Home » Stars! 2.6/7 » The Academy » "Not habitable", my foot! (Some numbers on the economics of colonising reds)
| "Not habitable", my foot! |
Sun, 26 May 2019 11:51  |
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 magic9mushroom |
 | Commander |
Messages: 1361
Registered: May 2008 | |
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Today I did some number-crunching regarding the colonisation of planets that Stars! calls "not habitable" and the player community mostly calls "red". And because I rarely get sick of the sound of my own voice (own typing?  ), I decided to share it.
First, some basic refreshers on how reds and maintaining reds work:
- Reds have negative percentage values equal to the number of clicks they are outside your habitability range. Thus, they range from -1% to -45% (though the latter is rarely seen, as the race must not have any immunities and must also have fairly-narrow hab).
- Reds kill (red%/10)% of the population on them per turn, regardless of how much population is on them. This therefore ranges between 0.1% and 4.5% killed per turn.
- Reds function as 5% worlds for the purposes of population cap. So, for an average OBRM race (not JoAT, HE or AR), 55,000 population can operate installations and produce resources at full efficiency, and a further 110,000 can produce resources at half efficiency but not operate installations.
- The exception to this is AR, since AR have population caps determined by starbase hull and resource efficiency determined by habitability. AR treat reds as 25% worlds for the purposes of resource generation.
- To maintain a red, you need to have some source of population growth (usually a green planet) constantly supply population to replace the die-off. Since planets don't produce population when they're fully loaded, this means you'll have to sacrifice some production on the world you're using to grow pop in order to maintain the population and production on the reds.
- The most efficient places to grow population for non-AR, non-IS races are very-high-value greens, as the population produced at a given %hold varies with the square of hab (due to both growth rate and cap being set by hab) while resources sacrificed only vary linearly with hab.
- AR, however, grow pop equally-efficiently on any green over 25%, as hab does not affect their population caps. Obviously, they will grow less pop on lower-value worlds, but they will also sacrifice fewer resources. The reason I specify "over 25%" is because the AR resource formula bottoms out at 25% hab, so lower-value worlds will sacrifice the same amount of resources as a 25% planet while still growing fewer pop.
- IS, of course, do not need to sacrifice production at all to maintain reds, as they can simply park a freighter in orbit to overflow pop to the red. This also negates most of the micromanagement involved, so using reds is standard practice for IS. As such, I won't be speaking about whether IS should use reds - we all know the answer.
- The optimal hold for a breeder generating population to maintain a red is the hold% that maximises (growth)/(lost resources), because growth directly determines how many reds the breeder can maintain. This is at 50% for non-AR and 54.8% for AR. Of course, some adjustment will be necessary in order to compensate for the non-continuous popgrowth formula and the integer number of reds available for colonisation.
Case 1: standard race
For our first case study, we'll be examining the question for a fairly standard OBRM HG race with 19% growth, 1/1000 pop efficiency and 11/9/15 factories. Growth does matter to the efficiency of colonising reds (as it affects pop growth on greens, but not red dieoff), but for the first part of this the factory settings don't; they're just to give some more concrete numbers.
Let's first look at the case of a 100% world supplying -15% reds populated to 100%. This is one of the more favourable cases.
A fully-loaded 100% world with its full 1650 factories built produces 2915 resources. To turn the world into a supplier for reds, as noted above, we drop it down to 50% hold (550,000), reducing the resources produced to 1458 (1457.5 rounds up) and sacrificing 1457. At 50% hold, the world will grow 16/9 * 1 * 0.19 * (1 - 0.5)^2 * 550,000 = 46,444 population per turn (call it 46,400). -15% reds at 100% capacity (55,000) kill 0.015 * 55,000 = 825 population per turn (call it 900). so our 100% world can keep a staggering 51 red worlds at that value. Each red builds 82 factories and produces 145 resources per turn, for a total of 7395 resources - 5.08 times the resources sacrificed!  Obviously, this is an amazingly-good deal.
Of course, 100% worlds don't grow on trees (unless you're a Claim Adjuster or you have the Genesis Device, I suppose  ), so let's also look at a 75% world supplying -30% reds, one of the worse cases (reds worse than -30% are pretty rare for the reasons given above).
A fully-loaded 75% world with its full 1237 factories built produces 2186 resources, which when we reduce it to 50% (412,500) becomes 1092, sacrificing 1094 while growing 16/9 * 0.75 * 0.19 * (1 - 0.5)^2 * 412,500 = 26,125 population per turn (call it 26,100). -30% reds at 100% capacity kill 0.03 * 55,000 = 1650 population per turn (call it 1700), so our 75% world can keep 15 red worlds at that value. Each red still builds 82 factories and produces 145 resources per turn, for a total of 2175 - 1.99 times the resources sacrificed. Still a pretty good deal, although the extra micromanagement and freighter overhead make it less so.
