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Overall AR economy formula Mon, 02 July 2007 21:04 Go to next message
Kotk

 
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Registered: May 2003
Inspired by Divisor settings thread i decided to publish a formula that i have used with AR. So (reasonably simplified by me) overall AR economy formula is:

AR Economy = Average Planet Value * sqrt ( Overall Population * Planet Count * Energy Tech / Divisor )

Like you see Simplified it is to great extent! Usually actual economy of well-pop-managed real AR race is bit more than the formula gives and badly-pop-managed AR does worse than it gives. Also I do not count reds or yellows in Average Planet Value or Planet Count. But generally it is the one i have in mind when designing AR race. Also it is the one with what i detect how well my pop is managed, if i dont beat it well then i have managed badly. Nod

For giving one practical example i open some random turn file:
1/10 AR at 40 planets of average value 80% with 86 000 000 pop, energy tech 24.
Should give:
0.8 * sqrt (86000000 * 40 * 24 / 10 ) = 72690
Research dialog gives annual res from all planets:
73763
So i did OK in that game but not overly good, probably was confident about my victory already. Now as homework, studs, open up your AR files and verify my formula. Very Happy

Lets now look at detail what that formula gives:

Raising that Average Planet Value quickly is most important since being outside sqrt. Unfortunatelly it maxes up around 80% (without reds) with 1-immune one day and no much to do about it. Wink Experiments with more immunities and TT are proven that these are bit too expensive for their up to 25% effect (100/80 = 125%).

Raising Energy Tech prematurely and by significant margin is also quite hard since it goes more expensive by Fibonazzi numbers while sqrt bites the effect into less and less. It is important to get energy up from 1 fastly. Energy is maxed at 26 one day and nothing to do. Wink

Factors limiting raising that Overall Population are (surprize) Planet Count, Average Planet Value, Growth Rate and Construction Tech. Growth Rate around 15% seems to be enough to grow LOTs of pop in reasonable time frame. Construction Tech 1
...

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Re: Overall AR economy formula Tue, 03 July 2007 01:52 Go to previous messageGo to next message
Dogthinkers is currently offline Dogthinkers

 
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Yeah... I agree that Planet count and quality feel like the biggest 'drivers' of an AR economy, more so than population or technology.

However, if my resources were above the formula you have given, I would consider my population management to have been *poor* not good. I usually want to be below that value.

Why?

If I'm beating the formula then it follows that I have more population on the high-hab worlds than the low hab worlds... This is sub-optimum for growth and, depending on the phase of the game, often sub-optimum for the resource integral.

If I want to maximise my population growth (and thus my resources 10, 20, 50 turns from now) then I should be doing the reverse.

It's a tricky balance, as always - more resources in the short term, versus more resources in the mid to long term.

In very early game, I probably want resources to pay for my expansion. In early to mid game I probably want to maximise population growth unless I have a critical need for resources. In late game I probably want to maximise resources.

With regards to dropping divisor to 1/9. That is certainly nice... It gives 5.4% more resources. More to the point, it gives thm right from 2400. If by spending the same points into hab you can improve the average hab by ~5% then that would be a comparable investment (better in the long term due to higher growth as well as the resources, but gives a slower payoff!) The times when one will be better than the other, will depend on the hab you've managed to buy already, of course.


[Updated on: Tue, 03 July 2007 02:00]

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Re: Overall AR economy formula Tue, 03 July 2007 04:23 Go to previous messageGo to next message
Kotk

 
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Dogthinkers wrote on Tue, 03 July 2007 08:52

However, if my resources were above the formula you have given, I would consider my population management to have been *poor* not good. I usually want to be below that value.

Nay. If your resources are below of what the formula suggests then you have either overmanaged or undermanaged your population. In both cases it is bad. Nod
This formula gives resources below what you never want to be. It is the bottom limit. If you have bested it does not mean you managed pop in a ultimate way, just that you did not manage it too poorly. Nod
Quote:

If I'm beating the formula then it follows that I have more population on the high-hab worlds than the low hab worlds... This is sub-optimum for growth and, depending on the phase of the game, often sub-optimum for the resource integral.

