FreeOrion

Why did you fail your psychology class, PC?

All I'm saying is: Remember the KISSes you love so much.

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Time flies like the wind, fruit flies like bananas.

Ablaze: Well if you want a good game you are going to HAVE to have some formulas that describe various phenomenon. Everything from Population growth to ship speed to research, ALL will be governed by some formula and someone has to come up with those. Also in the "real" world ALL processes natural and man-made are governed by various formulas, some that look surprisingly similiar to the "s-curve" we have been talking about. So before you are too quick to dismiss this concept of "math" remember, it is important whether you want to deal with it or not. When you get right down to it, all ANY game is, is a collection of numbers and formulas that happen to be portrayed to the player in a favorable and fun way.

Also just a friendly heads-up your post could be construed as trolling which is unprofessional as well as against the forum rules. So be more careful in the future when you reply to the various topics.

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Aquitaine is my Hero....

But wasn't the idea to have a function that would give you "diminishing returns" in both directions? E.g. you could pump in more and more money to get a job done faster but each constant increase would cost you more than the previous or OTOH you could increase the time needed to do things cheaper but each reduction in cost would mean an ever increasing amount of time.

If so, then the S-curve has to be tilted "upwards". Well, you could of course have thought the axis reversed but then we are talking about the same thing.

The actual numbers of whatever function is chosen aren't a problem as any function can be shifted and scaled along either axis. For example the arctan function can be expanded to:



And now you can just assign appropriate values for the constants A-D:

A: Scale along X-axis
B: Shift along X-axis
C: Scale along Y-axis
D: Shift along Y-axis

For example, if you want the function to be zero at neg.inf. and one at pos.inf. then just use A=1, B=0, C=.5, and D=.5. Of course, in the actual game we would shift and scale the func to values meaningful in the game.

And if you want to play at plotting functions go to http://www.quickmath.com and select equations->plot. Try plotting "y=arctan(x)" so that we all have a basic idea of what the function looks like. (A range of x=-10 to x=10 and y=-2 to y=2 is appropriate for the basic arctan func)

tut tut PC, will you ever learn?

Besides, when you get right down to it the most that any game is is a collection of multiplies and adds and mostly movements from one register to another.

If you want to continue this go ahead and PM me.

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Time flies like the wind, fruit flies like bananas.

har har, Very clever ablaze, fortunetly we aren't programming in assembly and therefore don't need to worry about CPU registers and the like, and besides thats STILL math.

Now back to the topic at hand, Pembroke I believe your formula will be fine for anything that has diminishing returns, industry, food production even research. Of course we will have to scale it so that the number along the x-axis accurately represents the number of colonists or industry or something. Those numbers (assuming we use this formula) will be nice to modify by tech etc. You get an efficency tech (reduced dimishing returns) and you simply shift along the x-axis so you can put more people onto industry and get a greater output. Its a pretty simple formula and should suit our purposes nicely.

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Aquitaine is my Hero....

Their is another nice Equation that I think would be good for use to use

Y=(X Cubed) - X

If anyone has a graphing calculator (like I do) you can plug this in see a nice graph that resembles

0000/
0/\/0
/000

For Large negative values of X, Y is negative, for Large positive values of X, Y is also Positive. But close to zero the trend reverses. A small positive X values gives a negative Y return and a small negative X gives a positive Y.

For the Diplomacy function I was thinking of Y is an AI oponents diplomatic adgustment towards you, either adding points (they like you) or subtracting points (they hate you). The X value is based on a comparison of overall strength. Its (Oponent Strength - AI Strength). If I am stronger then the AI then my X value is greater, if I am weaker its negative.

The result of all this is one of 5 generalized states of affairs. 1 - I am vastly more powerfull then the AI and it is submissive towards me (cause they want to avoid my wrath). 2 - I am sligtly more powerfull then the AI and the AI dislikes me, I am not powerfull enough to intimidate them and they see me as a competitor. 3 - I am equal to the AI and it has a nutral stance towards me. 4 - I am sligtly weaker then the AI and they are friendly towards me in the hopes of gaining a submissive, yet usefull Alie. 5 - I am hugly weaker then the AI and it sees me as an easy victom.

