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Resource integral hold for IS? 
Wed, 26 September 2012 10:53 

magic9mushroom   Commander  Messages: 1154
Registered: May 2008  

I know that the hold to maximise resource integral on filling to 100% with any other race is 48%, but has anyone worked out what it comes to for resource integral filling with IS, accounting for freighter growth?
I've got the feeling that unlike for a normal race, the result's going to depend on hab value (since ground growth vs. freighter growth changes with hab) but I'd like to get a feel for the ballpark.
(I wish my CAS calculator still worked. Then I could do all of this trivially by myself.)
[Updated on: Wed, 26 September 2012 11:01] Report message to a moderator


 
Re: Resource integral hold for IS? 
Sun, 30 September 2012 07:05 

magic9mushroom   Commander  Messages: 1154
Registered: May 2008  

neilhoward wrote on Sun, 30 September 2012 20:01How do you come to 48%?
Well, I didn't do that particular calculation myself.
The thing you need to minimise is resource loss, which is given by:
integral((max resources  current resources) over the time from 33% to given hold) + (max resources  hold resources)(time to fill at given hold).
The firstorder approximation of (max resources  hold resources)(time to fill from 33% to 100%) gives an answer of exactly 1/2 (I have done that calculation), but that is an approximation.
(This doesn't work in the IS case because of freighter growth and the possibility of overpop.)
[Updated on: Sun, 30 September 2012 07:07] Report message to a moderator



Re: Resource integral hold for IS? 
Mon, 01 October 2012 13:43 


Hi ,
overpop is possible also for other races.
Also it would always depend on how many Planets you own and how big your univers is (with breeders).
If I play IS i normaly look how moch grow the Planets have if it is lesser then 50% of my grow i load them up to maximize popgrow. Some times I change this to build out some Planets a little bit faster for Resources for research. But i think it is different to say you should take 48% Kap as for a 40 % Planet the Freigthers would be better anyway ... so I would say you have to do it idividual for your empire/Planets.
ccmaster
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Re: Resource integral hold for IS? 
Tue, 02 October 2012 21:34 

magic9mushroom   Commander  Messages: 1154
Registered: May 2008  

joseph wrote on Wed, 03 October 2012 08:16If you look at the thread http://starsautohost.org/sahforum2/index.php?t=msg&th=35 73&start=0&rid=256
You will see I posted about the best resource integral for an f IS
Most of the same applies to a factory one.
Its a lot more complicated than for a standard race.
Yes, I realised that the optimum strategy is a moving hold rather than a static hold. I'm not sure that your calculations are sound, though. Since popgrowth is maximised when at 25% for an IS, shouldn't the moving hold start there and not at 33%?
Assuming you have OBRM, 20% growth, and 366700 pop:
Having it all on the ground (33.3%) would give a growth of (64/81)*20% = 57900 pop growth
Having it set to overflow to 25% (ie, 264800 on the ground and 101900 in orbit with the rest of the freighter filled with boranium) would give a growth of 10200 in orbit (overflowing onto the ground to give 275000) and then 55000 growth on the ground, for a total pop growth of 65200.
Since the general idea of resource integral for IS is to start out by favouring pop and move to favouring resources once the orgy's going, shouldn't you hence start putting pop in orbit at 25%?
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Re: Resource integral hold for IS? 
Sat, 13 October 2012 20:40 

Braindead   Chief Warrant Officer 3  Messages: 186
Registered: April 2005 Location: Seattle, WA  