The formula gives resources what you get if you divide all AR pop evenly on all its planets. It equals to maximum possible to squeeze out of AR race only on case of 3 immune. If you ever achieve such management level then going further is overmanaged and never correct to do. If you manage pop correctly, then in all stages of a game you have more resources than that number suggests.

With other points you gave i fully agree, just that you misunderstood the nature of the very formula. Wink


[Updated on: Tue, 03 July 2007 04:52]

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Re: Overall AR economy formula Wed, 04 July 2007 18:16 Go to previous messageGo to next message
Dogthinkers is currently offline Dogthinkers

 
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Not at all... I don't think I misunderstood anything... I'm very familiar with that formula, it's not something new to me.

Maximising resources and maximising growth are mutually exclusive for AR after average 25% max capacity is reached.

This logic still stands:
Quote:

If I'm beating the formula then it follows that I have more population on the high-hab worlds than the low hab worlds... This is sub-optimum for growth and, depending on the phase of the game, often sub-optimum for the resource integral.


The only case I can think of where it wouldn't be true, is where I didn't have enough pop to pass 25% capacity across the empire.

The formula assumes a dead even spread of population across the worlds. To go above it, there simply *has* to be an imbalance of population in favour of the higher hab worlds. If this is the case and if capacity is at 25% or above, then population growth is being sacrificed to get these extra resources.


[Updated on: Wed, 04 July 2007 18:22]

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Re: Overall AR economy formula Wed, 04 July 2007 19:10 Go to previous messageGo to next message
Kotk

 
Commander

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Dogthinkers wrote on Thu, 05 July 2007 01:16

The formula assumes a dead even spread of population across the worlds. To go above it, there simply *has* to be an imbalance of population in favour of the higher hab worlds. If this is the case and if capacity is at 25% or above, then population growth is being sacrificed to get these extra resources.

Oh there is the disagreement. I believe that once you are in planet filling stage of the game then with AR:
Deal Filling better hab planets full first is best strategy.
Deal Filling low hab planets (or even the reds) full first is worst strategy.
Deal Spreading pop even is middle strategy. Nod
Seems that you suggest the opposite. Rolling Eyes

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Re: Overall AR economy formula Wed, 04 July 2007 20:54 Go to previous messageGo to next message
Dogthinkers is currently offline Dogthinkers

 
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I suggest it (best strategy) varies based on the stage of the game and on the immediate situation.

Stalling growth by filling the breeders first, is not always wise, even though it does give more resources in the short term. It optimises resources for the current year, rather than optimising the integral over x years. So it is false to present that it is 'best strategy' - that would imply that it is always the ideal thing to do.

The formula merely shows the middle line - what you would have if pop is evenly spread.

No need for roll eyes smiley...


[Updated on: Wed, 04 July 2007 21:28]

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Re: Overall AR economy formula Wed, 04 July 2007 22:10 Go to previous messageGo to next message
Kotk

 
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Dogthinkers wrote on Thu, 05 July 2007 03:54

It optimises resources for the current year, rather than optimising the integral over x years. So it is false to present that it is 'best strategy' - that would imply that it is always the ideal thing to do.

Yes, but thats why i suggest 'best strategies' because i am certain that these are ideal things to do. Very Happy Studying the integrals shows that AR is way different from other PRTs. It is resource integral that matters with them not the pop integral.

Holding planets at 33% and filling one after one starting from highs gives better integral.
Holding planets at 33% and filling one after one starting from lows gives worse integral.

