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 Post subject: A Building Question
PostPosted: Thu Aug 21, 2008 6:17 pm 
AA Warrior
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Now that I've got SD combat straightened out, I was wondering about how boosted credit production is calculated.

I know that a planet at 100% produces credits 3 times faster than a planet at 0%. So I imagine this would be an exponential type derivative equation.

dm/dt = c*3^m

where m is money, t is time, and c is a constant (something like colonists*credits produced per colonists per tick).

This seems like the simplest, most elegant way of doing things. When m is 0, dm/dt=c*3^0=c, and when m is 1 (for 100% credits), dm/dt=c*3^1=3*c

So it all looks very nice. I can then use the solution from solving the differential equation to optimize credit production. I just want to ask if this is correct: is this how production works? I could do a little experiment and test it out, but I'm lazy, and that'd be of quesitonable accuracy. :P I think I will do the experiement just to be sure, but it won't be accurate, so I would like a yes or no answer.



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 Post subject: Re: A Building Question
PostPosted: Thu Aug 21, 2008 8:52 pm 
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From the Settings:

Colonists needed to produce 1 Credits each turn: 100
Planet Credit Production Rate: 2.0
Production Multiplier: 5.0

I'm pretty sure the base production is worked out via Colonists/100
Then the production percentage is applied, so for a credit planet that'd be 86-87%
Then the percentage of max credits is taken from the Production multiplier and added to that figure for production percentage.
I think Credit Boost digs are added after that, as a boost of x% of production. But I can't be sure.

There's definitely something I'm missing, because I've been told that the best credit producing planets tend to max out at around tech level 250 or so. By my calculations, since you get a larger max population as you increase tech levels, the population can just keep on going up. More population = more credit production. And if you keep on increasing techs, more max credits = more credits produced around the 90% mark.
But apparently it doesn't work so simply. Spending trillions on one planet doesn't give the same benefit as spreading it across 5. I don't know why that's the case, but I don't particularly like it.


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 Post subject: Re: A Building Question
PostPosted: Fri Aug 22, 2008 10:01 am 
AA Warrior
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Instinct, I can answer your question.

After you keep upgrading past levels like 250, the colonists do continue to increase, but linearly. The max credits increases exponentially. So the ratio of colonists to max credits decreases.

Yes, you will be able to produce more credits at higher percentages simply because the max is higher, but remeber this: the max multiplier you can get is (I thought) 3. Maybe it's 5. Whatever. As you keep upgrading, you are asymptopically approaching that ideal multiplier, but you can't exceed it, so your advantages slope off. This means the only advantage you get that grows steadily is the colonist number, but this, while steady, grows linearly and slowly. So in the end, the amount of money you make per day also increases linearly (even though you accumulate the money exponentially over the day), while the amount of money ON the planet increases exponeitally, proportionally to the price (the multiplier, I've computed, is 140).

The more money on the planet, the more you risk losing. And really, the money is not doing you any good just sitting there as production credits. And it takes a LONG time to accumulate that. Time is money, so while you're waiting, your losing money. If you stop upgrading somewhere between 230 and 260 you're better off. Remember, you DO make more money, but it's not a lot more, so it's not worth the time, effort, and risk of having all that money just sitting there.

You really only need to upgrade to the point that every time you consolidate, you're not dropping the credit percent too low. And so note here that this means that consolidating off a level 235 planet (2T max) three times a day works just as well as consolidating once off a 252 (6T) or so planet a day, since you end up with the same credit percentages after each consolidation. This is excluding the minimal effect of a few more colonists. (I know this from experience) If you don't have the time to do the consolidations and you want to make the same amount of money, you have to put in the time of upgrading your planets more and allowing them to accumulate more base production credits.

The question I have is just to confirm the math I think is used, so I can calculate exactly what level I should ugprade my planets to for optimal produciton without having to waste exorbitant amounts of time.

Back on topic.

Quote:
From the Settings:

Colonists needed to produce 1 Credits each turn: 100
Planet Credit Production Rate: 2.0
Production Multiplier: 5.0

I'm pretty sure the base production is worked out via Colonists/100
Then the production percentage is applied, so for a credit planet that'd be 86-87%
Then the percentage of max credits is taken from the Production multiplier and added to that figure for production percentage.
I think Credit Boost digs are added after that, as a boost of x% of production. But I can't be sure.


