Maximizing Renaissance Expansion

Stalker0

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There has been a lot of debate on whether expansion past the early game is truly "profitable". I'm still about iffy on it myself, though the change from 7% to 5% for new cities has helped a bit. However, I wanted to consider some ideas to maximize a colony to get the best bang for your buck.

Renaissance cities (often on an island or another continent) are made for a few purposes:

1) Resources: Either to grab a unique lux (or in best cases, 2 new luxs), or some strategic resource that you need.

2) Strategic: Its a defensive or offensive position against a rival.

3) Yields: Raw "stuff".


Its the Yields I want to look at. How well can you make a colony actually produce a net benefit for your civ? My thoughts on best ways to do that.

  • No investment: Off the bat I want to get controversial, and curious what others think here. Without investment its going to take longer to get the colony running, but gold is in theory one of the best yields you get for a new city....however, if you start spending that money in investment you will very quickly create a debt that city will never pay off. So part of me thinks the way to go is just let the city build as fast as it can build, and collect what you can from it.
  • Science or culture, not both: So as soon as you plop down the city, you have incurred a 5% science and culture debt, and the clock is ticking. I think trying to maintain both culture and science to high levels is likely folly. I think its best to just focus on one (with a process) and accept the trade off. Otherwise again your investing too much into the colony.
  • Minimum building, then stop growth and process. I think probably the best way to get your bang for the buck with a colony. Make the buildings your going to make, then stop growth (to prevent happiness), put as many specialists as you can afford, and then switch to a process....and then that city just becomes a puppet for all intensive purposes. That way, while in the longest term you start to lose out, you in theory get a boost in yields in the mid game that you can utilize for a better overall game.
The Buildings
So under this model, the key question is: What is the minimum list of buildings that should be built? Its a tough one, and definitely would like feedback on this. My thinking is:

1) Maximize base Supply: Supply is one of the good benefits of expansion (and you need additional supply to offset the defense costs of your colony).
2) Forego Production for the most part: Our goal is to build and get out, investing hammers to get more hammers is not what the plan is here. Aka no windmills!
3) Maximize Gold and Science/Culture (I'm going to assume science for my list below).
4) Need defense buildings up to Arsenal: Arsenals may have been voluntary at one point, but the AI is too good at naval endeavors now, so a coastal city has to have an arsenal to be competitive.

Obviously pioneers will give you some of these buildings, this is just meant to be a full list.

Buildings (Hammer Cost / Maintenance)

Supply Buildings
  • Lighthouse (144 / 1)
  • Harbor (343 / 2)
  • Barracks (103 / 1)
  • Armory (294 / 2)
Defense Buildings
  • Walls (103 / 1)
  • Castle (294 / 2)
  • Arsenal (1000 / 6)
Science Buildings
  • Council (61 / 0)
  • Library (144 / 1)
  • University (294 / 2)
  • Public School (1000 / 3) [I'm debating here, its a big jump in expense, but if we are maximizing on science specialists it is a big boost in science.]
Gold Buildings
  • Market (103 / 0)
  • Bank (500 / 0) [Banks base value isn't all that great, its more about the boosters to other buildings and the science return, which we wouldn't get here. So I'm thinking we may forego banks in this case]

Other Buildings
  • Monument (61 / 1) [so cheap for the price, and you need it to get the borders moving]
  • Amphitheater (192 / 1) [still cheap for the culture, but every expense matters]
  • Chancery (294 / 3) [generally one of the biggest boosts in the game yield wise, and the specialist is good for a city just making as many raw yields as possible.]
  • Gardens (294 / 3) [debating this one, I don't know if the 25% more GP will matter much in the colony, but I may need it just for the urbanization reduction]
  • Wire Service (1800 / 6) [While its very expensive, its generally a really good return. If I have 5 allies as a diplo civ, thats +10 science. We lose 450 science by making this building instead of using more science process, which is a 45 turn to pay off....usually worth it]
  • Observatory (500 / 4): [If you have rationalism, a no brainer but I won't assume it for now.]
  • Corp Office (846 / 6): [Once a corp gets going usually the benefits are going to be worth that cost]

Benefits and Cost
So if we ignore the bolded buildings for now, that puts us at a bill of:
  • 5,884 hammers (aka 1,471 science through process)
  • 34 GPT
I'm currently looking at a Greece game I'm playing in which I had 8 cities and 1 puppet before I started Renaissance expansion. I ran the numbers, and based on my current yields at this moment, my new colony would need to generate 14.3 SPT to stay even, and 14.6 CPT. That's with Authority Greece, so the science might be a low end number. However, if I get into big wars later, the passive culture I gain will mean the extra cost of a colony is even more keenly felt.