But there's still an issue here - nobody actually has that many reds! Your average 3-wide HG, with hab widths of 60/60/68 (1-in-3), has only 2.7x as many reds as 75%+ breeders with 7/7/11 terraforming, and your average 1-immune 2-narrow HG, with imm/40/30 (1-in-7), has 4.1x as many reds as breeders with the same terra (with full terraforming, it's 0.14x and 1.8x respectively - the 3-wide has very few permanent reds). Of course, one solution is to simply only use the best breeders for maintaining reds and fill the rest in, but another idea is to increase the population on the reds to 300% or 165,000. This is far less efficient than the first 55,000, as the extra population works at 50% efficiency and doesn't operate factories or mines, but, well... let's run the numbers. Note that these calculations are "marginal" - they assume you're already keeping all your reds at 55,000, and ask whether the extra 110,000 is efficient.
Let's first look at a 75% green sending its pop to -15% reds. The resources sacrificed and pop gained per 75% world sre still the same - 1094 resources sacrificed for 26,125 population per turn. However, this population is now being used to boost red worlds from 100% to 300%, resulting in an extra 1650 deaths per red and only 55 more resources (due to the half efficiency and lack of extra installations). The 75% world can only afford to do this for 15.8 red worlds, but this only produces an extra 869 resources - not enough to make up those lost on the breeder. So taking red worlds to 300% isn't cost-effective...
...or is it? There are a couple of ways to make the numbers friendlier:
1) Only overpop reds with a low kill rate. This increases the amount of reds each breeder can keep topped off. A 100% green can afford to top off reds up to -15%, and a 75% green up to -11%. Of course, you probably don't have many 100% worlds left after (theoretically) using them to bring your reds up to 55,000, so for a race like this you can probably only get up to -12% or -13% profitably (and considering the lack of mines operated by the overpop, it may not be worth going quite that far).
2) Be factoryless. This is, obviously, a pregame decision, but consider - because you don't get factories from overpop, the resources gained by a factoryless race from overpopping reds (vis-à-vis leaving them at 55k) don't change, whereas the resources they lose on a breeder are much less. A -f race in the last example above would lose only 412 resources from dropping the 75% breeder to 50% hold, and therefore would profit from the 869 overpop resources (2.1x the sacrifice). In fact, factoryless races gain from overpopping all their red worlds, even those at -30% (since basically all -f take an immunity, there are none worse than that).
The take-home message from this for standard races is:
1) All standard races benefit significantly more from building red planets to 100% than they do from filling good breeders beyond 50%.
2) Filling red planets to 300% should only be done for relatively-mild reds for HG races; -f races benefit from doing it to all of them.
Case 2: Alternate Reality
As noted above, the drawbacks of reds for AR are almost completely different from those for standard races; about the only thing in common is the kill rate. I'm going to be assuming 15% growth, 10 divisor, 16 Energy and a 100% breeder planet - the divisor, energy and (as noted above) the breeder habitability don't matter, although %growth does. First, let's check the case for filling -15% reds to Orbital Fort capacity (250,000).
A 100% world at 3 million pop produces 2191 resources; reducing it to 54.8% (1,644,000) makes it produce only 1622 resources (sacrificing 569) but grow 89,566 population per turn (call it 85,000 after losses in transit for 1-2 years). -15% reds kill 3750 pop per turn (call it 3800), but produce 158 resources each; the 100% Death Star can afford to support 22 of them, for a return of 3476 resources - over six times what was sacrificed.
Again, though, this is far more reds than you'll have in your territory, even with AR's usual one-immune two-narrow hab; imm/30/30 has only about 1.5x as many reds as it does planets above 25% after full terraforming, and while most of them won't be able to support 22 this way, they'll all be able to support at least 5 and most at least 10. So let's see what happens when we go up to Space Docks. Again, we're theoretically doing this as a marginal thing, so we'll assume the reds already have 250k.
The 100% world still sacrifices 569 resources for ~85,000 pop. The extra population on the Space Dock reds kills another 3750 pop per turn per red (thus allowing 22 to be supported), but the increase in resources is only 66 per red - the extra population is only 41% as efficient, because of the square root. So the return here is only 1452 resources - still 2.6x what was sacrificed, and enough to clearly be worth it even on -30% reds, but not as good. But 2 Death Stars maintaining 23 Space Dock reds at 500k is still clearly far too many reds; guess we're building Ultra Stations or Death Stars on reds after all. This is going to get a bit repetitive, so I'll just list the cutoffs for each 250k or 500k (these might vary by a percent either way with Energy tech).
500k -> 750k: worth it down to -29% (inclusive)
750k -> 1M: worth it down to -25%
1M -> 1.25M: worth it down to -22%
1.25M -> 1.5M: worth it down to -19%
1.5M -> 1.75M: worth it down to -18%
1.75M -> 2M: worth it down to -17%
2M -> 2.25M: worth it down to -16%
2.25M -> 2.5M: worth it down to -15%
2.5M -> 2.75M -> 3M: worth it down to -14%
3M -> 3.5M -> 4M: worth it down to -6% (getting into overpop here...)
