Beyond Earth game mechanisms : Health

[Xenotitan]

This depends how late in the game you are and on your current empire.

Given a new city increases science costs, it has to reach a certain amount of science output before it will cover the cost of itself. This payoff time can be longer than it takes for you to win the game (or research all the techs you need to win the game). In that case, expansion is not the correct choice, even if it is neutral health impact.

There can be an exception for harmony victories where you immediately buy the buildings that accelerate your win condition, but it seems like you need quite a few to drop the turn count.

I do agree that there is a point where there is no point to expanding any more. But expanding remains viable almost until the end of the game because trade routes mean a new city gives decent returns right off the bat. Also, each new city is only +5% increase to base tech cost, it doesn't take much to be worth that small penalty.

Prosperity after the free colonist is all about staying healthy. And staying healthy is not worth the effort. The bonuses from the other trees far outshine being healthy. You can already expand infinitely even without the prosperity tree. In fact, you would do it more quickly without prosperity and largely ignoring health (or optimally keeping it over -20 because that and only that slows down your expansion... and not by much).

Out of the 12 virtues not on the way to the free colonist, only 3 affect health. A big theme of prosperity is health but it isn't ALL about staying healthy, or even mostly about staying healthy.

 

[Roxlimn]

Xenotitan:

A new city using 2 of its routes for external trade (assuming it's settled in a location that's not cut off) in the mid to late game will optimistically have an output of 20 bpt, though it is usually a bit less. This constitutes about 5% of 400 bpt. So long as the empire-wide output is less that than, each city can recoup the science expansion cost fairly quickly. As the bpt amount goes over that, it becomes harder and harder for new cities to increase research rate.

400 bpt is more than enough to navigate the tech tree comfortably, though it is far from enough to exhaustively research every tech before the game ends. I'm open to the idea that this amount is too large and that the breakpoint ought to be lower.

 

[Xenotitan]

The 5% increase is 5% of the base cost of the tech, not the current cost that is based on how many cities you already have. At just your cap the increase is the same, at 21 cities an increase of 5% of the base costs is 2.5% of the current cost. So the calculation is actually more complicated than "does this city make more than 5% of my current bpt?"

 

[Roxlimn]

No. It's actually not more complicated at all. Assuming that the capital is making all the science, the breakpoint is at 400 bpt. That's the lower limit. The current cost doesn't matter. All the additional other costs is the cost of each city as it is added to the colony. What this means is that the threshold for breakpoint should be lower than 400bpt. You get diminshing returns at something like 350 bpt and about 10 cities, I estimate. Could be wrong, but that's where I'm eyeballing it.

Of note - 10% per city penalty was so severe that players in Civ5 did best with no more than 4 cities - and only that much because you got freebies up to the 4th one.

 

[Lord Yanaek]

And staying healthy is not worth the effort. The bonuses from the other trees far outshine being healthy.

Because of course other trees easily gives you +20% , and

Not saying that high health is the way to go but i think it's one way to go and some people tend to ignore it too hastily. But again, the game is still recent and we probably did not explore all the possibilities. Just because it's possible to play and win with low health does not mean it's (always) the best way to play.

 

[sprang]

The 5% increase is 5% of the base cost of the tech, not the current cost that is based on how many cities you already have. At just your cap the increase is the same, at 21 cities an increase of 5% of the base costs is 2.5% of the current cost. So the calculation is actually more complicated than "does this city make more than 5% of my current bpt?"

T4 base costs are 2480, T4 Leaf techs are 3210. 5% is 120 for T4, 160 for T4L.

The relevant calculation for marginal research benefit is your tech rate, in TURNS. Will the city contribute more science before the tech is researched than it's marginal increase in per-tech cost?

If you have a single 400 bpt city, that's 8 turns per T4L tech (okay, okay, 402). You found your second city, on turn 250. For a T4 leaf tech, your new city raised the cost by 160, to 3370. Now it will take 9 turns to research the tech. OH NOES! But you quickly buy a Depot, Autoplant, and three Routes, sending them to three foreign capitals. You get 15bpt from each, netting 45bpt. Your science rate went up by over 10%. In fact, your estimated turns is now 7.5! Most importantly, over those 8 turns, your new city will contribute 360 , far more than the 160 cost increase.