Science: So we are looking:
  • 9 base from buildings
  • ~10 from wire service
  • 10 from science specialists
  • 6 from civil servants
So 35 SPT. Subtracting the 14.3 SPT as our cost, we are gaining 20.7 SPT. Now that is our highest end estimate, as obviously my other cities will get better as well, and the 14.3 cost will increase over time. We should note that it will take 42 turns to pay off our hammer debt (aka if we have just made a crap colony and put it immediately on science process and built no buildings, I would generate more science than this colony would until 42 turns had past). Now in Renaissance we generally have another ~120 - 140 ish turns to go, so in theory this is still a good investment overall.

Instant Yield Quick Tangent
Spoiler :

Also just for fun, lets assume we have all of these buildings and specialists in place for the colony to grow from Pop 3 to Pop 12 (these are not realistic assumptions AT ALL but just to show what instant yields could look like). That would generate 15 * 9 = 135 science from the council, and 35 x .25 x 9 = 78.75 science from the university. That is a grand total of 6 turns worth of science. So under more realistic assumptions, its probably closer to 4-5 turns. I wanted to show that to note that in the long term, for a colony that we are going to cap and not have grow to massive proportions, the instant yields are not contributing a whole lot, so we don't have to think about them too much in terms of our overall benefits.


Gold: We have
  • 4 base from buildings
  • ~10 from chanceries
  • ~7 from city connection
  • 4 from civil servants
That's 25 GPT. So unless we can make up a lot of gold on the terrain (which one we go specialists shouldn't be that much), we aren't making a lot of gold. and note this is before I consider any gold investment, as soon as you do the colony's gold production becomes negative very quickly. This is important to show, a colony focused in this way DOES NOT MAKE MUCH PROFIT!!
 

Stalker0

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Ok so now with theory out of the way, I'm applying it to my current Terra type game. This is my recent colony, and I built it using the guidelines noted above:

Spoiler :

upload_2021-3-27_17-12-13.png



My notes:

1) Now this one doesn't have a lighthouse and harbor, but ultimately building all the buildings didn't take as long as I expected with a Pioneer, probably due to Tribute giving me 160 hammers a plot.
2) Adding in the observatory, my science process and better science specialists (plus the science for strategic resources), I'm gaining 60 SPT in early industrial. My new breakeven point is ~43 SPT, so I'm making +17 SPT. A fair amount lower than I was hoping, but with a little bit more growth I should get another science specialist and maybe a civil servant to shore it up. And of course the wire service still awaits me.
3) Culture Wise I'm generating 14 CPT (my religion gave me faith buy of amphithreater and opera house so I took advantage of that). My break even is ~40 CPT, so I'm losing 26 CPT.
4) Gold: Need to connect it but getting 26 GPT and maintenance is 24 GPT, so at base making just a little profit. That said, I'm getting +160 gold for every border expansion due to Tribute, so at least for the short term its definately going to be a money maker, and then will taper off later on.

So in summary: I'm gaining +17 SPT, +2 GPT (but with some big instant yields), -26 CPT, 2 Iron, and 1 Horse. Is it worth it? Honestly probably not, especially if you consider the additional costs of defending the city, the extra diplomacy penalties that expansion gives to the AI, and the fact that my CPT penalty will continue to rise. But lets check in it again later and see how it goes.
 

Stalker0

Baller Magnus
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So how is Pergamon doing with a little more growth?

Spoiler :

upload_2021-3-27_18-27-19.png



Science: 66 SPT, breakeven now at ~45 SPT, so making +21 SPT....a little bit better.

Culture: 13 CPT, breakeven now at ~38 CPT, so -25 CPT...about the same.

Gold: Now making +35 GPT with a -24 maintenance, so +11 GPT.


I also have a new colony (and this one was made by a colonist). I made it on Turn 311, so lets see how it grows.

Spoiler :

upload_2021-3-27_18-33-25.png

 

Stalker0

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So lets see how Miltetos looks on Turn 343 (32 turns later).

Spoiler :

upload_2021-3-27_19-15-14.png



1) Colonist + Authority's production bonuses allowed me to build all of the required buildings pretty quickly.

2) Science: 60 SPT vs ~57 break even. A combination of my main cities started to work specialists as they settle down, plus an influx of GS through faith buying...is making those remote bonus look more and more unattractive.

3) Culture: 9 CPT vs ~45 break even, -36 CPT

4) 40 GPT vs 33 maintenance, so +7 GPT.


So while I'm able to stand up these colonies "quickly", it doesn't seem that I'm generating much benefit from them. I'm also at the point where my supply is more limited by my gold income than my actual supply number, so I don't really need more of that. So it seems the colony at this point is pretty "useless" save for the few extra strategics I gain.
 

