[NFP] Yield of Science under different population

[Lily_Lancer]

Assuming we have 7 amenities for each city, +4 campus with all of its buildings, powered, 2 Science CSs with each having 6 envoys (average scenario if we start with standard 12 CSs), double adj card & Rationalism, how much Science will we generate for different population cities?

4 Pop: Amenity 5 (Escatic) (4*0.5+4*2+(1+2+3)*2+(2+4+8)*1.5)*1.2=51.6 Science

6 Pop: Amenity 4 (Happy) (6*0.5+4*2+(1+2+3)*2+(2+4+8)*1.5)*1.1=48.4 Science

8 Pop: Amenity 3 (Happy) (8*0.5+4*2+(1+2+3)*2+(2+4+8)*1.5)*1.1=49.5 Science

10 Pop: Amenity 2 (Content) (10*0.5+4*2+(1+2+3)*2+(2+4+8)*1.5)*1.0=46 Science

12 Pop: Amenity 1 (Content) (12*0.5+4*2+(1+2+3)*2+(2+4+8)*1.5)*1.0=47 Science

14 Pop: Amenity 0 (Content) (14*0.5+4*2+(1+2+3)*2+(2+4+8)*1.5)*1.0=48 Science

16 Pop: Amenity -1 (Displeased) (16*0.5+4*2+(1+2+3)*2+(2+4+8)*2.0)*0.9=50.4 Science

18 Pop: Amenity -2 (Displeased) (18*0.5+4*2+(1+2+3)*2+(2+4+8)*2.0)*0.9=51.3 Science

20 Pop: Amenity -3 (Unhappy) (20*0.5+4*2+(1+2+3)*2+(2+4+8)*2.0)*0.8=46.4 Science



So 4 pop yields the most science in the upcoming update, if you have 7 amenities per city.

 

[Lily_Lancer]

In other words, the new update encourages us to do severe birth control until every city is ecstatic, or have +5 amenity.

The Ecstatic bonus is so huge that growing population feels like only a waste of precious amenity.

 

[anonxanemone]

The only advantage populous cities have is spare people to be assigned as specialists. But assigning specialists for just +2 yields doesn't seem as rewarding if a productive tile can be worked instead.

 

[Datgingah]

Are you sure the ecstatic/unhappy bonuses are multiplied on top of the rationalism effect? I was under the impression multipliers were added together first before multiplying.

if so that makes rationalism drop to 80% at 15 pop and at 60% at 4 pop, which would obviously favor the 15 pop

 

[greenOak]

This is pretty sensitive to the amount of amenities you have. If you do the math with six or eight amenities per city, size 16 maximizes science output. Also, amenities won't be distributed equally throughout your empire.

EDIT: Here is the chart for 6, 7, and 8 amenities per city.

 

[Lily_Lancer]

This is pretty sensitive to the amount of amenities you have. If you do the math with six or eight amenities per city, size 16 maximizes science output. Also, amenities won't be distributed equally throughout your empire.

EDIT: Here is the chart for 6, 7, and 8 amenities per city.

View attachment 578612

You work on housing, food, grow your city to 16, just to get comparable amount of science output as a city of 4. Ridiculous, isn't it? Why not save those efforts to settle/capture new cities?

 

[greenOak]

It's a fair point, but the relative value of small cities has existed long before the changes to amenities. With the old amenity system, using your assumptions of 7 amenities per city, a size 4 city would have produced 47.3 science, while a size 10 city would have produced 53. Size 16 would've maxed science output at 56. So you would have to grow 6 population for roughly 6 more science more science per turn (or grow 12 more population for 9 more science per turn). Now you have to grow 12 pops for 4-5 extra science (given the right number of amenities). It's definitely gotten worse, but the ability of small cities to produce close to the amount that a large city could has always been a quirk of civ 6. Nevertheless, even the most serious min-maxers have found reason to build at least a few large cities.

 

[Pietato]

How are you building everything, though?

 

[Equilin]

Can you pull the max power of Rationalism (+4 campus and full buildings) consistently with only 4 pops tho? Unless pillaging hard to buy them i doubt it

 

[KKirrin]

4 pop cities have a lot of synergy with work ethic, esp in tundra where you won’t grow much passed that anyway. Easy enough with chops too when you’re just spamming cities though research labs can be a bit of a pain

 

[Pietato]

4 pop cities have a lot of synergy with work ethic, esp in tundra where you won’t grow much passed that anyway. Easy enough with chops too when you’re just spamming cities though research labs can be a bit of a pain

That would mean you only have a Holy Site and a Campus, though.

 

[AntSou]

Assuming we have 7 amenities for each city, +4 campus with all of its buildings, powered, 2 Science CSs with each having 6 envoys (average scenario if we start with standard 12 CSs), double adj card & Rationalism, how much Science will we generate for different population cities?

4 Pop: Amenity 5 (Escatic) (4*0.5+4*2+(1+2+3)*2+(2+4+8)*1.5)*1.2=51.6 Science

6 Pop: Amenity 4 (Happy) (6*0.5+4*2+(1+2+3)*2+(2+4+8)*1.5)*1.1=48.4 Science

8 Pop: Amenity 3 (Happy) (8*0.5+4*2+(1+2+3)*2+(2+4+8)*1.5)*1.1=49.5 Science

10 Pop: Amenity 2 (Content) (10*0.5+4*2+(1+2+3)*2+(2+4+8)*1.5)*1.0=46 Science

12 Pop: Amenity 1 (Content) (12*0.5+4*2+(1+2+3)*2+(2+4+8)*1.5)*1.0=47 Science

14 Pop: Amenity 0 (Content) (14*0.5+4*2+(1+2+3)*2+(2+4+8)*1.5)*1.0=48 Science

16 Pop: Amenity -1 (Displeased) (16*0.5+4*2+(1+2+3)*2+(2+4+8)*2.0)*0.9=50.4 Science

18 Pop: Amenity -2 (Displeased) (18*0.5+4*2+(1+2+3)*2+(2+4+8)*2.0)*0.9=51.3 Science

20 Pop: Amenity -3 (Unhappy) (20*0.5+4*2+(1+2+3)*2+(2+4+8)*2.0)*0.8=46.4 Science



So 4 pop yields the most science in the upcoming update, if you have 7 amenities per city.

