Galaxy Size and Tech Costs

For what's not in 'Top Priority Game Design'. Post your ideas, visions, suggestions for the game, rules, modifications, etc.

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Impaler
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#31 Post by Impaler » Thu Jan 27, 2005 7:50 am

Perhaps the aim should be to calculate the "Expexted Fill time" of the galaxy, aka the point when major expantion into unclaimed space slows/stops and empires are bumping up against each other.

This would be equal to the

T = Log Base B Power P

B = Expected Growth Rate

P = (# of Stars in the Galaxy / # Empires at game start)

This will give us the number of turns to reach Fill up on any given map, and P will be the number of systems each race would be expected to control on average. I am ofcorse assuming all empires start at 1 system, extra systems will throw off the equation.

Durring this early game phase we want tec costs to incresse in a predictable way each game without any modification for Galaxy Size because size has not yet caped anyones growth rate. After T has passed the growth in tec cost slows down to reflect the fact that expantion (other then conquest) has for the most part stoped.

If we use such a system then we should make the player aware of the passage of T time so they realize whats happening (nothing is worse then hidden game mechanics). Some kind of Game event with some fluff explination could be used to inform the player. For example we could say that at T the "Galactic Senate is reformed after a thousand years of Anarchy and this Galactic institution assists and stimulates Research Efforts across the Galaxy" thus changing the underlying equations that control tec costs now that the Mid/Late game is getting underway.

Alternativly a simpler "After X% of Galaxy is settled, trigger Galactic Senate Event" if we want to dispense with the mathematics (probably a better idea anyways as its much simpler to grasp).

Now our job becomes simpler, rather then one single complex equation to describe Tec costs throughout the whole game we need 2 simpler equations, on Early game equation the dose not take Size into account, and a Late game equation which dose. When the switch over occures the new equation should lower tec costs across the board resulting in a plesent "tec flowering" following the switch (accompanied by lots of tec trading as well). This will firmly mark the transition into Mid Game and ominously pre-lude the coming large scale galactic warfare.
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Geoff the Medio
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#32 Post by Geoff the Medio » Thu Jan 27, 2005 10:46 am

Impaler wrote:T = Log Base B Power P
Does that mean:

T = ln(P) / ln(B)

?
Some kind of Game event with some fluff explination could be used to inform the player. For example we could say that at T the "Galactic Senate is reformed after a thousand years of Anarchy and this Galactic institution assists and stimulates Research Efforts across the Galaxy" thus changing the underlying equations that control tec costs now that the Mid/Late game is getting underway.
I'd really like to avoid any sort of "game event" style solution. Ideally the basic game mechanics should resolve the issue automatically. If we have to use events and such, it places unnecessary restrictions on other aspects of the game design and plot, and might make modifications more difficult to get working properly.
...pre-lude the coming large scale galactic warfare.
That there will always be a distinct late-game large scale galactic war, preceeded by peaceful expansion is another assumption we should not build in to the game... or at least that we should not assume we will decide to build in at this time.

Anyway, I maintain that it should be possible to solve this problem by making actual tech costs a function of galaxy size and base tech costs only... ie. no time dependence, and no dependence on the size of empires or percentage occupancy of the galaxy. We just need a function that doesn't increase the cost of low cost techs, and increases more expensive techs to a greater degree with larger galaxies.

IMO it doesn't matter if a function is complicated in this case, as there's nothing the player can do to alter the adjusted costs of techs, so the player doesn't need to know what the function looks like. All that matters to the player is what the cost of the techs is, which is just a number. (If the player wants to alter tech costs in a particular game, s/he would be able to adjust the player-controlled tech speed option during galaxy setup...)

A function might look something like this (to start... needs tweaking):

adjusted:=(base,galsize)->base^(0.5+500/(1000-galsize))

where adjusted is the updated cost of a tech for a specific galaxy and tech, base is the base cost of a tech (eg. 10, 80, 150 or 1000 RP / turn) and galsize is the number of stars in the galaxy (~10 to 500)

Also reasonable looking is skdiw's suggestion:
skdiw wrote:In the number example I gave, the reference is t^1.4. so t^a, where a=1.4. A "large" galaxy may have an inherent code value of b=0.1 so when you do calculation, you go t^(a+b) or t^(1.4+.1) or t^1.5. So a "yo mama" size galaxy might have b=0.2 for example.
where t = base tech cost or tech "level".