Other holds like 50% or 60% give similar results.
Laughing

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Re: Overall AR economy formula Thu, 05 July 2007 00:22 Go to previous messageGo to next message
Dogthinkers is currently offline Dogthinkers

 
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But it's not ideal for all cases. The game is just not that simple. Having a higher population makes you more able to handle losses due to enemy action, and to be able to exploit newly gained worlds. You also need population to be able to exploit red worlds. If you fill your breeders, where will the population come from to fill those needs? This is why I choose to play a little bit below the 'simple' resource curve - sacrificing ~1-2% of (current) resources to gain nice population reserves, seems a worthwhile sacrifice to me. As always, it depends on the current in-game situation. Models and theory help to prepare us, but once the game starts... Kinda like the time as -f IS I dropped all my half-made orgies onto my planets in the 40's, sending my population growth negative, so I could (successfully) resist a rather nasty -f CA who had just eaten my homeworld.

Incidentally, when I looked at a fixed pool of planets, all my optimisation models told me I should let my planets grow freely, once all were over 25%. This was looking at a variety of durations between 20 and 50 years and despite a very cheap and arbitary single year travel time between worlds. I was a little bit surprised to see this result, at the time, as it's so unlike the other races Laughing

As I've mentioned, in the very early game I emphasise short term resources, to ensure I can take and hold the territory I will need. In the early to mid game I emphasise population growth to ensure I will *remain* competitive. In mid to late game, I will emphasise resources, to secure victory. I really struggle to see how this is a 'wrong' strategy.

I should add, I'm not talking about extremes here. I want to keep the breeder worlds at 50% or less (not so low as 25%). Below the breeders, I'll still fill top down, just as you suggest - The 75% worlds will get filled before the 50% worlds do - it's just that the 90%+ worlds won't get filled for a long time - they're too important a source of population to let them go above 50% for long.


In 'The End', my popul
...



[Updated on: Thu, 05 July 2007 00:37]

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Re: Overall AR economy formula Thu, 05 July 2007 06:38 Go to previous messageGo to next message
Kotk

 
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Dogthinkers wrote on Thu, 05 July 2007 07:22

If you fill your breeders, where will the population come from to fill those needs?

When I reach growding with AR then i breed from low value planets. Simple example with 13 planets:

100%, 100%, 97%, 95%, 90%, 88%, 87%, 86%, 81%, 72%, 63%, 46%, 35%

All are filled to 50%.
You suggest to breed from 3 best worlds and fill the rest.
I suggest to breed from 5 low worlds and fill the rest.
When we each reach the set goal then overall resources and yearly pop outputs of both results are same. Verify please. Wink
So our goals are same ... so question is whose road is simpler? Surprised

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Re: Overall AR economy formula Thu, 05 July 2007 11:22 Go to previous messageGo to next message
joseph is currently offline joseph

 
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You goals and end point are the same.
However the route you take to get there is different.

Dogthinkers takes the low road (low resources).
and you take the high road (high resources).
Dogthinkers will be in pop land before you.

What will happen is you will get 2 curves (both heading up) for resources. And also 2 curves heading up for pop.

Dealing with the pop curve first (because its simpler) Dogthinkers will be a bit steeper and will reach max pop first (probably a number of years before yours does).

With the resource curve yours will rise faster to begin with (while filling good worlds and DT fills poor worlds) at the middle they will be raising at about the same rate (both filling average worlds)
at the end yours will rise slowly while DTs rises quickly (while filling bad worlds and DT fills good worlds).
If ammount of pop was not included then yours would be better (at all points in time) both for total resources and resources per turn.

What Dogthinkers is hoping is that the increase in pop of his method over yours will produce more resources due to more pop
and at some point the extra resources from pop will be larger than the loss of resources due to living in lower hab worlds.

This point will come.

The question is if the point comes soon enough that the later years where he has more resources per turn are sufficient to give him more total resources over the whole period.

On top of this you also have to factor in the idea that early resources are worth more than late resources.