CrazyG

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I love mathematical analyses like these.

I think you might have gone processes a bit too early.

First I want temples everywhere, assuming you have the grand temple (which why wouldn't you?) 2 culture is decent and 5 faith is a solid boost. Unless faith was weirdly low value this game?

Beyond that I think you could invest a little more into culture, even if your goal is science and gold. Looking at the arena as another building I think is worthwhile almost always. You already have a barracks and a forge.

In that tundra city the caranvasary is worth considering and then you can consider custom houses and banks for the full gold-combo. If you build a road to that city then you should get at least one road-village.
 

Alpharius

Chieftain
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Jan 10, 2021
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I love mathematical analyses like these.
I feel the exact opposite xD

As I play to relax and have fun; doing rigorous computations would make it un-fun.
Though I do appreciate when someone else does it, it's interesting in a way.

On the main topic though, I take it the conclusion is post-Renaissance cities aren't worth settling in the long run from a raw-yield standpoint?
 

stii

Emperor
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Messages
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Yeah it is nice to see you trying out these things. I'm not surprised by the result but it is still worth trying different things to see if they work.

I generally find I have infinite gold so I'd probably try the opposite direction where you just rush buy everything. Converting gold into other resources seems like it has some value.

Having to build Arsenal everywhere seems miserable so I think you'd be better off trying to settle just off the coast and save all that cost.


But overall I think the basic issue is that civ is a lot about snowballing an early advantage. So any later city that takes ages to get neutral runs against that.
 

azum4roll

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It depends on your policies (and unique components). If you have Progress and Industry it's always worth to found new cities and spam buildings (invested) as long as you can defend them.
 

Stalker0

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It depends on your policies (and unique components). If you have Progress and Industry it's always worth to found new cities and spam buildings (invested) as long as you can defend them.

Its a fair question, does the instant bonuses of progress and industry help offset some of the costs....and perhaps even give us some real benefits? hehe I may have to do a real deep dive to know for sure, but as a quick approximation.

So looking at my example city above, I am currently at -36 CPT and +3 SPT, and in modern era I would make 50 C per building, as well as 50 science.

Now the million culture question is....what is the average time to build a building? So taking a look at miletos, doing the average build time of remaining buildings, its about 8 turns (note that alot of the cheap buildings already got made). So lets drop that to 4 turns assuming constant investment (which means that any chance of making gold profit on this colony goes up in smoke, but lets assume that tradeoff). Now yes industry gets more hammers and investment power, but lets also remember that without authority I am losing out on major sources of gold and hammers as well. So lets just use 4 turns as an extremely rough approximation (at some point I may try to do an actual in game example to see the real deal).

At 4 turns, that translates into +12.5 CPT and +12 SPT. So we have offset our culture cost a little bit, but ultimately our colony remains unprofitable on culture. Now with constant building we would get a little more base culture from yields, but we aren't offsetting a 24 culture deficit I believe.

With +12 SPT that puts us at +15 SPT, ok a little better now. However, in comparing buildings to processes, I am losing 11 SPT by building a building instead of running a science process, which means that +12 SPT I am getting is just barely profitable as compared to simply running the process myself. So until I get to build more science buildings, I am not gaining that much science, though I would gain more science in the initial building run of the colony.


So my napkin math suggests that even with progress and industry. this colony would not be that profitable, but I respect that my numbers are assumptions and approximates, and the best answer is to do a deep dive into the working of a colony. So I'll add that to my list, as it will be quite a bit of work to track.
 

Stalker0

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Since one of my major assessments is based on how much science and culture and new colony "costs", its probably time I show my math to ensure I am doing that assessment properly. So here is my method.

1) Acquire Total Science
Spoiler :

upload_2021-3-29_9-18-28.png


1,556 SPT in this case

2) Acquire Instant Yield Science, which is the 10 turn average divided by 10.
Spoiler :

upload_2021-3-29_9-23-16.png



So 933 / 10 = 93.3

3) Acquire SPT of colony

Spoiler :

upload_2021-3-29_9-24-42.png



60.8

4) Adjust final science total to subtract out colony science: Total Science + Instant Science - Colony Science (colony needs to be adjusted by 21% because of the current resolution bonus).

1,556 + 93 - (60.8 x 1.21) = 1,575

5) As each city adds 5% to total science requirement, our breakeven is 5% of the science we get from Step 4:

1,575 * .05 = 78.75 SPT


The Flaw
Now there is a flaw in my math. While I am accounting for the colony's base SPT in my calculation, I am not separating the colony's instant yield (aka from council and university) from the 93 total instant yield. Aka I am assuming the colony is contributing none of the 93 instant yield. The reason is there is no UI for that, I would have to track that myself, and I just haven't been doing that:) So....does it make a big difference, is that flaw so bad that it invalidates the results?