I belive SMAC used something like this and as you can see quite a lot of interesting and thoughtfull strategy can come out of a very simple equation (if you consider anything with a Cube in it simple). The AI is generaly a Black Box as far as the player is conserned so we could put any kind of formula we wanted in their and as long as the AI isn't dumb as a bag of drowned Cats no one will mind.

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Fear is the Mind Killer - Frank Herbert -Dune

Economy proposal idea (a consolidation of other ideas I've had so this may sound similar but is different in key respects)

For each of the Four Resources, instead of buildings, the planet has a 'facility level'.

The production of each of the four resources is equal to
Base Value*Race Pick Bonus*Active Facility Level

the Active Facility Level for a resource is the lower value of
Facility Level for that Resource or
Population devoted to that Resource * Max Facility Level/Pop unit

The Facility Level would require PPs to build and maintain, and PPs spent on 'Planetary Development' would be divided up based on which FLs were farthest from their max. (FLs that were beyond their max could be scrapped outright, and if an FLs maintenance wasn't paid, enough of it would be scrapped so that the maintenance could be paid.. scrapping would yield PPs)

Major and Minor Focuses would determine the population distribution..or the target population distribution.

major: +40% minor:+20% Base:10%
Allow Major and Minor Focuses to be the same.

A major or minor focus might be the requirement for some techs to be applied (allowing even more higher facility levels for that resource)

(therefore changing focus would be instant but achieving its effects would take a while as the facilities for the new focus are built)

Money is probably best thought of as mobile production points, unless we have free market mechanisms, which would get complicated.

Production points would go into one of a few areas
1. Consumer goods (increasing/decreasing this level of spending makes people happy/unhappy until they get used to the new level)

2. Planetary Development (building and maintaining Facility Levels, possibly Terraforming)

3. Trade (PPs must be spent to get a return of PPs back)

4. Military/Ship construction + maintenance


Military and and any Non-Local Planetary Development are only built by taxes, but the fraction Not spent on taxes can go to 1, Local 2, or 3. (amount determined by how developed planet is already, etc.)


Actually, something similar to the MOO3 system could work here

Minerals->PPs

PPs->RPs (similar to minerals being used for Industry) making Research Worlds rare things supported by multiple Industry worlds. This would add a 5th category of PP spending, Research (which could be invested in either privately or governmentally)

Spending PPs in any non-Local Manner would be subject to diminishing returns (max optimum Military Expenditure based on Shipyard Capacity, max optimum(or just max) Reseach expenditure based on Research capacity, Max optimum investment from outside based on base Industry value)

You could just rename PPs AUs.. Industry produces money which is then traded or taxed. (actually, the AUs/PPs the government gets from trade should probably be based on tax rates too... the remainder spontaneously redistributed as a bonus to the populations.)

Also two Basic ways to do diminishing returns
1. with an asymptotic max (you'll never get more than this but you can get closer)

2. no limit (which can be more or less severe ie it can be exponential or simply polynomial)

I made the mistake saying the s-curve looks like PC's formula; it looks more like acrtan with rotated axis. Anyway, I think most people got the idea.

I like krikkitone econ plan except for the part that pp -> rp. I think pp should be seperated from research. I really like the idea of how the development of buildings built off taxes instead of pp.

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I like having to build facilities for production. It has happy Moo1 associations.



I think the rules for when things are scrapped may need a closer look. Say if you aren't using that extra factory now, but with population growth you might need it again in a just a couple of turns? Maybe you don't pay maintenance on stuff you aren't using, but the unused facilities gradually dissappear once maintenance debt equals the scrap value?




Would this allow fractional people, or just the closest whole-number approximation? I vote for closest whole number. Or even better, completely meet percentage commitment to primary first, then secondary, then the other's in order of percentage commitment. That way you aren't likely to waste people on little 10% commitments until the planet has decent pop.



This aspect seems elegant.



Agreed, but do we assign any kind of loss in the coversion process to account for increased flexibility? (2 pp lost in taxes = 1 AU in the treasury) Or maybe just say an inherent moral-lowering effect of taxes is enough?