If you spam late cities, there are two models.
1) They are largely undeveloped, very low pop, and they will have little or no base science - maybe 3-5bpt. But you would use all three TR for Ext, with no incoming routes, so net 40+ bpt is easy.
2) They are more developed, with buildings and tile improvements. You probably use one TR for internal production to pump it up, either incoming or outgoing. But the city itself will have a larger population, in the 4-8 range, and will include some basic buildings, like Clinic, Cytonursery, and Laboratory. That's almost 15 science right there (pop + bldgs) - enough to cover the missing External TR. Add some academies or science-producing resources, and you're far ahead. With still two ExTR, you'll easily get over 40 bpt total from the city, especially considering that building and tile/terrain science is subject to Virtue modifiers.

If 40bpt is a reasonable return on a new late game city, then your marginal science return from the city is negative ONLY IF you are teching faster than 4 turns per T4 LEAF tech. That means 800bpt in an OCC, +5% for each city you own. 6 cities? 800 + 30%, or 1040bpt.

What about cheaper techs, where a fast turns-per-tech means less benefit from your new city? Most T3 techs are 770, T3L 1160. T3.5 is 1160 (Mechatronics, Alien Ethics, Transgenics), with T3.5L at 1820. 1160 per tech means the cost rises 58 for each extra city. It's hard to get 58 science from a spammed city, but 29 isn't so tough. So if you are planning on teching lots of these T3 leaf techs in one turn each (i.e., your science is far OVER 1160bpt), postpone your city spam until afterwards.

Note that for the 770 T3 techs, 5% is 38.5 , and that IS a feasible per-turn-rate with spammed cities. Thus, for all technologies at T3, T2L, or cheaper, spamming cities is ALWAYS worth it.

Obviously, this only applies to science costs. Virtues and Health = YMMV.

tl;dr: Regardless of how many cities you currently have, adding another city can increase your science rate if:
1) it takes you longer than 2 turns to research T3.5 technologies
2) it takes you longer than 3 turns to research T4 technologies
3) it takes you longer than 4 turns to research T4L technologies.

 

[Roxlimn]

The calculation depends on having 3 15 bpt routes. I don't get that many routes from a size 1 city, possibly because I don't always have AI capitals on coast - certainly not 3. In general, 1 is good. I have had games where none of the AI Capitals were on the coast, so 15 bpt in that game was impossible, even in the late game.

At 8 bpt or less per external route, new cities net around 24 bpt assuming you're going to just essentially let them rot, less otherwise. This corresponds to the breakpoint of 400 bpt - that's the point at which new cities are science-neutral.

With this rate in mind, the return or breakpoint-turn for new cities in terms of science is significantly lower. A new city flush with Academies getting 100 bpt is definitely worth getting, but those Academies take Worker turns to finish - and that cuts into the new city's science utility. Close to Victory Conditions (within 20 turns), the new city's science output may not matter at all.

Moreover, the Health is also taken into consideration, since the basic Knowledge +10% total Science requires positive Health. New cities that will cost negative Health will have to make up the Health quickly, or make a massive amout of Science to compensate. Critical breakpoints of this nature (vis a vis Science vs expansion) currently occur at 0 and at +20. Those are reasonable points at which to consolidate and build more Health in lieu of expansion (assuming normalized ETRs at 8 bpt or 20-25 max bpt per new city).

 

[player1 fanatic]

Also is nobody thinking about culture? Every extra city gives penalty for virtue aqusition. And it can not be compensated by TR.

Now sure you can play in such way to only grab virtues of strategic importance, and then start spamming cities, after key virtues are taken.

In my oppinion for rexing you needd to be deep either in prosperity OR industry (not both, that is unneeded overkill) to get their ending health virtues which will help all cities to support all their health on their own.

 

[Roxlimn]

For Prosperity, you need 7 Virtues to reach Eudaimonia, assuming that you don't spend 2 early Virtues on the Free Colonist. This actually is acquirable surprisingly fast (equivalent to full 5 Tier 1 Virutes and 2 Tier 2).

Frugality
Workforce Initiative (free worker)
Pathfinders (Explorers have 3 extra Expeditions)
Gift Economy (+3 Energy per foreign TR)
Mind Over Matter (+7 Global Health)
Hands Never Idle (+2 Energy per Specialist)
Eudaimonia (25% less negative Health)

With Artist or Aristocrat, cities start at 4 negative Health, immediately reducible to 3 with Clinic. Health neutral comes at size 5 or 6 with Pharmalab and Cytonursery.

