war is war no matter who started it.

 

[Minh Le]

Total peace? Does that mean game over if another civilization declares war on you? Cause in my book, war is war no matter who started it.

No I cant do that ofc, it just means Im not gonna declare war on anyone (what I do frequently )

 

[Owlbebach]

Assuming each addition city produce average total amount of yield equal to 50% of your capital and increase cost by 7%, we have total cost is 1.07^N, and total yield is 0.5N where N is number of new cities. Solve the equation: 1.07^N=0.5N we have N=46. So the break even point is 46, less than that number any addition city bring benefit

those 7% are additive, not multiplicative, so it is 1,07 for 2 cities, 1,14 for 3 and 1,21 for 4 cities.

Also, even if every new city quickly comes up to speed in population/infrastructure, at some point adding new cities cannot mathematically overcome the tech cost penalty. If the tech cost increase is 7% then I think the soft limit on cities is 14 (and that's assuming the city is instantly producing the average science of all cities right from the turn it is settled). In practice, the actual soft limit is probably much lower, like 9 or 10 I would guess, as it takes a while for a city to get up to speed and dig you out of the hole of settling it.

For both of you - back in time my friend made a formula for that, you can see it here https://forums.civfanatics.com/threads/new-version-october-9th-10-9.623188/page-4#post-14887300
You only need to adjust numbers, it was 10% per city back then, and i believe thanks to this formula people understood that 10% is too much

 

[Minh Le]

Wow its too complicated. Im not that good at math. I guess Im gonna play the way I feel right then

 

[YukiN]

Additive means there is no real cap from science and culture unless the city is really bad. Multiplicative means each new city needs to be 7% of your current empire's yields, which is a lot more challenging. Do we a source that conclusively states which it is?

 

[Owlbebach]

Additive means there is no real cap from science and culture unless the city is really bad. Multiplicative means each new city needs to be 7% of your current empire's yields, which is a lot more challenging. Do we a source that conclusively states which it is?

It is additive. For sure. You can easily check it in game

 

[crdvis16]

those 7% are additive, not multiplicative, so it is 1,07 for 2 cities, 1,14 for 3 and 1,21 for 4 cities.


For both of you - back in time my friend made a formula for that, you can see it here https://forums.civfanatics.com/threads/new-version-october-9th-10-9.623188/page-4#post-14887300
You only need to adjust numbers, it was 10% per city back then, and i believe thanks to this formula people understood that 10% is too much

I think that formula is written such that puppets increase tech costs as well? I think that was the case back then but no longer is, right? My understanding is that puppets do NOT increase tech/policy costs (puppet's only drawback is some unhappiness and severely reduced city yields). So I'm not sure that formula is helpful or not.

Also, my understanding was that every new non-puppet city increases current tech costs by 7% which would be multiplicative in my mind, and which is why you can't go much beyond 10ish non-pupper cities or so on a standard map before you start hindering yourself.

If it's additive then at 14 non-puppets your next non-puppet would only need to hit ~3% of your total science to be helpful I think.

 

[crdvis16]

Just did a quick check in-game and it seems to be additive, NOT multiplicative (the rounding of science/culture costs makes the curve a little noisy but it definitely seems to follow the additive curve and not the multiplicative curve). That makes it a bit easier for newly settled cities to become net positive in science and culture. It would be an interesting exercise to track the science/culture output (and maybe all of the other yields as well even though they don't suffer from diminishing returns) of cities in a game to see how long it takes from when they were settled until they become a net positive.

Perhaps I'll do that in my next game to get a better idea of how wide is optimal and I'll report back what I find.

 

[Owlbebach]

I think that formula is written such that puppets increase tech costs as well?

No it is not. In that formula N is number of non-puppets and M is number of puppets. And i have only N in denominator

 

[chicorbeef]

Is Love really that bad? I've never actually picked it but it seems like it can scale pretty well later on.

 

[Gazebo]

Is Love really that bad? I've never actually picked it but it seems like it can scale pretty well later on.

Love is all you need.

G

 

[yogiebere]

From the link Owlbebach included, here's the updated formula for science (and culture too I suppose) for annexed/puppeted cities (m=puppet,n=annexed). Of course assuming all cities are equal and not including capital bonuses, wonders, policies, trade routes, etc.

https://www.wolframalpha.com/input/?i=plot+y+=++(n+m*0.2)/(1+0.07*n)+from+0+to+20

Analysis: pretty much always a good move to annex over puppet for the raw culture/science, not factoring in maintenance costs or happiness.

