[6.2] Optimizing a Q10 Planet...not what you think.

Ok some additional details for the math heads:

1) I put in a .001 discount rate on cumulative research. This means that research gained on Turn 75 is worth about 92% of research gained on Turn 1. This is the recognition that research early is better than research late.

2) Joe helped me recognize that the approval function has a ceiling component. However, in my work the values from the XML did not match what I was seeing in the tooltips or on the planets. What I did was I charted the data points and created a cubic trendline with over 99% R2 confidence. I found the results of this more closely aligned with what I saw in game (though not perfectly either).

3) I quasi brute forced these numbers. Basically I set up excel to run all of the numbers each turn. When it hit a point that a new building was built, I manually entered the building from the build order (because all of these buildings have the same cost), and adjusted the adjacency depending on the position chosen. I did this for each building built, so 10 buildings with each order (was actually faster than it sounds once I got the hang of it).

You know you can move population via transports (or colony ships) to fill up the population to max. Currently I'm using my poor planets as people farms and pushing them to my production planets. It's making 

Interesting about the factories. Think I am still stuck in GalCiv II Eco with that.

Out of curiosity, did you account in any way for approval effects? I'm asking because if you assume a base 3 morale, 5 population, and +5 production for a colony and normalize things to a colony with 50% approval (+0% production due to approval), the base production accounting for approval effects is actually reduced by adding a farm. A colony with 5 maximum population, 3 morale, +5 production has a normalized maximum production of 1.025, a colony with 7 maximum population, 3 morale, +5 production has 0.982 normalized maximum production, a colony with 5 maximum population, 5 morale, +5 production has a normalized maximum production of 1.25, a colony with 7 population, 5 morale, +5 production has a  normalized maximum production of 1.215, and a colony with 7 maximum population, 7 morale, +5 production has a normalized maximum production of 1.433. If all output multipliers come from planetary improvements and we're dealing with a class 10 planet with +2 maximum population per farm, +2 morale per morale structure, and no effects from anything that isn't a farm, morale structure, or output boosting structure built on the planet, then the configuration with 5 maximum population and 5 morale will be superior to the configuration with 7 population and 7 morale as long as the output bonus per output boosting structure is at least 13.1%, and it'll always be superior to the other configurations (the only one which has a chance of surpassing it is the 5 population 3 morale configuration, and in the absence of non-structure bonuses, you'd require an average "bonus" of -29% per structure for that configuration to come out ahead on a class 10 planet).

Joe,

I did. What I did was assume a base 2.4 morale to start (assumed some large empire penalty but not a lot. Than as the planet grows each turn I adjusted the approval accordingly. Theoretically the planet would gain approval from other effects and lose it through even more effects, I did not take those into account.

I attempted a farm by itself, a farm with an entertainment network, a hospital by itself, and a farm with a hospital. All of these configurations were inferior to the one with a single entertainment network over 75 turns. The closest one was a single factory.

What I will try next is starting with much lower morale, and see if 2 entertainment networks become optimal (aka is maximizing approval that strong of a contender).

One thing I did not take into account was a research project, which you have indicated in another post provides a slight advantage with a 1% manufacturing slider than pure 100%. I will try to find that equation and add it in.

You can check this more easily than by playing with a spreadsheet to figure out the total output over 75 turns. If A1 is the approval modifier in case 1, b1 is the output multiplier from non-structure sources, and N1 is the number of tiles available for output multiplier structures in case 1, and A2, b2, and N2 are the corresponding values for case 2, then the break-even bonus per tile is

B = (A1*(1 + b1) - A2*(1 + b2)) / (A2*N2 - A1*N1)

in order for case 2 to offer the same output as case 1. If A2*N2 > A1*N1, then for an average bonus per tile of b > B, case 1 will be worse than case 2, while if A1*N1 > A2*N2 with an average bonus per tile of b > B case 2 will be worse than case 1.

If we assume that b1 = b2, then the average per-structure bonus for case 1 to be better than case 2 has to be -100%*(1 + b1) or worse if case 1 has 0% approval and case 2 has 50% approval. If case 1 has 50% approval and case 2 has 100% approval, than case 2 is better than case 1 for an average tile bonus of 100%*(1 + b1) or less.