I think we should eventually have some mechanism like this, but it surely won't be in v.2. I think there needs to be something to keep people from just keeping consumer goods at zero and toughing it out. Maybe part of the effect is global average consumer good level? People get really pissed when they see people in Empire B with so much more stuff....



Trade should be in, but not yet. I see this as an area in which to apply a lot of ingenuity to get the effects people want with a relatively simple system.




In your model, everything already costs PPs indirectly (for facility construction and maintenance). I would just make Industry facilities moderate construction, low maintenance, research is high/high, mining high/low and farming low/moderate.

One other thing that could be interesting: diminishing returns for farming and mining facilities. Facilities start out producing whatever the planetary value is, but after a certain number are built (depending on size) the production for each new facility starts to drop until it reaches the minimum efficiency (hydroponics or ultra-poor, as the case may be). If you have reasonably high planetary population caps (that increase with technology or special construction) you can have a situation where you have lots of people, but your food and minerals are really limited by available real-estate.

That's all

Actually, If you do that, then there is no reason to have planetary max populations... since Industry is limited by mineral output, and research by Industry for maintenance, you could just have a planets 'mineral+farming' maxes (which would have to go up with tech)

(of course with 0 migration and an always positive growth rate, you need max populations... but still... Oh well, I've been waiting for an empire game to provide Trantor for a long time, I can wait a bit longer.)




Well I was assuming fractional population units (at least for the purposes of where people worked).

I think I came up with a slightly better idea on the scrapping +switching focuses though. auto scrapping would take place when the total demand of facilities for people, or their maintenance costs were more than was available. Switching focus would, rather than switching population, switch the 'target level' for the facilities (based on current population). Facilities would be built towards their target level, and any facility that was beyond its target level would be the first on the scrap list when scrapping was done. Population would be divided evenly among the facilities based on their need. (so a half developed Farm world, switching to Industry would continue to keep the stable level of farms, and growing level of Industry operational until the demand for people exceeded the population, and then the farms would begin to be scrapped, bit by bit... The same would happen if development money/production..either governmental or private local...was not enough to pay for maintenance)





What I was thinking is
1PP-> 1AU
AU when spent (for example on a world with 100 PP Total at a 25% tax rate)
AU:PP output
25:25
200+25:100+25
400+200+25:100+100+25
800+400+200+25:100+100+100+25

(maybe not a 2x but maybe a 1.5x.. but thats a testable number)

Possibly also a lag (so that boosting spending past the 1st row takes X turns per row (or goes X rows per turn).. ie to account for all the shipping time from the rest of the empire, getting stuff out of storage, etc.)

So both a lag and seriously diminishing returns (although I wouldn't cap it, so you could run a world at 100x its bas production, it would just lead to overflow the AUs it would cost you..actually that probably would be about the area to cap it)



I was thinking about keeping all maintenance + construction costs the same for each type (made my balance calculations easier) but I think that might be better, because then building research capacity is a long term commitment, and if you break that commitment, you lose what you put into it. (plus that would allow some method of building up a farming world, without going heavy industry 1st.)




Well I figured consumer goods would only be something you could control indirectly by means of the tax rate ie, the untaxed* gets split between consumer goods and development... but population's could have a desire for a rise in the CG level which would decrease unrest. (comparative CG levels would be good too. Maybe not global average, but say an Imperial average comparison effect, your people compare their average to the empires that you know about.. increasing or decreasing unrest.)

* When I was first thinking about this I thought it should only be production, but then I thought about those poor worlds that would be farming/mining/research worlds, and then figured the CG level, as well as the amount they Want to spend on building/maintaining local facilities. would be best proportional to the total production (minerals+food+Industry+research..possibly with a *factor for each of the nonIndustry portions).
That would assume they get some consumer goods in trade, and their economic development spending would still be limited to the amount of untaxed production available. (part of the idea here is that you could 'theoretically' run a 0 tax empire and ecoonomic buildings would still be built.. of course there would be no military, no exploration, no colonization, no world to world trade (since I'm figuring the shipping bill for mines and farms comes from the treasury.. although perhaps it could be subtracted from overall production... actually that might be better..It's the same way I'm thinking of doing empire to empire trade, it simply adds a bonus or penalty to all world's pretax production) ok back to the list

no military, exploration or colonization
no terraforming or pollution cleanup
no subsidy of developing worlds

essentially, you would only have to spend tax money/make decisions on semi-worthwhile things (I'm even thinking of a possible freemarket type devplan, where the people get a bit of a say in the focuses of the world... essentially, an autodevplan... totally shut offable of course, but probably with some benefits. (lower unrest, bonus to efficiency... or not). That would allow a player to ignore the economics (mostly, they'd probably have to beef up research in their own dev plans) and just focus on what they wanted to spend the money on.