Maximizing cumulative resources over N turns is not a trivial calculation. The following factors have major contribution to this:
* planet value
* f vs +f race
* for a +f race, concentration of G, cost of factories and efficiency of mines/factories/pop. Oftentimes, you can get way more resources by dumping a freighter of G on the planet than by optimizing pop growth.
* ships available at the planet (if you have 500k pop and only one privateer, you can't do much. Same if you have a super freighter and 400k pop.)
* overall minerals and resources that you have  can you afford to build more freighters for colonization/distribution of minerals or do you need to use all of your existing ships for this?
* how far into the future are you looking
* number of neighboring planets (it's not practical to only focus on one planet since in a game you would want to optimize your total resources)
In my opinion, optimizing for maximum resources over time is a theoretical exercise, which doesn't have too much application in real games. I've played IS a lot and my rule of thumb these days is to put enough people on the ground to keep up with tech/building and react to what's happening in the game (is anyone sending a huge fleet after you?). The rest is focusing on maximizing population growth. Having hordes of pop available at your disposal will enable you to colonize more planets faster, use your colonists instead of bombers and overall will give you way more benefits than having optimum resource growth. Plus, it will save you a lot of time since you don't need to do silly calculations.
braindead
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Re: Resource integral hold for IS? 
Mon, 07 August 2017 04:42 

magic9mushroom   Commander  Messages: 1154
Registered: May 2008  

Update: I solved for the optimal holds as a function of planet habitability, pop efficiency, factory settings, population growth rate, and pop available (yes, all of them are relevant). I got working formulae for the case where the optimal hold is between 0 and 25% of capacity, and for the case where the optimal hold is between 100% and 300%.
The case where the hold is between 25% and 100% is much, much harder; it's a casus irreducibilis cubic over most of the practical cases, with three real solutions of which only one is the desired hold (the others, TTBOMK, represent a local worstcase and a local bestcase that's worse than the actual bestcase). As such, I do not believe a general algebraic formula is very useful in this case; your best bet if you really want to wring out the absolute max is to graph (growth)/(resources lost) vs. hold for specific values of all those parameters and find the maximum numerically. Assuming, of course, that I didn't bugger up the arithmetic somewhere, which is unfortunately a distinct possibility when trying to wrestle with cubics.
So much for my vaunted aptitude with algebra and calculus.
The one exact solution I've found that's practically useful (i.e. doesn't require adjusting holds every turn to use) is the first case, between 0 and 25%. It turns out that it's always better to have either a "zero hold" (100 colonists kept on the planet as a flagpost + setting the overflow) or a 25% hold (setting the overflow such that the colonists on planet + overflow = 25%) than anywhere inbetween (of course, these holds converge when the overflow becomes large). The changeover point is when
pop = (1  hab * (2  PGR)) * (2 * PE + FE)/(PE + FE)
where
pop = the amount of population you have at the world (in freighters and on the ground), expressed as a multiple of the world's maxpop (so 550,000 pop on/around a 50% planet with OBRM = 1)
hab = the planet's habitability, expressed as a fraction (so 25% hab = 0.25)
PGR = your growth rate, expressed as a frac
...
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Re: Resource integral hold for IS? 
Wed, 09 August 2017 08:11 

magic9mushroom   Commander  Messages: 1154
Registered: May 2008  

Okay, after spreadsheeting it I've got a fairly good idea of what the solution looks like on greens.
Phase 1: 0% hold (100 colonists on the planet, but overflowing as normal)
Phase 2: 25% hold (i.e. colonists on planet + overflow growth = 25%)
Phase 3: gradually creeping up from 25% to 50%
Phase 4: 100% hold (yes, there's another discontinuity)
Phase 5: gradually creeping up from 100% to 300%, ending at the final 300% hold
Phase 1 only takes place on lowhab planets (155% for the usual 1920% growth), as the formula from my last post implies. High hab also extends phase 3 substantially in both directions, which is somewhat intuitive as this is the phase where planetary growth is highest.
Having factories accelerates the progression through to phase 4, since 300% hold doesn't boost factories and as such 100% hold is prioritised. For factoryless races the holds are surprisingly low  it's well past 200% population available before a f goes to phase 4, and on lowhab planets even the 25% hold might be delayed until there's 100%+ available.
Phase 5 is controlled entirely by growth rate; factory settings and hab are irrelevant, as the planet is already 100% full. Phase 5 starts when:
pop = 2.92 + 0.16/PGR
and of course finishes at:
pop = 2.76 + 0.48/PGR (this being the amount of pop needed to sustain 300% hold)
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