(both of these don't have the property that for large base tech costs (it. later techs), the adjusted cost is proportional to galaxy size... though whether that's actually necessary / desirable is debatable...)

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#33 Post by Geoff the Medio » Thu Jan 27, 2005 11:12 am

skdiw wrote:First off, most game ends way before saturation(tail flat end part of S-curve). You can't say that once you conqurer all the land, the saturation begins, because that's when players start teching and really that's when pp sky rockets. I have never played a game where the game saturated. That's why I said a expo or power function will do just fine because we don't need to bother with saturation if we never get there.
This makes a lot of assumptions about how games will play out in order to justify not worrying at all about end game tech cost balance... This is not wise, IMO.

For one thing, FO is supposed to be somewhat different in other games in that you don't build lots of generic buildings at every planet... Instead, you'll have a few really big wonder-like buildings that have big effects, perhaps with some area of effect for production enhancers. This means that you might not have any way to start teching and suddenly generating huge spikes in your planets' productivity... the only way to increase production is by increasing meters, and mostly buildings increase meters, and you have rather limited building options... so FO may be more prone to saturation that other games you're thinking of...
Secondly, the growth nature of expo creates less monotonous games because it creates shifts in the game. In the early game, each empire have access to all the essential techs necessary to get them started because techs are cheap. Mid-game, players have to plan a bit and pick their strategy to victory (whole point of 4X). By late game if the game doesn't end yet, each of the transcendent techs drastically changes the face of the game depending on the branch the player wants to specialize.
This is not a unique feature of expoential growth. Simply having large base costs for late-game powerful techs achieves the same thing.

Re: recursive tech tree:
I fail to see how this suggestion results in the same number of techs being researchs at any time independent of galaxy size...

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#34 Post by LonghornXtreme » Thu Jan 27, 2005 9:11 pm

Some of these ideas just don't make sense to me...

It does make sense that sheer empire size should have some sort of different affect on research. BUT I think that research comes about by infrastructure FOR research instead of sheer empire size... (i.e. look at China vs Japan) BUT having larger amounts of sheer resources and population tends to make implementing that research infrastructure much easier.

What I'm trying to say is that penalizing an empire solely cause it is larger than another is IMHO not the right way to go about messing with RP costs. Once players figure out how the system works they will find the 'most efficient' tech order and expansion limits and then play the game the same way each time.... which will further compound any attempts by the creative team and the programming team to 'predict' the galaxy fill rate.

The game needs to REWARD the empires that can expand to GOOD systems.

I think the way to do this is by having rising RP costs as the tech's become more lucrative. The empires should constantly be having to build technology infrastructure (think Moo2's autolabs, planetary university etc. I'm not saying Moo2 got this totally correct, but I think that's the right way to create 'plateaus' in the tech race) IF they want to increase the rate of their research.

This also limits the larger empires advantage in that if the underdog empires know which systems harbor strong research centers, they can make a strike on one system and retreat, thereby cause the larger empire to take a cut on RP, and have to expend production to rebuild their technology infrastructure... and so on... they also have to worry about mounting a response and now have to worry about an aggressive opponent intent on crippling their own research in an attempt to gain even footedness...

Perhaps we could also add some sort of bonus to research centers that have been around for X (big number) number of turns... I.e. mimicking institutes like harvard or the sorbonne....

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#35 Post by Geoff the Medio » Fri Jan 28, 2005 12:17 am

LonghornXtreme wrote:What I'm trying to say is that penalizing an empire solely cause it is larger than another is IMHO not the right way to go about messing with RP costs.
I concur:
Geoff the Medio wrote:...solve this problem by making actual tech costs a function of galaxy size and base tech costs only... ie. no time dependence, and no dependence on the size of empires or percentage occupancy of the galaxy.
I think the way to do this is by having rising RP costs as the tech's become more lucrative.
Most suggestions in this thread are based around this... the "base cost" of a tech would be higher for later techs, and lower for earlier techs. What I'm hoping to work out is a good adjustment (increase) to the base cost of techs that depends on galaxy size, in order to keep the tech progression rate with respect to turn number consistent between different galaxy sizes.
Perhaps we could also add some sort of bonus to research centers that have been around for X (big number) number of turns... I.e. mimicking institutes like harvard or the sorbonne....
Good idea. The long term best research buildings could start of mediocre, and build slowly over time, whereas better short term ones wouldn't increase, leading to a now vs. later player choice.

