Math for MOO

[Charis]

I couldn't help myself. Seeing the elegance in the growth curve which peaks in
the middle and slows down for both lowly populated and nearly full planets,
I knew there was a mathematical optimum in there. *NOT* an in-game, blindly use
this number optimum, but an 'all other things equal, if you want to maximize the
empire growth rather than the growth of one planet' estimate of how many to send.

I've made a post for our succession group with more details at:
Optimizing transport size

But here I'll just give the bottom line equation, an interesting growth curve graph, and
an example.

d = (m*P - M*p) / (M+m)

where d is the optimal number to transport, P and M are the current and max population values
for the first planet, and p and m are the current pop and max pop for the colony.

Exmaple: For a homeworld at 57 of 100 and a colony of 2 of 80
transport_optimal = ( 57*80 - 2*100 ) / (80 + 100) = 24.2 colonists.

The reason why sending more is effective is due to the lack of steepness in
the growth curve surrounding that "planet is half full" mark:



I stress again this is just a mathematical optima for empire growth, not a suggestion
that for a given game situation it's the "best choice." That will depend on many factors,
in particular whether you plan to continue with factory production on the homeworld or
if you will be building some ships in the near term. (Second caveat: I'm a total newb! :P )

Charis

[Drasca]

That's basically what I do too.

The sending population beyond halfway point, not the figuring out the math part =)

I wonder if population growth is calculated before or after sending off the colonists. It makes a difference in calculation. Hmm. Anyone know before I go testing?

[Sirian]

A fine analysis. That chart is especially useful. Would make a fine addition to the charts page on my site. (Prod).

- Sirian

[Erick the Red]

I agree with your match, but I believe I have a different way of thinking about the problem that may make it more intuitive.

The growth rate can be written as r = G * p * (1-f) where G is the growth constant, p is the population, and f is the fraction of the total population.

The growth rate per person will be r / p = G * (1-f), and for constant G the maximum empire wide rate will happen when 1-f is the same for all planets. If there were two planets with the same value of f, then shifting population would cause there to be a lower growte rate per person at the planet with more people.

Anyway, the math should be the same, but if you look at it this way it tells you that the optimim would be to keep all your planets at the same fractional population level if they all have the same growth rate. I just go by this general rule of thumb.

[Ozymandous]

I don't have hard facts to back this up but I have seen the econ slider change from 'clean' to 'waste' and the "+1" pop growth change to "+4" when I select to transport colonists but before they actually leave.

It seems like the game treats the colonists as both there and also partially gone or something.

[T_McC]

I believe the effects you are seeing are caused by the game allowing factories to "sit idle". As you move colonists from a developed planet, less of the (already built) factories can be used, and only those that are used generate pollution.

If this were true, when you transfer from a slightly-developed planet (more people than factories) the Eco Slider should go from 'clean' to 'waste', as you'd probably be generating about the same amount of pollution, but have less total BC's allocated to clean-up. [Smaller number of people can still use all the factories, but you have less 'citizen BC']

I've seen the other effect also (same Eco allocation results in Pop +X), but off the top of my head can't figure out what conditions have to exist to see it. Maybe once your citizens can generate more than 1 BC just for being there? If you see this primarily (exclusively) as the Klackons, that's probably the answer.

;-) (I think that smiley is for "Who Farted"?)

[Charis]

I don't think it's just sitting idle. I think the game does try to show you what
the growth rate and waste and RP values will be if the chosen number of colonists leave.
But it's not committed at this point, you can still change the number to go, or tweak
them as Sirian discussed.

In other words, the display and calculatations are projections based on the number
currently 'planning' to go. They're accurate though, and will be the real values used.
Kinda nice actually! If they did NOT have this mechanism, you would be left guessing how
to set the sliders and risk having the system in a waste condition.

Charis

[barron of ideas]

I need to approach this negative thought very carefully, as there is a lot of benefit to more knowledge of how the game works, but at some point, if the game is "solved" there is no play value left, except for the "sid" level players who put artificial restraints on their play (always war, one planet challenge, build no military of a particular type, no fast units, etc).

I suppose I could just not read the game killer threads, but then I miss a lot too. Think about how the palace jump trick and ring placement and the other exploits killed CIV3 until it was patched, and patched, and changed in the process until it is not really the same game in some ways. We don't have the prospect of patches, 1.3 is all the MOO 1 there is ever going to be. Please don't "solve" it for me so I have to play impossible with one hand tied behind my back for there to be any challenge left. Riight now I am happy, with 4 opponents on Average with a medium sized Galaxy, playing the Psilons. I am glad for the stategies and other hints I pick up around here. But don't get so helpful there is no more game left.

If Sirian can still play it after all these years, maybe there is no "final solution", but if there is, please don't look too hard. He can't play Average and won't play the "easy" races because it is no challenge to him. If you want to go there, more power to you, but how much analysis really needs to be done?

And the other possibility is paralysis by analysis. If there is too much "bookkeeping" to make an optimum move, how much playing will get done. I don't really want to solve a mathematical equasion before I decide how many workers to send to a new planet. I suppose if you do, that should be your choice, but then, whouldn't you prefer to read a nice book on elementary complex differential equasions rather than merely play a game.