Actually, I'm hoping planetary population caps can be increased with some type of reasonably expensive building. Let the planetary population cap represent the point where environmental carrying capacity and pollution really start to bite. You can always build more if you really need to, but is it worth it?



That sounds good.



Diminishing returns sounds good. I'm thinking a lag would be too much complexity. Besides, I'm sure we aren't modeling delays in transport of food and minerals. Why treat production differently?

Now that I think about it, there should be some offset here. In your above example, instead of 100 being the factor around which everything doubles, it should be 100+X. The X is there to allow reasonable development of colonies with zero or almost zero base. I'm also wondering if maybe the curve shouldn't go flat at some point. If you're paying 20 times the normal cost of an item, you're essentially bringing everything in anyway.



That would be nice. We might also dream up factors that could affect the proportion of untaxed wealth going to CG.



Something is missing here. If a planet is industry-poor but productive in another area, they won't have any money to build more farms, mines, etc. If they are getting some CG from trade, who builds those CG? On the other hand an industry-heavy world gets its food and minerals for free and also gets all the local CG and PP for development. Maybe if food and minerals are transferred, PP should be transferred in the opposite direction? If you are running a surplus in food or minerals, reward drops proportionally? Who pays for research?

It starts to sound a little complicated, but it seems there are three options:

1. The expansion of resource worlds (Farming and Mining) will be very slow without significant local industry or significant subsidies. Even subsidies would be very expensive if the local industrial base is small.

2. Resource development doesn't require PP, or only the special infrastructure requires PP and these have to be built by heavy subsidies.

3. Resource flows are balanced by PP (or AU) flows. Industrial worlds still tend to be richer but resource-extraction colonies tend to expand in proportion to their efficiencies. Ulta-rich or Gaia planets would be swimming in money due to the great extraction efficiencies. They could also be a great cash-cow for the government due to taxes and tariffs.

One benefit of option 3 is that low-tax economy still develops in a reasonable way. The player doesn't have to continually direct subsides at resource worlds to get the needed stuff built. More complex, but potentially less micro-management. And a better 'feel'.

Actually if the curve went flat at say 20x normal cost it wouldn't need to be 100+X... assuming 0 base, then the 'flat point' is simply straight shipping totally pre-fab stuff in from around the empire. [no assembly required :) !! ]

The delay was meant as a way to penalize large empires (where it would depend on empire sive v. engine speed in some manner..and as for food, minerals, those are something that, in my plan, get distributed evenly around the whole empire according to need, and I can assume some type of 'need anticipation' wheras 'speed building' is a player decision.

But you're right as long as diminishing returns are in, the delay is unnecessary for conversion cost. (it was more for that large empire penalty)



I was primarily thinking 'level of development' (since all wealth would either go to taxes, CG, or local development spending... so a more developed world, as % of population required, would spend more on CG and less on development)



I really like this one, in my initial 'Freighter model' all Resources were put in a Imperial pool where the non-blockaded production/demand ratio was determined, and then the amount that was received was based on the need (so all porlds throughout your empire would get 160% of the food and 130% of the minerals needed for example, and all the excess would go into local reserves)

The same could be done for money... Here's the idea

Each Resource (Research, Industry, Food, Minerals) Generates a certain # of AUs, which are then taxed. Consuming a resource, even to put it into storage, costs the same amount of AUs as it did to produce it. (The untaxed $ goes to pay for all Food and Minerals since they are all consumed either by people, factories, or Reserves the taxed $ go to pay for all Research, so the remaining money is equal to the amount of production globally). The same model can then be used for Industry costs...