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#36 Post by skdiw » Fri Jan 28, 2005 4:49 am

This makes a lot of assumptions about how games will play out in order to justify not worrying at all about end game tech cost balance... This is not wise, IMO.
Hehe. You can ask for other players opinions as well. The growth pattern of just about anything including your favorite 4X strategy games looks like that. In fact, ppl come to these forums and complain about it in one form or another.

I believe most games these days have some sort of point system and a history when you beat the game; Check it out sometimes.
For one thing, FO is supposed to be somewhat different in other games in that you don't build lots of generic buildings at every planet... Instead, you'll have a few really big wonder-like buildings that have big effects, perhaps with some area of effect for production enhancers. This means that you might not have any way to start teching and suddenly generating huge spikes in your planets' productivity... the only way to increase production is by increasing meters, and mostly buildings increase meters, and you have rather limited building options... so FO may be more prone to saturation that other games you're thinking of...
Acutally there are a lot of buildings in FO! They just called "infrastructures" instead. Basically they are buildings in your normal 4X game sense, but they are just auto-build.

FO gonna grow the same--it's the law of nature. I'll bet my soul on it!
This is not a unique feature of expoential growth. Simply having large base costs for late-game powerful techs achieves the same thing.
True, but I rather change 1 number (expo constant) than change 20 numbers depending how many late game theory and refinements are there. Don't know about you, but I'll if I'd go crazy if I have to Beta test or make improvements when there are other variables/numbers to worry about.
I fail to see how this suggestion results in the same number of techs being researchs at any time independent of galaxy size...
It's complicated and I don't want to go through math since that prolly means writing forever. Basically it kills off the stauration region.

Aq don't think it's necessary and I agree with a good tech tree (and you did a nice job with the names and diagrams btw). I just thought it was neat idea, especially for the techer players out there.


If you are really worry about this problem, why don't you try making base tech cost just match your diagram you drew?
:mrgreen:

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#37 Post by Black_Dawn » Sat Jan 29, 2005 6:34 pm

I just wanted to try pitching an HFOG system here one more time:
However the formula, (deduction% = #systems_in_empire) is too simple.
Simple formulas are easily understandable and moddable by fans. I agree with you that your formula is better (sqare root of #systems_in_empire)
Be aware that any scheme for determining HFOG determines base HFOG, and that as the game progresses, the player may research methods for reducing HFOG, or initiate government programs to reduce it. This is not to mention any racial abilities/game events which would reduce HFOG for you empire.

The advantage of HFOG as an RP reducer over other schemes is that it allows an equal playing field early game, and slows down larger empires later on. The reason I say "agile" small empires is a good thing is that it gives players who have been expanding slowly or who have had early setbacks a chance to catch up or even turn the tides in the late game. If large empires have all the advantages (population, production, research), then players who can expand quickly early game can coast to a win.

I don't really care what system you use to determine HFOG (and I like your idea in the other thread :) ) , as long as the end result is equivilent to larger empire = slower production & research. This deals with both the small vs large galaxy issue and the large empire advantage issue. Buy two Orion Guardians, get one free! :D
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#38 Post by Geoff the Medio » Sat Jan 29, 2005 8:21 pm

Black_Dawn wrote:The advantage of HFOG as an RP reducer over other schemes is that it allows an equal playing field early game, and slows down larger empires later on.
Which is fine for a specific HFOG system, but for the reasons given above, it's better to have separate adjustments for HFOG (in general, not just RP), and correction of reserach costs for galaxy size (RP only).
This deals with both the small vs large galaxy issue and the large empire advantage issue.
But it doesn't deal with them both as well as separate adjustments for RP and general HFOG would. Keeping them separate means we can adjust one without messing up the other. They are rather different problems with different (IMO) best solutions, so using one formula for both just doesn't make sense.

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#39 Post by LonghornXtreme » Sun Jan 30, 2005 3:07 am

I don't really care what system you use to determine HFOG (and I like your idea in the other thread Smile ) , as long as the end result is equivilent to larger empire = slower production & research.
That just doesn't make any dam* sense... The larger empire should be able to out produce and out research a smaller government. That's why for smaller empires to jump up they must ally with other empires in order to be relevant.

This whole HFOG idea sounds like some sort of UN-esque system to penalize the successful empire...

The type of game we are playing here is 4X.. exploring and expanding is HALF the GAME. He who dominates in the first half of the game should have an upper hand.