4M -> 4.5M -> 5M -> 5.5M -> 6.5M -> 7M -> 7.5M -> 8M: worth it down to -5%
8M -> 8.5M -> 9M: worth it down to -4%
Yes, seriously. It's better for AR to overpop near reds into the millions than it is for them to fill their greens, to the point that you might actually be running short on greens to do it with and have to pop-balance among reds balancing efficiency against death rate! Of course, it'll take a rather long time to actually grow that much pop, so considering you're AR you've probably won by then.
Still, the point stands: AR should always use reds over filling >25% greens, unless there aren't any reds around.
FAQ:
Q: Does this diminish IS's "capacity" advantage?
A: Not really. IS's "sacrificed" resources are a big fat zero due to the flying orgy - if another race is using reds, they're not filling their breeders, while IS can have that cake and eat it too. They don't need nearly as much micro to use their reds due to the ability to park the maintenance orgy overhead. And lastly, overpopping greens really is IS-only. Taking a 100% green from 100% to 150% cap (1,100,000 -> 1,650,000) produces 33,000 deaths - the equivalent, marginally, of a 60% red. Taking it from 200% to 300% cap is the equivalent of a 160% red. And you lose a prime breeder doing it. IS's advantages in this area are very real.
Q: What about intersettling?
A: Whoops, there goes my essay. 
Serious answer: There will usually be at least some mutual reds in an alliance, unless one of the partners is a tri-immune HE. Still, it's true, this does cut down on opportunities to exploit reds.
[Updated on: Sun, 26 May 2019 22:39] Report message to a moderator
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| Re: "Not habitable", my foot! |
Wed, 29 May 2019 14:01  |
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magic9mushroom wrote on Sun, 26 May 2019 17:51Today I did some number-crunching regarding the colonisation of planets that Stars! calls "not habitable" and the player community mostly calls "red" [...]
A fully-loaded 100% world with its full 1650 factories built produces 2915 resources. To turn the world into a supplier for reds, as noted above, we drop it down to 50% hold (550,000), reducing the resources produced to 1458 (1457.5 rounds up) and sacrificing 1457. At 50% hold, the world will grow 16/9 * 1 * 0.19 * (1 - 0.5)^2 * 550,000 = 46,444 population per turn (call it 46,400). -15% reds at 100% capacity (55,000) kill 0.015 * 55,000 = 825 population per turn (call it 900). so our 100% world can keep a staggering 51 red worlds at that value. Each red builds 82 factories and produces 145 resources per turn, for a total of 7395 resources - 5.08 times the resources sacrificed! Obviously, this is an amazingly-good deal.
Excellent approach, so simple and at the same time extremely efficient and convincing that I am almost ashamed to admit that I've never thought about it before. The genius of science, to ask the right question so obvious that everybody wonders how could this have not been asked ever before.
And this from somebody who repeatedly made quite some use of red planets in recent games... but my intention behind was mainly gaining minerals (low hab warmongering IT always short on minerals). Adding factories I did only without ever giving it much thought because I had those planets set up with an automated freighter anyway and definetly without being aware of the economic impact.
Thanks a lot, incredible helpful data and a well done analysis upto the min/max points.
Copied and stored for future games...
[Updated on: Wed, 29 May 2019 14:06] Report message to a moderator
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| Re: "Not habitable", my foot! |
Wed, 29 May 2019 19:21 |
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| magic9mushroom |
| Commander |
Messages: 1361
Registered: May 2008 | |
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iztok wrote on Wed, 29 May 2019 20:36Your numbers already did show that in games I'd play (some 30 planets per player) one 75% "breeder" would be sufficient to pop all the reds I'd expect to get in my share of the universe.
Quote:OTOH when those conquest give me lots of planets, then I start hitting RL and Stars! hard-coded limits, and colonizing reds just compounds them.
Good points.
Quote:Please do add a TL/DR for mere mortals. 
BR, Iztok
I kinda did, actually, with the last paragraph of each section.
Altruist wrote on Thu, 30 May 2019 04:01The genius of science, to ask the right question so obvious that everybody wonders how could this have not been asked ever before.
Oh, it's been asked and answered before, I just haven't seen anyone pony up the hard numbers before. For instance:
Wreck wrote on Sun, 15 May 2005 10:25This is generally the best use for pop. Any PRT, not just IS, can benefit from red planet colonization. IS are a bit better in that they can grow pop to replace red-planet losses without having to lose productivity on their green worlds.
As for whether to overpop normal worlds or do red planets - reds are a much better deal. Overpop on a normal world will quickly get to 1.5% losses, or 3.0%, etc.
The only real problem with red planets is that there aren't enough, assuming a reasonably viable race design. A single 100% planet can grow enough pop to keep ~20-30 reds topped off. But nobody plays races with ~1/20 greens after terraforming.
Altruist wrote on Thu, 30 May 2019 04:49What's TL/DR?
"Too long/didn't read".
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