Its nice to be informed and to be able to play a good game at a high level. At some point along the road, we run the risk of making it too easy so it isn't a challenge to play. Please think about your goals before you publish your findings. I don't know MOO can be "solved", but I don't know it can't be.

[Zed-F]

We have several experienced players here who play on impossible and still find the game fun, and who have not needed to resort to variantism to find challenge. Most impossible games for me now are not a real big challenge, if I get a "good" start, but they can still be fun to play. Moreover, the game will also throw out the odd curve ball where the terrain is challenging or I come up against an aggressive neighbor with a big fleet and a bad attitude before I'm ready to deal with him. Witness Sirian's Kitten Kaboodle game -- if he had not taken the Diplo victory when he had had the chance, he would have been in a spot of trouble. Even if you are not that thrilled with the idea of variantism, Hard and Impossible should still be enough to keep you going once your play improves enough that Average doesn't cut it anymore. As for deliberately holding yourself back so as to preserve the challenge level at Average... I'm afraid I don't understand that at all. Isn't that why there's more than one difficulty level? Maybe that's not what you are trying to say and I'm reading something into your comments that's not there.

As far as micromanagement and "puzzle-solving" goes, I don't rely on mathematical formulae to compute my every move, but I don't just wing it, either. Rather, I rely on good judgement to get the broad strokes right at the strategic level; tactical micromanagement of exactly how many colonists to send where when is less important than understanding general principles. Micromanagement is most valuable at the beginning of the game when you have the least things to worry about, but even then it's not a make-or-break proposition. I think Sirian would interject something here about "puzzle-solving being meaningless at the tactical level because this is a strategic game, and like chess, can't be reduced to a puzzle-solving exercise."

Possibly you're missing what RB is all about, if I haven't misunderstood your comments too badly, but I'll let Charis and Sirian respond to that point since they will do so far more eloquently.

[Charis]

First, thanks for your comments even though they shared a dissenting thought. I was a little suprised, but I see your point and am glad you made the bost, barron. I have two key points to make in response...

- For me, the mathematics lurking underneath the surface of a strategy game are fascinating. When something is cleanly implemented and has a 'simple' underlying structure that lends itself to optimization, the joy of calculus overwhelms me and I must figure it out. This type of analysis is at least equally interesting as the game itself for me. ^_^ Now, to find something out and not report it or to see actions in a SG which are distinctly suboptimal, I just can't do.

- More important, there is a HUGE difference between a game formula and a math formula. A formulaic game is one in which instructions like "build a base, train 7 grunts, research advanced swordplay, attack nearest base, claim victory". It reduces gameplay to a set of instructions, good in any situation, which you blindly follow and do well. From my own play so far and Siriian's lucid articles, I don't think Moo lends itself to formulaic play at all. Rather, as one gets better as a player he develops tactical tools which he pulls out of his strategic toolbox based on the situation. The purpose of my analysis, and sharing it, it to hone ONE of the tools in the toolbox - the "transport colonists to maximize empire growth" tool. If a player falls in love with this tool, he will NOT play the best game and will use it in situations for which it does not apply. He will have a nice hammer and all the world will look like a nail!

Again, I love to hone tactical tools - it's one of the the values I bring to a game or a group. What I learn from others is *strategy* - when to use a given tool. Maximize homeworld population growth, maximize homeworld factories, max empire growth, max growth curve through terraforming +20, minimize time to a base on every planet - each one of these is a different strategic objective which will require a different tactic. The greatness of the game comes from the richness of the strategic decisions and the fact that you must adapt to the situation and circumstances and your own play style to be able to choose what to do. No amount of math can undermine or replace this.

I try pretty hard to have disclaimers in posts such as this one, saying what it's good for AND what it's not, and reminding folks not to use it blindly. (If they do, it will be to their detriment, it will not crack the game and make it soo easy).

Also, I can't play a game where I don't *deeply* understand what's going on. That's why MOO3 was such an abject abysmal failure for me. It's why I go nuts in Civ3 trying to understand corruption, combat and statistics, and love micromanaging economy and production. If I'm going to stick with MOO (mind you, I'm still in a 'trial phase' ;-) it will only be if the mechanics are both understandable from a quantitative viewpoint and fun)

For example, I'm doing some "Research" research :P There's a lot of conflicting advice on the net and a at least a partial confusion in the SG on the 'specifics' of how changing the sliders will affect things. If it works out as I hope, I'll have some very useful guidelines and explanations that will sharpen that often dull tool. But it won't break anything, because by far the biggest questions will remain: i) WHAT do I want to research and for what strategic purpose, and ii) tactically, what is it I want to do - minimize total cost, minimize expected time to learn a tech, maximize "interest" from ongoing projects, or minimize how much I have to tweak. The math of the analysis will NOT answer any of those secondary questions at all, but they WILL give some specific recommendations for carrying out each of those tactics.

Anyway, I hope that explains my reasons better, and I hope allays any fears that this type analysis could ever harm the game play itself.
Charis