The first two things I already covered and are accounted for by the constant multiplier "c" in the equations from the last post. The third line you posted is not clear.

"Then the percentage of max credits is taken from the Production multiplier and added to that figure for production percentage."

You surely don't mean you take the 5 (production multiplier), add say .9 to it (percentage) to get 5.9 as the multiplier. That isn't correct, and probably not what you meant, but it sounds like it. I also figured the thing about the credit boosting digs.

Basically, my question was about the math involved in your third line of explanation, which, I apologize, but you did not satisfactorily answer.



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 Post subject: Re: A Building Question
PostPosted: Sun Aug 24, 2008 8:53 pm 
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Sorry for the confusing wording, that is a really misleading statement.

The three lines are basically saying:
Max production credits C = Colonists /100
Production Percentage P
Percentage of Max Credits M
Production Multiplier = 5
credits produced C

c = CP(M*5)

Credit boosting digs add based on c.

That's the equation I run on, but I haven't tested it since I wasn't confident in it. It doesn't account for "Planet Credit Production Rate: 2.0", which isn't the multiplier either, and I have no idea where it fits into the equation. So I kinda gave up.


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 Post subject: Re: A Building Question
PostPosted: Tue Aug 26, 2008 7:18 pm 
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Wow! Bad man. You gotta be sharper than that. By that, no credits means no production. Wrong. I actually decided to do all the complicated differential equations, so I have a model now, but it's hard to test, since it's all over such a slow time period, and really pretty complicated, again. And it's continuous rather than discrete, which the game is. Whatever... hope it works.



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 Post subject: Re: A Building Question
PostPosted: Wed Aug 27, 2008 12:10 am 
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Oh yeah. Base credit production has to be applied before you can throw on the modifier.
Told you I'm no mathemagician. :lol:

But testing should be relatively easy.
it's not too difficult to capture data, at least. Just keep a window open on the Planet Status screen, printscreen and paste to MS Paint and save that, then repeat every tick. It's a pain because the population changes every time, but at least you can know by how much.
Then just compare the results with your expected answer with the same data inputs in your model.


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 Post subject: Re: A Building Question
PostPosted: Wed Aug 27, 2008 4:03 pm 
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Well I consider the process you just described way too much work ;)

Colonist increases are negligible, since they're just under max.



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 Post subject: Re: A Building Question
PostPosted: Fri Aug 29, 2008 3:04 am 
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You're happy to ignore colonist increases and it's STILL too painful to capture at least 2 consecutive ticks of data? :shock:


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 Post subject: Re: A Building Question
PostPosted: Fri Aug 29, 2008 1:32 pm 
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2 ticks is nowhere near enough info. It'd be over the course of a day or more. Maybe a few days.

And you seem to think this is some sort of contradiction. Ignoring colonist increases (which really is negligible at max colos since I haven't gained over 100k colonists in weeks) is laziness, as is being too lazy to record credit production.

But again, 2 ticks wouldn't be close to enough. The equation I got works on a large scale, telling me how much I can expect to make a day with optimal produciton at different techs and stuff. Since growth is discreet and the equation continuous, it wouldn't be too acurate on a small scale.



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 Post subject: Re: A Building Question
PostPosted: Mon Sep 01, 2008 2:56 am 
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I would have thought you'd be looking for a way to accurately predict how many credits you'd produce based on colonists, credit production percentage, max credits etc on the next tick. You'd be able to use that to work out how many ticks, and thus time, it would take to get to max credits based on the input of max credits, current credits, production percentage and colonists.

Ignoring colonist production within the calculation necessarily makes the calculation inaccurate over the course of time, unless colonist amounts change negligibly over the time period you're calculating for.


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 Post subject: Re: A Building Question
PostPosted: Mon Sep 01, 2008 11:15 am 
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Quote:
I would have thought you'd be looking for a way to accurately predict how many credits you'd produce based on colonists, credit production percentage, max credits etc on the next tick. You'd be able to use that to work out how many ticks, and thus time, it would take to get to max credits based on the input of max credits, current credits, production percentage and colonists.

Ignoring colonist production within the calculation necessarily makes the calculation inaccurate over the course of time, unless colonist amounts change negligibly over the time period you're calculating for.


