The "cities tech cost" and it's implications

[kaspergm]

I have a question: If you capture a city, your science cost will go up. What will happen if you raze the city - will the cost stay increase, similar to how it works with culture and policies, or will the penalty go away once the city is gone?

 

[DeutschDachs]

Just finished my first game with a cultural victory, but I was also the science leader by far (noble). Yet it was the longest game I've played since maybe Civ III. Game ended in 2001 with me as far as Satellites. Most of the AI was still an era or two behind. Not sure if this is the result of this, but I thought I was doing poorly and it turned out the computer was struggling to kick out the beakers too

 

[The QC]

I may have missed it, but there are very few real numbers and calculations in this thread. From a quick calculation, the 5% penalty looks extremely harsh to me. Let's see how it evolves over time:

• Without libraries, beakers are equal to your population. Researching Writing costs 55 beakers. The 5% increase means each city increases the cost by 2.75 beakers. I don't know if that rounds up or down, but roughly it seems that at this stage a city needs to have a population of 3 in order to not slow down your research. Not a problem yet...
  
• With libraries, each citizen produces 1.5 beakers. When aiming for Philosophy for the National College, you presumably have libraries. Philosophy costs 175 and, with a 5% increase per city, each city adds 8.75, rounded up to 9, I guess. In order to generate 9 science, a city with a library has to have a population of 6 to break even. It already gets harder!
  
• With the National College built, each citizen in a city with a Library generates 2.25 beakers per turn. Until Education you don't get anything else that increases science. Education costs 485 beakers. A city adds 5% to that, which means 24.25. Divided by 2.25 this leads us to the awkward number of 10.(7), which, again roughly, means that a city needs to have a population of 11 and a library in order to not be a drain on your science at that point. Seems really, really harsh to me. Of course, cities have other benefits apart from generating science, but it looks like overall only big cities will be able to break even and not be a drain on science.

DISCLAIMERS:

• The numbers are taken from the online Civilopedia, which may or may not be up to date or reflective of the numbers in BNW.
• The calculations are based on my understanding of the system, which may be flawed.
• I haven't seen a clear confirmation that the increase is 5% and I saw a 3% elsewhere. Being in Europe, I can't check.

If anyone who's more knowledgeable could shed some light here, it would be nice.

 

[RealHuhn]

I may have missed it, but there are very few real numbers and calculations in this thread. From a quick calculation, the 5% penalty looks extremely harsh to me. Let's see how it evolves over time:

• Without libraries, beakers are equal to your population. Researching Writing costs 55 beakers. The 5% increase means each city increases the cost by 2.75 beakers. I don't know if that rounds up or down, but roughly it seems that at this stage a city needs to have a population of 3 in order to not slow down your research. Not a problem yet...
  
• With libraries, each citizen produces 1.5 beakers. When aiming for Philosophy for the National College, you presumably have libraries. Philosophy costs 175 and, with a 5% increase per city, each city adds 8.75, rounded up to 9, I guess. In order to generate 9 science, a city with a library has to have a population of 6 to break even. It already gets harder!
  
• With the National College built, each citizen in a city with a Library generates 2.25 beakers per turn. Until Education you don't get anything else that increases science. Education costs 485 beakers. A city adds 5% to that, which means 24.25. Divided by 2.25 this leads us to the awkward number of 10.(7), which, again roughly, means that a city needs to have a population of 11 and a library in order to not be a drain on your science at that point. Seems really, really harsh to me. Of course, cities have other benefits apart from generating science, but it looks like overall only big cities will be able to break even and not be a drain on science.

DISCLAIMERS:

• The numbers are taken from the online Civilopedia, which may or may not be up to date or reflective of the numbers in BNW.
• The calculations are based on my understanding of the system, which may be flawed.
• I haven't seen a clear confirmation that the increase is 5% and I saw a 3% elsewhere. Being in Europe, I can't check.

If anyone who's more knowledgeable could shed some light here, it would be nice.

Your math looks flawed. When each city adds 9 beakers to the total requirement of Philosophy, it doesn't mean you have to generate 9 beakers per turn and city to break even.
It means that each city has to generate an additional 9 beakers during the whole process of researching the tech.
For example, G+K rules, 4 cities need 9 turns to tech to Philosophy.
So in BNW, each city has to generate 1 additional science per turn. That means every city needs +1 pop.

Also, the NC only has an effect in one city.

Overall, your numbers look worse than they really are. However, +1 pop in each city still is a lot.