All of this comes with the related costs, of course. It's not cheap. You're either spending a lot of turns, a lot of Energy, or you're using up TRs to generate Food and Hammers for the new city. Total base Culture Cost is 504.

Due to citizens not producing native Culture, valuation for Culture is different (but costs even more Energy, Hammers, or Turns). Each city increases Virtue Cost by 5%, but generally produces much more than that. As an example, the first City with Artist Colonist only produces 6 Culture (+1 HQ, +3 OER, +2 Artist). The second city will quickly produce +5 Culture per turn - an 80+% increase in Culture. Once accessory buildings are researched (Feedsite Hub, Xenosanctuary), rapid building of such in many cities ensures very rapid Virtue acquisition.

 

[sprang]

The calculation depends on having 3 15 bpt routes. I don't get that many routes from a size 1 city, possibly because I don't always have AI capitals on coast - certainly not 3. In general, 1 is good. I have had games where none of the AI Capitals were on the coast, so 15 bpt in that game was impossible, even in the late game.

At 8 bpt or less per external route, new cities net around 24 bpt assuming you're going to just essentially let them rot, less otherwise. This corresponds to the breakpoint of 400 bpt - that's the point at which new cities are science-neutral.

With this rate in mind, the return or breakpoint-turn for new cities in terms of science is significantly lower. A new city flush with Academies getting 100 bpt is definitely worth getting, but those Academies take Worker turns to finish - and that cuts into the new city's science utility. Close to Victory Conditions (within 20 turns), the new city's science output may not matter at all.

Moreover, the Health is also taken into consideration, since the basic Knowledge +10% total Science requires positive Health. New cities that will cost negative Health will have to make up the Health quickly, or make a massive amout of Science to compensate. Critical breakpoints of this nature (vis a vis Science vs expansion) currently occur at 0 and at +20. Those are reasonable points at which to consolidate and build more Health in lieu of expansion (assuming normalized ETRs at 8 bpt or 20-25 max bpt per new city).

Actually, the calculation doesn't depend on 15bpt or 8pt, except in the trivial sense. Sure, if you've just halved your expected science return from these cities, then you should double my turns-per-tech guidelines, because that's the only change.

The important thing to recognize is that there is no magical threshold of numbers of bpt; rather it's dependent on your current turns-per-tech, because that scales with number of cities and is the primary factor which determines if your new city will be able to contribute enough science to be worth using.

So, if you want to assume only 20bpt from a new city (which I think is absurdly low)...
Regardless of how many cities you currently have, adding another city can increase your science rate if:
1) it takes you longer than 2 4 turns to research T3.5 technologies
2) it takes you longer than 3 6 turns to research T4 technologies
3) it takes you longer than 4 8 turns to research T4L technologies.

Again, health and culture mean YMMV. But I'm just trying to put the "spammed science city" into the proper frame.

 

[player1 fanatic]

Actually, the calculation doesn't depend on 15bpt or 8pt, except in the trivial sense. Sure, if you've just halved your expected science return from these cities, then you should double my turns-per-tech guidelines, because that's the only change.

The important thing to recognize is that there is no magical threshold of numbers of bpt; rather it's dependent on your current turns-per-tech, because that scales with number of cities and is the primary factor which determines if your new city will be able to contribute enough science to be worth using.

So, if you want to assume only 20bpt from a new city (which I think is absurdly low)...
Regardless of how many cities you currently have, adding another city can increase your science rate if:
1) it takes you longer than 2 4 turns to research T3.5 technologies
2) it takes you longer than 3 6 turns to research T4 technologies
3) it takes you longer than 4 8 turns to research T4L technologies.

Again, health and culture mean YMMV. But I'm just trying to put the "spammed science city" into the proper frame.

You know, science does overflow.
Just because in some specific scenario science boost will not improve time to get the next tech, it will improve the tech after it.

Every point of science matters.

 

[Roxlimn]

sprang:

Sure. The difference is that I routinely go sub-8 turns on T4L technology in the late game - 1000 or so bpt is not a problem and I don't need a lot of spammed 15 bpt routes to do it. Indeed, in such games, normal bpt from TRs only average about 100-200. The way I see it, the 15 bpt per route Apollo players expect is a distortion of what the mechanics were built for.

The right correction isn't to change the mechanics. The right correction is to nerf Apollo ETRs by 75%.