I don't mind the idea of HFOG as a modifiable penalty for other reasons... but slowing down research and production is just stupid if the only qualifier is empire size.

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#40 Post by Geoff the Medio » Sun Jan 30, 2005 7:11 am

LonghornXtreme, see the other thread about HFOG and related ideas, and see if some of the alternatives are more palatable:

viewtopic.php?t=974

I've been pushing a system that's more than just a penalty to resource production, and which is a whole interesting and important part of the game in of itself. A nice preachy and overly theoretical diatribe is this post:

viewtopic.php?p=17591#17591

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#41 Post by Ablaze » Mon Jan 31, 2005 10:50 pm

As far as I can make out, geoff, you're purposing a system in which the cost of a tech increases over time.

I think that any system like that is fundamentally flawed. There are two cases to consider 1) what if you want to allow people to start the game after it is already in progress, and 2) this system does not take into account the problem of competent vs amateur players. A large group of amateur players could progress through the game at a fraction of the speed of experienced players, and find that halfway through the exploration and expansion phase tech prices were already massively inflated.

I've thought about it and the best way I can see to implement such a system would be to assign each tech a tech cost like normal, but then when the game starts recalculate the costs based on some equation like x = x * y / z
where x is the tech cost, y is the number of empires, and z is the target number of empires.

For instance if the target number of empires is 10 and there are actually 6 empires and the tech in question costs 240 research (and the maximum RP per turn that can be spent on this tech is 60) then:

x = 240 * 6/10
=> x = 144RP or rather 60 points for 2 turns and 24 points the last turn.

if there are 12 empires then:
x = 240 * 12/10
=> x = 288RP or 60 for 4 turns and 48 the last turn.

This system has its own set of flaws, however. Like the issue of the last turn in which a non-even amount of technology is spent. Incidentally, this isn’t an issue in the (non-turn based) game I’m making. Despite that, I still like how Impaler’s idea sounds better. I think his idea adds life to the game, while a passive equation would probably leave newbies wondering why technology prices change every game (IOW, make it more confusing for newbies.)
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#42 Post by Geoff the Medio » Tue Feb 01, 2005 12:36 am

Ablaze wrote:As far as I can make out, geoff, you're purposing a system in which the cost of a tech increases over time.
GAHH!! NO! I'm not! I've been quite clear...
Geoff the Medio wrote:Anyway, I maintain that it should be possible to solve this problem by making actual tech costs a function of galaxy size and base tech costs only... ie. no time dependence, and no dependence on the size of empires or percentage occupancy of the galaxy.
Geoff the Medio wrote:I said "grows linearly with galaxy size", not "with time".
Geoff the Medio wrote:...I think we should be able to make up a function in terms of base tech cost and galaxy size and number of empires that does the job without any parameters that depend on the gamestate (turn, empire(s) size). ...
However your first reason for not wanting a turn dependence are rather odd... hardly a "fundamental flaw"
1) what if you want to allow people to start the game after it is already in progress,
I find it unlikely this will be an issue... and if it was, we'd have to give a late-starting player a big tech jump anyway for them to be able to compete. In game this could be explained as having them break off from another empire and retain the knowledge they had before doing so... or some other similar situation. And this is really an issue for the HFOG system to deal with (giving smaller empires a boost to catch up, among other things) and not a correction meant to keep the tech progress rate, from the start of the game, consistent between galaxy sizes.
I've thought about it and the best way I can see to implement such a system would be to assign each tech a tech cost like normal, but then when the game starts recalculate the costs based on some equation like x = x * y / z
where x is the tech cost, y is the number of empires, and z is the target number of empires.
Please read the thread. This doesn't work because at the start of the game, until all of the galaxy is colonized, the RP production doesn't depend on galaxy size. Thus if you started in a huge galaxy with few empires, your techs at the start of the game would be far too expensive.

This formula would be fine for the end-game, when galaxy_size / #empires does give a good estimation of average empire size.

What we want is a function that looks like

xnew = xold * galaxysize / empires

for large xold, but looks like

xnew = xold

for small xold.