For example, I've seen Bridger15's live stream of a cultural victory and he really struggled to get any mid/late game tech in under 15-20 turns.
He only had 1-3 cities in early game but decided to expand onto a few islands. Overall, he had 8-9 cities I think on a large map (modifier was only 3% I believe, don't quote me on that). Yes, he didn't prioritize science buildings until later in the game but progress still felt extremely slow.

On standard size, it's 5%.

 

[kaspergm]

With the National College built, each citizen in a city with a Library generates 2.25 beakers per turn.

I think only NC affects the city in which it is build, so other cities would still be 2 beakers per pop?

Of course, cities have other benefits apart from generating science, but it looks like overall only big cities will be able to break even and not be a drain on science.

I think we have to accept that it is now part of the game design - like it or not - that cities will slow your science a bit until they reach sufficient size. Will that make teching slower? Yes. But it will affect all players equally (bared whatever bonuses AI always gets), so in that regard this is not really a problem in itself. Furthermore, given how people have long complained that late game eras zip by way too fast, and how new expansion adds content to those late eras mostly, not to mention that this feature will mostly affect those later eras where you have many cities, I think this feature does make sense with what the designers wanted to achieve.

Question is, however, whether this will reduce the number of viable strategies, which might end up working against the game.

 

[The QC]

Your math looks flawed. When each city adds 9 beakers to the total requirement of Philosophy, it doesn't mean you have to generate 9 beakers per turn and city to break even.

Ooops! Of course! And the comment on the NC is also correct...

I have one more question: have libraries changed to adding 1 beaker per pop or are they still at 1 beaker per 2 pop?

I'm trying to find a way of calculating a city's break even point because this would give me a clearer idea of the impact, but you're right that this depends on how many turns the research requires.

I think we have to accept that it is now part of the game design - like it or not - that cities will slow your science a bit until they reach sufficient size. Will that make teching slower? Yes. But it will affect all players equally (bared whatever bonuses AI always gets), so in that regard this is not really a problem in itself. Furthermore, given how people have long complained that late game eras zip by way too fast, and how new expansion adds content to those late eras mostly, not to mention that this feature will mostly affect those later eras where you have many cities, I think this feature does make sense with what the designers wanted to achieve.

I don't really oppose the change, I'm just trying to get a better idea of the result. Or to start a scientific p) discussion on the result, given that it seems I don't have the brains myself .

 

[kaspergm]

Your math looks flawed. When each city adds 9 beakers to the total requirement of Philosophy, it doesn't mean you have to generate 9 beakers per turn and city to break even.
It means that each city has to generate an additional 9 beakers during the whole process of researching the tech.
For example, G+K rules, 4 cities need 9 turns to tech to Philosophy.
So in BNW, each city has to generate 1 additional science per turn. That means every city needs +1 pop.

At first I misunderstood what you wrote here, but when you say "every city" you actually mean "every new city", right? So when city has population of 2, it will break even, given this special case where research time for Philosophy is 9 turns. The shorter research time you have, the bigger population of new city needs to get in order to break even. Even so, this seems very manageable.

And to answer your question, The QC, according to MadDjinn it's still 1 beaker per 2 population with Libraries (also the Assyrian one!).

 

[RealHuhn]

At first I misunderstood what you wrote here, but when you say "every city" you actually mean "every new city", right?

Nope, in this scenario the four existing cities do need one more pop each compared to G+K.

Edit: Not 100% correct because I assumed the capital also adds 5% (which it doesn't). But you get the idea.

 

[kaspergm]

Nope, in this scenario the four existing cities do need one more pop each compared to G+K.

Edit: Not 100% correct because I assumed the capital also adds 5% (which it doesn't). But you get the idea.

Then I don't understand the math. We do agree that we're talking about researching Philosophy (175 beakers), so that the cost of an extra city is 0,05 * 175 ~ 9 beakers, right?

So let's then consider a case:
- We start with X cities, and they will research Philosophy in 9 turns.
- We then plant another city, which increases the cost of Philosophy by 9 beakers.

In order for the new city to be cost-neutral, it would just have to cover for its own cost across those 9 turns, right? So the new city would have to provide 9 beakers over 9 turns, corresponding to a population of 2 - with no changes whatsoever required in the other towns?

 

[pilot00]

Seems to me that ToA, fertility rights and the hanging gardens just got an indirect buff.

 

[RealHuhn]

Then I don't understand the math. We do agree that we're talking about researching Philosophy (175 beakers), so that the cost of an extra city is 0,05 * 175 ~ 9 beakers, right?

So let's then consider a case:
- We start with X cities, and they will research Philosophy in 9 turns.
- We then plant another city, which increases the cost of Philosophy by 9 beakers.