Seems to me that with 4 pop cities, by the time you finish a University it's already Christmas.

This analysis seems to be entirely done in a vacuum.

A High Pop city will finish buildings earlier and therefore take advantage of the yields provided by the buildings earlier, compared to a small Pop city. Something you don't take into account at all.

Then there's, you know, the whole rest of the game. How can you even sustain an army capable of defending your 4-Pop Science cities? And where's your culture coming from? Not Chichen Itza or other wonders since you won't be doing any wonder construction. You also won't be able to keep up in the CS game.

Also, you said powered. Powered with/by what? There ain't no power where you come from!

 

[Pietato]

Seems to me that with 4 pop cities, by the time you finish a University it's already Christmas.

This analysis seems to be entirely done in a vacuum.

A High Pop city will finish buildings earlier and therefore take advantage of the yields provided by the buildings earlier, compared to a small Pop city. Something you don't take into account at all.

Then there's, you know, the whole rest of the game. How can you even sustain an army capable of defending your 4-Pop Science cities? And where's your culture coming from? Not Chichen Itza or other wonders since you won't be doing any wonder construction. You also won't be able to keep up in the CS game.

Also, you said powered. Powered with/by what? There ain't no power where you come from!

Agreed. It should be a comparison of 7 population versus 15 population, not his nonsensical theorycraft.

 

[KKirrin]

That would mean you only have a Holy Site and a Campus, though.

Yup! It’s also fine to just have a 4 pop city with only a campus and no other district, particularly in the late game when you’re spamming small cities.

Not an either or sorta thing—you can and probably should still have a few bigger cities to hit eurekas, at least one that gets chopped up for ping—but If you can get close to the same amount of science from a 4 pop vs a 15 pop in the late game the former is more efficient, especially when districts are more costly but chops have scaled to compensate

 

[Lily_Lancer]

Seems to me that with 4 pop cities, by the time you finish a University it's already Christmas.

This analysis seems to be entirely done in a vacuum.

A High Pop city will finish buildings earlier and therefore take advantage of the yields provided by the buildings earlier, compared to a small Pop city. Something you don't take into account at all.

Production also doesn't only come from population. Work Ethic, Industrial Zone related bonuses, Trade Routes, Golden Age Bonus, Chopping and Harvesting, Too many sources. It is not hard for a city to chop from nothing to a research lab, only 4-5 Magnus chops or 6-7 normal chops.

 

[AntSou]

Production also doesn't only come from population. Work Ethic, Industrial Zone related bonuses, Trade Routes, Golden Age Bonus, Chopping and Harvesting, Too many sources. It is not hard for a city to chop from nothing to a research lab, only 4-5 Magnus chops or 6-7 normal chops.

You have no IZs if you're building Holy Sites for the Work Ethic Production bonuses. You have no trade routes since you didn't build CH or Harbours, and you'll be stuck to chopping Woods because if you chop Rainforests your pop will go up, which you don't want under this scenario.

 

[kryat]

Don't forget that you have no power if you only have HS and campuses, until green energy comes online. Also how do you chop without production or gold to build builders?

I think for a more realistic comparison, the rationalism multiplier should be 1.2 for cities with less than 15 and 1.8 for cities at or above 15 population, as a way of doing a rough expectation value for getting the +4 adjacency. I just don't see a way to reliably hit that +4 with pop 4 cities. You can pack your districts together, but that's not going to get you to 4 for a campus.

Or..

Since you went for a full population range, you could assume
+2 for cities at 4 or less
+2.5 for 5-10
+3 for 11-15
+3.5 for 16+

 

[Pietato]

Yup! It’s also fine to just have a 4 pop city with only a campus and no other district, particularly in the late game when you’re spamming small cities.

Not an either or sorta thing—you can and probably should still have a few bigger cities to hit eurekas, at least one that gets chopped up for ping—but If you can get close to the same amount of science from a 4 pop vs a 15 pop in the late game the former is more efficient, especially when districts are more costly but chops have scaled to compensate

Spamming chop cities late game is not really what this thread is about. It is about what gets you to the late game the fastest.

 

[Pietato]

Production also doesn't only come from population. Work Ethic, Industrial Zone related bonuses, Trade Routes, Golden Age Bonus, Chopping and Harvesting, Too many sources. It is not hard for a city to chop from nothing to a research lab, only 4-5 Magnus chops or 6-7 normal chops.

YOU HAVE NO INDUSTRIAL ZONES, NO MARKETS, NO HARBOURS, AND NO THEATRE DISTRICTS.

Do you understand now? You have no power, low production, no culture and NO TRADE ROUTES.

Plus, do you plan on razing every AI city?

 

[Duke William of Normandy]

YOU HAVE NO INDUSTRIAL ZONES, NO MARKETS, NO HARBOURS, AND NO THEATRE DISTRICTS.

Do you understand now? You have no power, low production and NO TRADE ROUTES.

You have one... From the free Trade Route at the Foreign Trade Civic.