I'm sorry, but most of your thoughts are misconceptions. First, my model is continuous, not discreet. Since production changes over time with more money, doing things one tick at a time is quite difficult. My model is continuous, not discreet. And as far as colonists, I consider them a constant. You do understand that planets have max colonists, right? Once they get within oh... say 1 million colonists of that max, they're not going to gain anymore really. They'll get a few, but EXTREMELY slowly. And 1 million colonists isn't enough to affect production anyway.

So yes, the change is negligible over the time I'm calculating for.



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 Post subject: Re: A Building Question
PostPosted: Mon Sep 01, 2008 11:31 pm 
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Setting your sights on calculating for max colonists is fine if that's the scope of your equation. It's just not how the code would do it, which is what I've always tried to emulate in my equations.
I think the derivative equation is pretty sound aside from an inability to adapt to colonist changes and dignitaries.


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 Post subject: Re: A Building Question
PostPosted: Tue Sep 02, 2008 5:41 pm 
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Yeah; I've been looking for a way around the code, basically. The game has no way of knowing how many credits will be on my planet in twelve hours, and it doesn't really care, but I want to know, so I have to figure out something that goes beyond the game.

I hope my equations are correct.

Something that's kind of funny is that if the planets didn't stop producing at 100% credits (but the constant remained), after a little while, the credit levels would actually approach infinity in a finite time period.

Here's the solution to the differential equation. I just realized I hadn't posted that.

Assuming that the base for the exponent in the differential equation is 3 (that's what I remember Tarnus saying)

C = m*ln(-m/(ln(3)*(2m/(3*ln(3)))*t-m/ln(3)))/ln(3)

where C is total credits at any given time, m is maximum credits (dependant upon techs, but for our puposes assumed constant), and t is time.

It is important to note our units for t. t=0 is taken to mean when the credit has 0 credits (so if we're starting with credits, our value for t must reflect that, and be nonzero) and t=1 is when the planet maxes in credits.

Obviously, in order to convert this to days, we must know how long it takes the planet to go from 0 credits to max credits. We don't need to observe this directly; it can be calculated with just noting how much we make in one day, and doing some more [tedious] calculations to adjust for nonlinear growth.

Also, note that if we aren't converting t to more normal units (days, hours, or ticks), it will always be a fractional value from 0 to 1.

Well there you go. I used a little ingenuity to figure out how the works better than the dev team probably knows. :P

I hope it's more useful to you than it was for me. I orginally set out to do all this to figure out how much I'd profit by upgrading all my planets 5 techs (raising m in the equation), but by the time I finished all the math, I'd gone ahead and done it anyway. It turned more into a challenge than an applicable formula for me. Maybe sometime I will get around to doing all the calculations and creating a perfect holy-grail type spread sheet for builders and how much they should upgrade their production planets in a given time frame to maximize production, but I haven't gotten around to it yet. lol


Last edited by Valience on Wed Sep 03, 2008 4:27 pm, edited 1 time in total.


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 Post subject: Re: A Building Question
PostPosted: Wed Sep 03, 2008 12:59 am 
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The spreadsheet I was working on (and subsequently abandoned) attempted to project colonists, ore, goods, organics, torps, fighters, energy and credits based on production percentages and current levels. I was hoping to get it accurate to the next tick, and then re-tool it to project from there out to however long.
Using that you could plan ideal production percentages for whatever you liked. It wound up being useful for figuring fighter/torp production percentages to even out the production of both, but that was about it. I didn't have:

Accurate calcs on ore/goods consumption for armor production
Accurate colonist growth calcs and thusly
Accurate credit production calcs

I did make some interesting graphs charting tech level Return on Investments.


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 Post subject: Re: A Building Question
PostPosted: Wed Sep 03, 2008 4:30 pm 
AA Warrior
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Ooops, left out a "/ln(3)" at the end of the equation. :P

Think you could give your spread sheet another shot with colonists=max colonists? All I care about is credits. I'll give that a shot myself, but I'd like to see what you can make of it, coming from a tick-by-tick calculation.

Tech level returns on investment? You mean planets? I've determined that max credits=140*cost of planetary techs. That was pretty easy. If you spend 1T upgrading your planet, it can hold 140T.

I'm going to be playing around with my equation in winplot for now.

Hmm... I'm checking that equation, and it looks like I did something a little wrong. When t=0, c doesn't = 0



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