If we want to get fancy we can make the formula even more tailored to some theoretical growth curve, like in this post:

viewtopic.php?p=17980#17980

But that's probably rather difficult to do, and assumes we know the growth curve, which we don't really...
Despite that, I still like how Impaler’s idea sounds better. I think his idea adds life to the game, while a passive equation would probably leave newbies wondering why technology prices change every game (IOW, make it more confusing for newbies.)
Impaler's suggestion for events part way through that lower tech costs is fine if that's what you want in a particular game, but,
Geoff the Medio wrote:If we have to use events and such, it places unnecessary restrictions on other aspects of the game design and plot, and might make modifications more difficult to get working properly.
We should have the game mechanics function "correctly" without relying on events. We can add in events as well, such as a mid-game tech flowering if we want, but the game shouldn't depend on there being such a flowering in order to keep everything in synch between games.

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#43 Post by Ablaze » Tue Feb 01, 2005 7:52 am

Geoff the Medio wrote:your first reason for not wanting a turn dependence are rather odd... hardly a "fundamental flaw"
I thought I heard you mention not wanting to limit other aspects of the game. I suppose you are right, though: I’ve never played a 4x game in which this was a large concern. It will be a concern in my game, however, which is why the idea occurred to me.
Geoff the Medio wrote:Please read the thread. This doesn't work because at the start of the game, until all of the galaxy is colonized, the RP production doesn't depend on galaxy size. Thus if you started in a huge galaxy with few empires, your techs at the start of the game would be far too expensive.
I can’t remember the last time I’ve posted without reading the entire thread first. My formula doesn’t actually take into consideration the galaxy size, only the number of empires. Irregardless (hehe.. I love that word.) of that fact, your point still holds. The equation can be complexified using a quadratic, or just by adding a delay to the slope. In that case my equation becomes x(f) + d = (x(i) – d) * y/z, or if x – d < 0 then x(f) = x(i). “d” is the delay and is some constant based on the galaxy size / the number of empires.
Geoff the Medio wrote:
Despite that, I still like how Impaler’s idea sounds better. I think his idea adds life to the game, while a passive equation would probably leave newbies wondering why technology prices change every game (IOW, make it more confusing for newbies.)
Impaler's suggestion for events part way through that lower tech costs is fine if that's what you want in a particular game, but,
Geoff the Medio wrote:If we have to use events and such, it places unnecessary restrictions on other aspects of the game design and plot, and might make modifications more difficult to get working properly.
We should have the game mechanics function "correctly" without relying on events. We can add in events as well, such as a mid-game tech flowering if we want, but the game shouldn't depend on there being such a flowering in order to keep everything in synch between games.
I heard you the first time. However I fail to see how the game functions incorrectly without these events. This is a question of game balance, not of the functionality of the game. Even with none of the systems in this thread in place the game would still function correctly, it would just have a smaller range of galaxy sizes that would be fun to play.

I’m not sure I understand your reasons for not wanting to use events for part of game balance. In fact, I’m sure I don’t. Perhaps you could elaborate?
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#44 Post by Geoff the Medio » Tue Feb 01, 2005 8:57 am

Ablaze wrote:I thought I heard you mention not wanting to limit other aspects of the game.
I want to avoid picking a solution that puts unnecessary limits on other design decisions. This isn't quite the same as worrying about a problem that would have occured anyway, even if we weren't having this discussion. If we can fix some target of opportunity problems, then that's fine, but we shouldn't go out of our way to bend an already complicated formula to cover another situation that's not really that important... (which arguably could be used to shut down this whole thread, I suppose, but IMO keeping tech progress rates consistent is rather important)
My formula doesn’t actually take into consideration the galaxy size, only the number of empires.
I apologize... I didn't read what you wrote carefully.

That said, how do you determine the target number of empires? Presumably this would be a function of the size of the galaxy? If target number isn't independent of galaxy size, I don't see how your suggestion would really fix the problem, as bigger galaxies would still have more RP production than smaller ones, so faster tech progress when full.
Irregardless (hehe.. I love that word.) of that fact, your point still holds. The equation can be complexified using a quadratic, or just by adding a delay to the slope. In that case my equation becomes x(f) + d = (x(i) – d) * y/z, or if x – d < 0 then x(f) = x(i). “d” is the delay and is some constant based on the galaxy size / the number of empires.
The basic idea seems like it might work, but:

I'm a bit confused about your notation... what is meant by x(f) + d on the left hand side? Why is that d there, and why is it on the left, not right right side?

And, I don't like the term "delay"... is this meant to be an actual time dependence? Given both of our dislikes for time dependence, this seems odd...