In order for the new city to be cost-neutral, it would just have to cover for its own cost across those 9 turns, right? So the new city would have to provide 9 beakers over 9 turns, corresponding to a population of 2 - with no changes whatsoever required in the other towns?

You forgot that the cities you've build before your "new" city have already increased the cost of Philosophy by 9 beakers each (compared to G+K). So your "old" cities also have to research 9 more beakers each. So basically every city needs one more pop in this case, not just your "new" city.

By the way, the requirements for a new city get exponentially higher when techs get more expensive. And I really don't like that. In G+K, it was already hard enough to justify settling new cities after turn 120 or so. Sure, now there are new tenets available, for example, new cities start with 4 population. But is that really enough to balance the huge increase in science? 5% of a late game tech can easily reach 250 beakers. That's 25 additonal beakers per turn when you're looking to finish that tech in 10 turns.

 

[kaspergm]

You forgot that the cities you've build before your "new" city have already increased the cost of Philosophy by 9 beakers each (compared to G+K). So your "old" cities also have to research 9 more beakers each. So basically every city needs one more pop in this case, not just your "new" city.

No, because that increase would already be counted into the 9 turns that is the base value that we have before we build the new city. So unless the 5 % increase of the new city ALSO applies to the increase of the old cities - which I pretty sure that it wouldn't do, because that was not the case with the social policies - the increase from the old cities is irrelevant.

 

[AlazkanAssassin]

You two are both right, in what you think is important. But you are not comparing the same things.
RealHuhn is comparing tech costs in BNW to costs in GnK.
kaspergm is comparing tech costs with N cities to tech costs with N+1 cities.
(either of you correct me if you feel i'm misrepresenting you.)

In my opinion, cost compared to G+K is irrelevant. The needed comparison is the cost of building/aquiring a single new city vs NOT building a single new city, in BNW.
In that comparison, the exisiting cities population makes no direct change, only the population of the new city. (well, higher pop core cities do make new cities LESS favorable, but indirectly)

to determine the needed population of a new city to break even:
[number of cities] is the number of cities you have BEFORE building a new one, including your capitol.
[tech cost]=[base]*(1+.05*([number of cities]-1))
[base tech cost]*0.05=[increased cost]
[tech cost] / [current total beaker rate] = [turns to research]
[turns to research] * [new city beakers] = [contribution of new city]
The break even point is when [contribution of new city]=[increased cost]

This set of equations can be manipulated into [new city beakers]=[current total beaker rate]*0.05/(0.05*[number of cities]+.95)
So the population required of a new city is:
[current total beaker rate]*0.05/(0.05*[number of cities]+.95)
or if you buy a library in the new city:
[current total beaker rate]*0.0333/(0.05*[number of cities]+.95)

(It is assumed that the capital does not increase tech rates by 5%)

 

[The QC]

So the new city would have to provide 9 beakers over 9 turns, corresponding to a population of 2

Why 2? Doesn't every citizen add 1 beaker? So, at that point, a new city would easily pay for itself. It gets hairier later, mind you.

 

[RealHuhn]

You two are both right, in what you think is important. But you are not comparing the same things.
RealHuhn is comparing tech costs in BNW to costs in GnK.
kaspergm is comparing tech costs with N cities to tech costs with N+1 cities.
(either of you correct me if you feel i'm misrepresenting you.)

In my opinion, cost compared to G+K is irrelevant. The needed comparison is the cost of building/aquiring a single new city vs NOT building a single new city, in BNW.
In that comparison, the exisiting cities population makes no direct change, only the population of the new city. (well, higher pop core cities do make new cities LESS favorable, but indirectly)

Yeah, you're right I guess. Thanks for noticing.
It's a mixture of both though. Comparing to G+K is still necessary because it shows that expanding in BNW has higher opportunity costs than before.

Also, we shouldn't discuss it based on my crappy example. 4 cities and 9 turns to Philosophy is a rather limited scenario. ^^
Fact is, it hurts expansive playstyles. By how much? Too much? Time and experience will tell.

 

[kaspergm]

You two are both right, in what you think is important. But you are not comparing the same things.

Oh I get it now, thanx for sorting it out. But yes, the relevant thing to look at is with compared to without that last city when evaluating what the impact of the new city will be.

Why 2? Doesn't every citizen add 1 beaker? So, at that point, a new city would easily pay for itself. It gets hairier later, mind you.

Oh, they do? I remembered it was 1 for every 2 pop, but I guess you are right. Will need to redo my math also then.