Here's a little exercise if you say a capital + policies + TRs + other bonuses adds 3 cities worth of science/culture and that cities after your top 5 only contribute .7 (assuming they just never reach the same potential as a core city that has more time to hit higher populations. Even then! It still gets to the point where you need to hit the ~12 city mark to make puppets better in terms of science/culture.

https://www.wolframalpha.com/input/?i=plot+y+=++(3+m*0.2+n-.3*Max[n-5,0])/(1+0.07*n)+from+0+to+20

I think I might be going for more than 8 cities in my next warmonger game! Maybe 10 or 11 depending on how many are prime locations

 

[Owlbebach]

From the link Owlbebach included, here's the updated formula for science (and culture too I suppose) for annexed/puppeted cities (m=puppet,n=annexed). Of course assuming all cities are equal and not including capital bonuses, wonders, policies, trade routes, etc.

https://www.wolframalpha.com/input/?i=plot+y+=++(n+m*0.2)/(1+0.07*n)+from+0+to+20

Analysis: pretty much always a good move to annex over puppet for the raw culture/science, not factoring in maintenance costs or happiness.

Here's a little exercise if you say a capital + policies + TRs + other bonuses adds 3 cities worth of science/culture and that cities after your top 5 only contribute .7 (assuming they just never reach the same potential as a core city that has more time to hit higher populations. Even then! It still gets to the point where you need to hit the ~12 city mark to make puppets better in terms of science/culture.

https://www.wolframalpha.com/input/?i=plot+y+=++(3+m*0.2+n-.3*Max[n-5,0])/(1+0.07*n)+from+0+to+20

I think I might be going for more than 8 cities in my next warmonger game!

Yeah, thanks. Actually i remember doing that in the past and 3 is a very good assumption for all non-city yields.

 

[Bromar1]

In the early game, yes. In the late game? No. Its true in case of GWAM because guilds are litmited, but not true in case of GS, because you basically have scientist specialists in every cities. The increase in cost can be compensate by extra science the cities produce, and with progress, my secondary cities are produce bigger than 80% of my capital, some even better. The point is in modern era, with more cities, you will have many more Great Scientists compared to Traditions and with bonus from Rationalism, you can pop them to jump ahead in tech for a science victory.

You get to plant a lot more early academies as Tradition, which further boosts later great scientists

 

[YukiN]

You get to plant a lot more early academies as Tradition, which further boosts later great scientists

How so? Bulbing only depends on how many you planted, not when you planted them.

 

[crdvis16]

From the link Owlbebach included, here's the updated formula for science (and culture too I suppose) for annexed/puppeted cities (m=puppet,n=annexed). Of course assuming all cities are equal and not including capital bonuses, wonders, policies, trade routes, etc.

https://www.wolframalpha.com/input/?i=plot+y+=++(n+m*0.2)/(1+0.07*n)+from+0+to+20

Analysis: pretty much always a good move to annex over puppet for the raw culture/science, not factoring in maintenance costs or happiness.

Here's a little exercise if you say a capital + policies + TRs + other bonuses adds 3 cities worth of science/culture and that cities after your top 5 only contribute .7 (assuming they just never reach the same potential as a core city that has more time to hit higher populations. Even then! It still gets to the point where you need to hit the ~12 city mark to make puppets better in terms of science/culture.

https://www.wolframalpha.com/input/?i=plot+y+=++(3+m*0.2+n-.3*Max[n-5,0])/(1+0.07*n)+from+0+to+20

I think I might be going for more than 8 cities in my next warmonger game! Maybe 10 or 11 depending on how many are prime locations

There is added complication on top of this that is a bit harder to model:

1) the number of turns it takes for the nth city to have its science/culture be a net positive, and then how many turns after that it takes for the city to make up for all the previous turns when it was a detriment. That total turn number needs to be less than the game length, preferably far less as early yields are typically stronger than later yields

2) science/culture per turn is only one aspect of tech/policy acquisition. There's also all of the other sources of science and culture: instant yields and great person generation. Is the nth city also contributing enough in those areas? It's probably behind in great people but doing well in instant yields is my guess but it's hard to model.

3) non-science/culture yields. There's no penalty on faith, gold, production, or military supply so more cities are probably always better in those areas. There are some diminishing returns for tourism where you might start hurting yourself by settling more cities, though, especially since it might be harder for the nth city to ever contribute well in tourism given the limited sources for it.

 

[yogiebere]

There is added complication on top of this that is a bit harder to model:

1) the number of turns it takes for the nth city to have its science/culture be a net positive, and then how many turns after that it takes for the city to make up for all the previous turns when it was a detriment. That total turn number needs to be less than the game length, preferably far less as early yields are typically stronger than later yields

2) science/culture per turn is only one aspect of tech/policy acquisition. There's also all of the other sources of science and culture: instant yields and great person generation. Is the nth city also contributing enough in those areas? It's probably behind in great people but doing well in instant yields is my guess but it's hard to model.

3) non-science/culture yields. There's no penalty on faith, gold, production, or military supply so more cities are probably always better in those areas. There are some diminishing returns for tourism where you might start hurting yourself by settling more cities, though, especially since it might be harder for the nth city to ever contribute well in tourism given the limited sources for it.

Certainly wide is not good for tourism. But I was mainly talking about War or Science victories where you need a good balance of science/culture.