Joseph
"Can burn the land and boil the sea. You cant take the Stars from me"

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Re: Overall AR economy formula Thu, 05 July 2007 19:16 Go to previous messageGo to next message
Dogthinkers is currently offline Dogthinkers

 
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Yes... My point is that my population total will be higher. I wonder what that formula says about races that have more population. Cool

When I decide that we are entering into the late game, or just that I urgently need to capitalise on my potential resources, I can switch methods and start maximising resources over growth - no need to wait forever. The race will have more population to work with than it otherwise would have at that point. The key is not to wait too long... To pick the right points to shift gears.

It's all about picking the approach that is most appropriate for the current state of the game.


[Updated on: Thu, 05 July 2007 19:18]

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Re: Overall AR economy formula Fri, 06 July 2007 12:08 Go to previous messageGo to next message
Kotk

 
Commander

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Registered: May 2003
OK, i have to agree ... yes my suggested strategy will win resource integral of any other strategy. Still it is maximum 4% and as long term average only about 2.5% better than Dogthinker strategy. Hypotetical guy however who just collects pop into freighters has got about 30% less resources than Dogthinker after 30 years period.

There may be cases when more pop overall pays it back. Dogthinker strategy has overall pop about 10% bigger than mine after 30 year period, The guy who collected into freighters may even have 70% bigger pop under hand at that moment (so he can practically fully pop another territory). So ... i can imagine cases when one or other is superior to my suggested strategy. Nod

There may be other hypotetical guy who collects onto reds. While that strategy kills about 1.5% of his collection per year so he is ~23% "poorer" than freighter collector after 30 years his resource integral is 15% worse than Dogthinker (so beats freighter guy). Also he does not need insane amounts of freighters. Smile

Still ... i usually take the resources. Only thing that would make me to avoid resources is an ally who is unhappy about my resources. Laughing I usually avoid such allies.

[edit: sorry miscalculated might of hypotethical guys Very Happy]


[Updated on: Fri, 06 July 2007 13:24]

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Re: Overall AR economy formula Thu, 08 April 2010 22:07 Go to previous message
Marduk is currently offline Marduk

 
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I ran through a few numbers and I think the best balance is to weight populations proportionally to the hab value (assuming the same orbitals, at least). So if you have 500k pop to split between four systems at 100%, 75%, 50% and 25%, I would suggest putting 200k at the 100%, 150k at the 75%, 100k at the 50% and 50k at the 25%. (500k pop/250% total hab = 2k pop/% hab at a system.) Resource production is not that far off from the maximum possible and pop growth remains good.

Having different orbitals at different systems only affects this in terms of crowding affecting growth and smaller population caps possibly affecting resource production. If crowding is becoming a problem then it is time to upgrade the orbital; if crowding is a problem and the orbital is a death star, it's not really a problem. Regarding where to fill first when filling is required, I'm inclined to fill the high value systems first. Their production is better and by the time filling is an issue managing pop growth should not be as critical.

Let's see... say you have a 100% system and two 50% systems, all with ultrastations, total pop one million. For simpler example math you have chosen a 10% PGR, have an En/10 coefficient and are at energy 10. I would advocate distributing the population so:

100% - 500k pop, 707 resources, 71 mines and 50k pop/year
(2x) 50% - 250k pop, 250 resources, 50 mines and 12.5k pop/year
Total 1M pop, 1207 resources, 171 mines, 75k pop/year.

If you split the pop up at 333k per system (334k at the 100%), your resources will be 1154, you'll have 174 mines, and you will breed 66.7k pop/year.

Hmm, now I'm noticing something about squares - it looks like the optimal distribution would have one-quarter the population at a world with half the hab value... let's see:

100% - 668k pop, 817 resources, 81 mines and 52.5k pop/year
(2x) 50% - 166k pop, 203 resources, 41 mines and 16.6k pop/year - roughly one quarter of the pop at the 100% world
Total 1M pop, 1223 resources, 163 mines, breeding 85.7k pop
...




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