The threshold isn't magical nor static. I was assuming that everyone could see that, because I think all the numbers and arithmetic we've been using is fairly elementary. However, while I respect turns-per-tech valuation (since turns are the ultimate currency in the game), bpt is more transparent and easier to estimate. Bpt and Turns per Tech are just two ways of expressing the same thing. That said, Turns Per Tech does bake in the current percent penalty from number of cities. Not sure how to express that better, actually, since the penalty for number of cities is static, and each city grows in science contribution as it matures. Ultimately, as with Health and Culture, the best way for a city to become Science-contributing is to grow very fast and get a lot of buildings or good tiles.

 

[sprang]

You know, science does overflow.
Just because in some specific scenario science boost will not improve time to get the next tech, it will improve the tech after it.

Every point of science matters.

Uh... unless the act of getting that point of science means you need even more science. Overflow is irrelevant.

If you are researching T4 leaf techs, founding a new city will raise the cost of those techs by 160 each. If you are researching fast enough that you get one T4 tech every two turns, that new city needs to contribute 80 science per turn to offset the increased costs of the the techs. Clearly, that's not gonna happen, regardless of how much overflow you have. In that case, founding additional cities *for the purpose of increasing your tech rate* will not work.

 

[sprang]

sprang:

Sure. The difference is that I routinely go sub-8 turns on T4L technology in the late game - 1000 or so bpt is not a problem and I don't need a lot of spammed 15 bpt routes to do it. Indeed, in such games, normal bpt from TRs only average about 100-200. The way I see it, the 15 bpt per route Apollo players expect is a distortion of what the mechanics were built for.

The right correction isn't to change the mechanics. The right correction is to nerf Apollo ETRs by 75%.

Then the first step is to just eliminate the 50% bonus for water trade routes. Because you're right - landlocked cities don't get 15bpt routes. Maybe THAT should be Hutama's ability: he keeps the water bonus, instead of +2 routes.

The threshold isn't magical nor static. I was assuming that everyone could see that, because I think all the numbers and arithmetic we've been using is fairly elementary. However, while I respect turns-per-tech valuation (since turns are the ultimate currency in the game), bpt is more transparent and easier to estimate. Bpt and Turns per Tech are just two ways of expressing the same thing. That said, Turns Per Tech does bake in the current percent penalty from number of cities. Not sure how to express that better, actually, since the penalty for number of cities is static, and each city grows in science contribution as it matures. Ultimately, as with Health and Culture, the best way for a city to become Science-contributing is to grow very fast and get a lot of buildings or good tiles.

I was looking at it more in terms of finding a good heuristic for when that extra city is worth it or not, and because turns-per-tech controls for number of cities, it's the better metric than pure bpt.

But also, you get two VERY different answers to the following question:
I have 300 bpt in a small colony, researching at around 8 turns per tech. Then I go on a rampage and conquer my continent, puppeting all the conquered cities. As martial law wears off, my science rises to over 500bpt, but my tech rate slows to 11 turns per tech. I can't max out bpt from the puppetd cities, and the governor keeps ignoring the academies I try to build, using Trader specialists instead (ugh!). Will founding more cities for TRs speed my science, or slow it down?

A bpt focus would suggest that my science rate is high enough already. But a turns-per-tech focus reveals that founding new cities for ExTR is a good choice here.

 

[Roxlimn]

sprang:

Then the first step is to just eliminate the 50% bonus for water trade routes. Because you're right - landlocked cities don't get 15bpt routes. Maybe THAT should be Hutama's ability: he keeps the water bonus, instead of +2 routes.

Even water routes don't get 15 bpt per route on Gemini and lower. The fact that the highest levels of the game get easier is clearly wonky. I don't get why people aren't asking Firaxis to nerf their (but not everyone else's) external TRs.

I confess that I'm not sure how I feel about the water routes. In Civ5, the strong incentive to have fewer cities and the fact that barbarian sea vessels abounded even in the mid game meant that sea vessels were more at risk, justifying the higher return. You also had to actually explore the world first. Neither of those are strong factors in CivBE, especially if you're doing Continental Surveyor.

That said, I have had games where establishing water routes were challenging. I've had several Hutama games where the Capital was landlocked.

I was looking at it more in terms of finding a good heuristic for when that extra city is worth it or not, and because turns-per-tech controls for number of cities, it's the better metric than pure bpt.