Anyway, if I'm not doing any more mistakes, if you research a technology with a beaker cost B, that you will at a given time get in T turns, the effective population P of a new city you settle in order to break even will be given at:

P = 0,05*B/T

For instance, in above case, where B = 175 beakers and T = 9 turns, the effective population would have to be P = 0,05*175/9 = 0,97 ~ 1. If new city has an average of 1 population over those 9 turns, city will not slow down science progression. Notice that current number of cities is irrelevant (although it will of course have an impact on the value of T).

What the formula shows is that effective population P scales with beaker cost B of the technology you research - in late game, you'll need a larger population. Also it is inversely proportional to time T, so the faster your tech rate is, the larger the city needs to be in order to not slow your science progression.

For instance, if you research Education (B = 485) in 10 turns (T = 10) you need an average population of P ~ 2,4 in a newly founded city (over those 10 turns) in order to not slow down your science progression. If you research Scientific Theory (B = 1600) in the same time, you need a population of P = 8 on average over those 10 turns for the city not to slow down tech.

However, presence of Scientific Buildings will considerable lower those numbers. Thus, a Library cuts the required population down to two thirds of that number (5,3 for Scientific Theory over 10 turns) while University cuts it down to half original value (4 for Scientific Theory over 10 turns). With Public School, another 10 % gets cut off original value. As a final example, in order to research Nanotechnology (B = 8135) a city with Library, University and Public School needs a population of about 15 (not counting free beakers from Public School, plus obviously specialists etc. will cut this even lower) in order to not increase research rate if you keep at 10-turn research period. So yes, settling a new city very late game WILL slow you down for a while.

Approximate formulas, not counting extra science from sources other than population, for the cases are:

No science buildings: P = 0,05*B/T
Library: P = 0,033*B/T
University: P = 0,025*B/T
Public School: P = 0,019*B/T

 

[RealHuhn]

I haven't looked into your new formulas but you definately have to add to the equation that every city you settle in early game, increases tech costs throughout the entire game. At some point, you will have a hard time to get enough science even in your older cities.

Stop expanding and simply grow tall is the alternative here because it limits the penalties. That's the true issue here. If it's overdone, wide strategies can potentially fail at science every time just like they did in G+K trying to win a cultural victory.
That's hard to measure with a simple mathematic formula.

 

[The QC]

I haven't looked into your new formulas but you definately have to add to the equation that every city you settle in early game, increases tech costs throughout the entire game.

Yes, that's exactly what I'm realizing. The more you advance, the more each city becomes a drain, even though previously it provided a bonus.

It looks increasingly harder to calculate the impact .

 

[AlazkanAssassin]

Yes, that's exactly what I'm realizing. The more you advance, the more each city becomes a drain, even though previously it provided a bonus.
It looks increasingly harder to calculate the impact .

They are only a drain if they stop growing, while your other cities keep growing.
If they keep growing they will keep up usefulness.
If all your core cities stop growing there is no way you will keep up with the 10 turns/ tech assumption in the numbers kaspergm calculated, and your newer cities will not have to grow at all to keep up.

However there is one point I would like clarified. Does the +5% compound with previous +5% increases or not?

 

[The QC]

Ok, I've made a relatively simple late game calculation.

Rocketry costs 6400 beakers in a void and it takes 8 turns to research at the time when MadDjinn is looking at it in his Beyond the Monument part 2 video.

A city adds 5%, which means 320 beakers that have to be re-earned by it in 8 turns. So, the city needs to provide 40 beakers per turn and, at this stage of the game, has no excuse to not have all science buildings. If I’m calculating correctly:

• A mountain-side city needs 6 population and all available science buildings to break even
• A non-mountain city needs 8 population and all available science buildings to break even

How that is calculated:

• Each population adds 1 beaker by default and 1 from the combined benefits of Library and Public School, so you multiply it by 2
• Public School adds 3 beakers straight up and Research Lab another 4, for a total of 7
• University adds 33% to all of that, Research Lab 50% and Observatory, which can only be built if you are near a mountain, adds another 50%

So, old cities will almost definitely be breaking even. You wouldn’t want to settle anything at this stage, though.

The conclusion is that the whole thing is quite fluid and will need a moment-based decision, rather than something pre-determined. Overall, if well handled, most cities will be adding and not subtracting science. Wide strategies are not bad per se, but they provide less of a science benefit than they did before. And weak cities are something to really avoid.

However there is one point I would like clarified. Does the +5% compound with previous +5% increases or not?

Indeed, that's something I haven't see clarified yet. It would change the calculation again .