CG is proportional to Untaxed AUs-amount consumed-amount Invested
Untaxed AUS-amount paid for food and mineral consumption +Government Spending
v. local Industry is what determines how much local Industry is overdriven.

*I'm thinking of food->minerals and back probably done from one Reserve to another with a decline (X:1 ratio depending on tech where X is Always greater than 1).

This means that food and mineral worlds will almost always have an overdriven Industry. (although food and minerals probably shouldn't be worth as much as Industry with a 1 mineral to 1 Industry ratio... maybe something like Industry, Research=1AU, Food, Minerals=0.25 AUs.. consumption and production costs). and Industry worlds will rarely be overdriven (unless you are upping ship production, and those would be the ones to do it in.)

This is neat since with this model you could open up trade with other empires in food and minerals (some portion of production is evenly distributed among the two, and the more productive empire in production v. consumption, will automatically gain a net total of AUs, because more is untaxed)

I Really like this (perhaps even a portion of Untaxed AU can go to pay for Research under certain governments... probably going automatically to economic research, and being subtracted from CG of course).

Also, if terraforming maintenance costs (in PPs) are included and depend on distance from the original EP, then that means Food worlds will not be well suited to extensively terraform, because they won't have the massive industry to make it easy (always overdriving). That means that food worlds would Always be most viable if they were Originally good habitats.
(that would have a problem with mining/research worlds though...perhaps more techs that increased max population, but only on uninhabitable worlds)


The slow development of Farm/Mine worlds could be counteracted by a lower cost of Those type of Facilities (Research Worlds Should take a long time to grow)..
Also, you Could stipulate that AUs 'spent' to overdrive a world's Industry don't all get the same yield, Local Development gets the first bunch, CG the next, and then Government Spending, that way an unsubsidized world Would continue to grow at about the same rate whether it was an Industry or Mining world, because Local development spending would be at full effectiveness most of the time anyways.

K1: I'm not following your proposal regarding taxed and untaxed money, overdriving, etc. Basically I can't tell when something is meant to be a dash or a minus sign, and the accompanying text is a little unclear.

I'm pretty certain we can come up with an approach along these lines that is clear and understandable.

In regards to taxation, I think he meant everything is converted to AU and untaxed = AU consumed by the empire and taxed means any remaining surplusses.

I rather see instead of food -> AU directly, just say food is always consumed locally first and surpluss goes to empire stockpile at some efficiency rate. Planets that are starving will use the stockpile. Any excess after that gets converted to AU. The other way of getting AU is from excess pp or unwanted rp.

By the way, buildings was passed

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Actually I was figuring on the 'redistribution according to need' of food and minerals, to allow for local stockpiles (to be used in case of blockade) that would be proportional in size to demand (because they would have accumulated from overall imperial surplusses)


As for taxes the idea was, I'll include an example (one planet empire)

1. Resources of various kinds are produced as is the accomanying AUs
100 Minerals (+25 AUs)
100 Industry (+100 AUs)
100 Food (+25 AUs)
100 Research (+100 AUs)

Total 250 AUs


2. Government (you) gets X% of those AUs

assume 60% tax rate
Taxed AUs= 150 AUs
Untaxed AUs=100 AUs


3. Resources (food and Minerals) are redistributed (and all consumed) which is paid for by the untaxed AUs

100 Food (25 AUs) and 100 Minerals (25 AUs) consumed.
minus 50AUs
Taxed=150 AUs
Untaxed=50 AUs

4. Resources consumed by the government (research) have their cost deducted from the Taxed AUs
100 Research consumed by Government minus 50 AUs
Taxed=50AUs
Untaxed=50AUs

{Note: there should be no research, food, or minerals left unconsumed, even if government takes up food or mineral costs for starving worlds or if business buys some research}


5. Untaxed money goes into development, remainder goes into Consumer goods
say 10 AUs to development leaving 40 for consumer goods
so
10 PP for development
40 PP for consumer goods

and the government can buy 50 PPs for whatever it wants on this planet for 50 AUs, (it can spend less and save the money for later, or it can spend more... but if it spend more than 50AUs, all of the planets 100 PPs will be used up and the government will start overdriving industry)