But also, you get two VERY different answers to the following question:
I have 300 bpt in a small colony, researching at around 8 turns per tech. Then I go on a rampage and conquer my continent, puppeting all the conquered cities. As martial law wears off, my science rises to over 500bpt, but my tech rate slows to 11 turns per tech. I can't max out bpt from the puppetd cities, and the governor keeps ignoring the academies I try to build, using Trader specialists instead (ugh!). Will founding more cities for TRs speed my science, or slow it down?

A bpt focus would suggest that my science rate is high enough already. But a turns-per-tech focus reveals that founding new cities for ExTR is a good choice here.

Actually a bpt focus would suggest that you need to found a bunch of cities, grow them fast and spam Academies on them. Such cities would become Health-neutral faster, and they'd get Science buildings, and they'd rocket to 60+ bpt about the time the Academies get done. (6x8 = 48 + 3 (laboratory) + 1 (Cytonursery) +1 (Clinic)) x 10% + 1ETR.

Such an output would clearly be beneficial until well past 1000 bpt.

 

[sprang]

Such an output would clearly be beneficial until well past 1000 bpt.

Isn't 1000bpt > 400bpt?

You said 400bpt was the breakeven point, that beyond 400bpt additional cities were a waste. That was the whole point of my hypothetical.

 

[Roxlimn]

Isn't 1000bpt > 400bpt?

You said 400bpt was the breakeven point, that beyond 400bpt additional cities were a waste. That was the whole point of my hypothetical.

Shrug. Like I said, that was meant to be an estimate. It's fluid based on play speed, map size, etc. etc. With 400 bpt on a normative peaceful colony, I'd be speeding through the tech tree. With a bunch of puppeted cities, not so much. Tech Per Turn is a nice heuristic that accounts for the puppeted states, but cities don't output in fractions of Tech per Turn.

 

[Xenotitan]

No. It's actually not more complicated at all. Assuming that the capital is making all the science, the breakpoint is at 400 bpt. That's the lower limit. The current cost doesn't matter. All the additional other costs is the cost of each city as it is added to the colony. What this means is that the threshold for breakpoint should be lower than 400bpt. You get diminshing returns at something like 350 bpt and about 10 cities, I estimate. Could be wrong, but that's where I'm eyeballing it.

Of note - 10% per city penalty was so severe that players in Civ5 did best with no more than 4 cities - and only that much because you got freebies up to the 4th one.

Assuming the capital is making all the science is ridiculous.

It is more complicated. You suggested the criteria was if a city would make at least 5% of the empire wide bpt. If x is the current bpt, and y is the amount a new city would give, the criteria is 5% <? y/x.

With it increasing the base cost, it gets more complicated. You want to reduce the number of turns to research something, cost/bpt. Say you have n cities other than your capital, then the criteria becomes base cost*(1 + 0.05*n + 0.05)/(x+y) <? base cost*(1 + 0.05*n)/x

(1.05 + 0.05*n)/(x+y) <? (1+ 0.05*n)/x

1.05x + 0.05nx <? x + y + 0.05nx + 0.05ny

0.05x <? y + 0.05 ny

0.05/(1 + 0.05n) <? y/x

Which at n = 0 turns into the original 5% <? y/x. At larger n, y doesn't need to be quite 5% of x though in order to make founding the city worth it in science terms. So if we're estimating y at 20 bpt, then if you have more cities the breakpoint becomes higher than 400 bpt, not lower.

 

[Roxlimn]

Xenotitan:

Actually, I think sprang's Tech Per Turn heuristic is useful in clearing away all of that algebra in this case. Briefly, the more science your Civ is already making, the more a new city has to make in order to make a positive difference in the outcome. Trivially, if your Civ was somehow making 5000 bpt, a new city's science output would probably be meaningless. If your Civ is somehow making less than 50 bpt, it's similarly trivial to make a new city that will contribute significantly.

However, you are correct. At the same bpt, a 20 city colony loses less by making another city than a 10 city colony, because the relative addition of a new city will have less fractional significance to the beakers it needs for a new technology.

I stand corrected. I conflated the two.

 

[ImmelmannTurn]

...
0.05/(1 + 0.05n) <? y/x
...

You can simplify that further. x is always positive so you can multiply with it safely and 1 = 20*0.05, so:

0.05/(1+0.05n) <? y/x

0.05x/(1+0.05n) <? y

0.05x/(0.05*20+0.05*n) <? y

x/(20+n) <? y