If it's meant to be a transition tech cost at which the adjustments starts to kick in (making already expensive techs more expensive, but leaving the cheap ones unchanged), then that's ok.
Geoff the Medio wrote:We should have the game mechanics function "correctly" without relying on events. We can add in events as well, such as a mid-game tech flowering if we want, but the game shouldn't depend on there being such a flowering in order to keep everything in synch between games.
I heard you the first time. However I fail to see how the game functions incorrectly without these events. This is a question of game balance, not of the functionality of the game. Even with none of the systems in this thread in place the game would still function correctly, it would just have a smaller range of galaxy sizes that would be fun to play.
Well, that's the thing... I want the game to be balanced and playable at as large a range of galaxy sizes as possible. It will probably be impossible to balance things adequately across all possible galaxy sizes without a system as proposed in this thread. And IMO a completely unbalanced game is not functioning correctly.
I’m not sure I understand your reasons for not wanting to use events for part of game balance. In fact, I’m sure I don’t. Perhaps you could elaborate?
If we use events to balance something unrelated to events, it means that we always have to have those same events in place for the game to be balanced. But what if someone wants to make a mod that doesn't have the same events? Their mod will be unbalanced unless they add equivalent events to it. This is an unnecessary restriction... we would be better, IMO, to balance things within the tech costs automatically, without relying on another game system to do it for us.

Using events as Impaler suggested also means we have to have some particular story or other set of events, and probably make various other design decisions in order to support those events. This means that every game has to have the same essential story, involving a flowering of research at some specific time, or the recreation of the galacitc senate and such and such a time. Why should the story be so limited by external factors unnecessarily? If tech was self-balancing, then it wouldn't be an issue, and the story could be chosen and altered freely, which is a better situation, IMO.

And more so, if we don't impose set events that have to occur as to keep things balanced, we can have a much more varied set of possible events that can occur, in response to a much wider range of possible gamestates. Conversely, if we need to get the gamestate into such a situation where a given event makes sense, we'll have to unnecessarily limit the possible ways the game can play out, so as to ensure the necessary situation arises each time.

Basically, systems should work on their own, in as many cases and ways as possible, without relying on other systems to fix them. Testing, modding, balance, and general freedom to design each subsystem work better this way, IMO. This doesn't mean various subsystems can't interact... It just means that they'll interact when we want them to to make the game more fun, but not when we use one system as a crutch to attempt to fix another.

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#45 Post by Ablaze » Tue Feb 01, 2005 9:00 pm

Geoff the Medio wrote:how do you determine the target number of empires? Presumably this would be a function of the size of the galaxy?
The target # is the number of empires you had in mind for the game when you made all the tech costs. i.e. when you said that lasers cost 240RP and had a max of 60RP/turn you were assuming a 10 empire game. If you were assuming a 5 empire game (and thus z = 5) you might have said that lasers cost 200RP.
Geoff the Medio wrote:If target number isn't independent of galaxy size, I don't see how your suggestion would really fix the problem, as bigger galaxies would still have more RP production than smaller ones, so faster tech progress when full.
Yes, this is true. I hadn't actually intended on creating a working equation. My intent was to create a passable example that I could use to debate a steady equation based system vs a level based system (Impaler’s idea.)

I’m still convinced that no equation can successfully address all the issues. If 15 people join a multiplayer game and then 10 of those people drop out before doing anything this model will break, and no amount of tweaking the equation will fix that. The level based system, however, would work fine.

I don’t think a specific message is important to the level based system. In my mind a message is thrown (freeorion does have a message pump, right?), something like EVENT_GALAXY_WIDE_TECH_ADVANCE and then it’s displayed by whichever mechanism seems appropriate. A traffic light in the tech screen could change from red to yellow to green for all I care. The point is that once this event is thrown technology is actually less expensive then before, for everyone.
Geoff the Medio wrote:I'm a bit confused about your notation... what is meant by x(f) + d on the left hand side? Why is that d there, and why is it on the left, not right side?
I guess that’s programmer’s math. I would just put “return (x + techDelay);” in my pseudocode and call it good. Subtracting d from both sides will bring it up to mathematician’s spec.
Geoff the Medio wrote:And, I don't like the term "delay"... is this meant to be an actual time dependence? Given both of our dislikes for time dependence, this seems odd...
It’s not dependent on time, but I can’t really think of a better word for it.
Time flies like the wind, fruit flies like bananas.

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