So to test, lets assume all 93 instant yield comes from the colony. We know that's a crazy assumption, but its the upper limit, aka just how much the analysis could possibly be off because of the flaw. The reality will be much less.

So step 4 now becomes: 1,556 + 93 - 93 (all instant yield is attributed to the colony) - (60.8 x 1.21) = 1,482
1,482 * .05 = 74.12 SPT. That is a 6% difference from what my analysis showed. Considering that most of my instant yield at this point in the game is coming from GS bulbs, its probably more like 1-2%.

So I stand confident that the assumption I have made is not skewing the results.
 

Stalker0

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OHHH!!! And this is why we write out our methods, because in doing so, I have in fact found a major flaw!!

The issue is Step 5: 5) As each city adds 5% to total science requirement, our breakeven is 5% of the science we get from Step 4:

1,575 * .05 = 78.75 SPT


The way city math works in Civ 5 is a little tricky. Effectively every city increases the original science requirement by 5%. However, when you look at the math city by city, the more cities you have, the less each new city has to contribute in order to meet that 5%. If that is not intuitive I understand, but here's a quick example. Lets say that I need 100 science at base to get my next tech. Here is how the science numbers grow depending on my number of non-puppet cities.

# of city| science required | % change from the last city
0 100 0
1 105 5.00%
2 110 4.76%
3 115 4.55%
4 120 4.35%
5 125 4.17%
6 130 4.00%
7 135 3.85%
8 140 3.70%
9 145 3.57%
10 150 3.45%
11 155 3.33%
12 160 3.23%
13 165 3.13%
14 170 3.03%
15 175 2.94%
16 180 2.86%

So even though my science requirement is growing by 5% of 100 every time, if you look at how much growth that is between the last city and the new one, the percentage is going down. So this is a big deal!

That means my 5% number is step 5 is wrong. Because this is my 16th city, the breakeven % is only 2.86. So that means, my breakeven number is actually....


1,575 * .0286 = 45 SPT! So that is a much lower number, and could mean a major difference in the result. I'll have to go through the work again to see if it changes the conclusions. It probably just reaffirms that I need to do a real deep dive of a colony anyway.
 

Rean

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It depends on your policies (and unique components). If you have Progress and Industry it's always worth to found new cities and spam buildings (invested) as long as you can defend them.

This is how I'd evaluate it usually, if I can build it up fast enough and have the ability to defend it there's no real limit to how many cities I'd settle.

Policy wise Authority can also be really good for new cities if you have some border growth bonuses to get more tribute pops, they help a lot to build up a city, especially for the first few buildings when you still have very cheap border growth in the city.
 

azum4roll

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So lets drop that to 4 turns assuming constant investment (which means that any chance of making gold profit on this colony goes up in smoke, but lets assume that tradeoff)
I would usually be swimming in gold if I pick Progress and Industry. Also don't forget the investment discount and the additional 10% production reduction from Industry. You also want to rush Bank first to maximize the science gain.
 
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Stalker, are you taking into account the bonus science yields from investing, considering you could/should build a bank first in your later cities and invest in every building?
 

Stalker0

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Stalker, are you taking into account the bonus science yields from investing, considering you could/should build a bank first in your later cities and invest in every building?

I have already started my more in depth analysis, so I will try a few options, including this and the progress aggressive building play. So lets see what the science shows!
 
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Cool. Also take into account which buildings you're building and what's the average build time in the first 75 or so turns after founding with a pioneer and building a bank and in the following 75 or so turns, because once you've built the bank you can focus first on a whole lot of hammer-light buildings, such as walls, herbalists, stone works etc., iirc, which means you get a lot of science and culture faster than later on.
 

Stalker0

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Cool. Also take into account which buildings you're building and what's the average build time in the first 75 or so turns after founding with a pioneer and building a bank and in the following 75 or so turns, because once you've built the bank you can focus first on a whole lot of hammer-light buildings, such as walls, herbalists, stone works etc., iirc, which means you get a lot of science and culture faster than later on.

I've got it all in my sheet, and feel free to head on over to General Balance, I have the first 34 turn results posted.
 

DeAnno

King
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Feb 22, 2011
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If you are Industry your first major colony of the lategame also has Broadway to consider and its massive instant yields, though to get it into a baby city you probably need to use a GE and maybe even some hammer routes.

This is also only really practical when all the AI do rationalism and you have no competition for it.
 
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