If you sacrifice (1 - x)*100% of your production to generate manufacturing points to get a bonus of B from a project, and you apply the other x*100% of your world's production to the desired output type, then you see a net benefit so long as the total bonus to the desired output type is less than

b = (x*(1 + B ) - 1) / (1 - x)

where B is the expected bonus from the project, x is the fraction of production dedicated to output of the type corresponding to the project, and b is the maximum bonus output to the desired output type for which using the project is not harmful. B can be computed as

B = 0.05*ceiling(s*(1 - x)*(1 + m)*P / 10)

where s is the fraction of manufacturing going to social projects, m is the planet's bonus to manufacturing, P is the planet's base production, and B and x are as defined above. A first guess at the optimal value of x is

x = min(1, 0.5 + 100*(1 + b ) / (s*P + s*P*m))

where b is the planet's total bonus to the desired output type, P is the planet's base production, m is the planet's bonus to manufacturing, s is the fraction of manufacturing dedicated to social production, and x is the fraction of the planet's output dedicated to the desired output type. This is the optimal value of x under the assumption that B(x) drops the ceiling function and is instead 0.005*s*(1 - x)*(1 + m)*P; because B(x) really has a ceiling function in it, this isn't actually the optimal value of x, but it should get you into the ballpark. Remember, though, that because there's a ceiling function involved in B(x), you can get a much better bonus from the project than is assumed in the equation for the optimal value of x.

I realize my math fu is not what it used to be, but I don't see any time components in there. As approval effects not just productivity but growth, its relationship to total output is not linear.

Effectively I am not trying to determine what configuration is producing the most research at 75 turns, I am determining the configuration that has cumulatively produced the most research over 75 turns. I don't see how this simple equation would account for that, I believe some type of integral function would be required.

True, but the point of that test is to check maximum output to see if the lower approval world actually has a chance of producing more over time. A Class 10 planet with 0% approval and 9 tiles spent on production buildings cannot possibly produce more research over time than a Class 10 planet with 50% approval and 7 tiles to spend on production buildings if both planets only have output modifiers from on-planet improvements or have the same non-improvement non-approval output modifiers because its maximum output is lower, despite having more output buildings.

You don't need to check the time values if one case has both a slower build up and a lower maximum output. It simply cannot catch up, so there are no conditions under which it'll be the superior choice. No need to check the time dependencies, but if you want to, then go ahead.

Also, the verb is "affect;" "effect" is a noun.

Which is all well and good, except that your numbers are highly dependent on initial conditions. Starting at 3 population is probably going to give a much different picture than starting at 0.5 population, and starting at 5 population will probably paint a different picture than either (for starters, no growth dependency here unless you have a local or global food bonus of some sort). It makes a big difference if your empire's economy is sufficiently strong to just rush every improvement on the planet, because that means that during the infrastructure building phase you can set all production to research. It makes a big difference if you're expecting the game to go on for another 100 turns or another 1000 turns (and this can go either way, depending on when you run out of technologies to research).

What I gave tells you who wins in the limit as the number of turns passed goes to infinity, and it also tells you whether or not it's worth checking the short-term picture. Your numbers give you who wins in the short term under an unspecified set of initial conditions.

There are basically four possibilities for each configuration in the short term:

1. Slow build up, high maximum output
2. Slow build up, low maximum output
3. Fast build up, low maximum output
4. Fast build up, high maximum output

These are relative to the other colony configuration in the comparison. Case 2 is obviously inferior to all the other cases; therefore, any configuration which can be marked as being case 2 relative to another configuration can be eliminated from your list of things you need to check when seeking the best configuration. Case 4 is obviously superior to all the other cases, so any time you can identify one of the configurations in a comparison as being case 4 you don't need to run both configurations through the spreadsheet. The possible combinations of cases are 1-2, 1-3, 1-4, 2-3, 2-4, and 3-4, and we don't need to run the spreadsheet to determine the winners of pairings 1-2, 1-4, 2-3, 2-4, and 3-4. Thus, the only time we need to run the spreadsheet to determine the winner is if we have a pairing 1-3; this is the only pairing where one colony can gain an advantage during the build up phase and lose it in the long run.

You know that if you start from the same population and the same morale and only one of the two configurations builds morale structures that the colony that has the morale structures has the faster build up (though how much faster depends on when the morale structures come into play and how much of an effect they have on the output). Therefore, if you can identify the configuration with morale structures as also having the higher maximum output, you don't need to run the spreadsheet, because you know that the configuration with morale structures has a higher steady state output and a faster build up; there's no way that the other configuration can catch up. Should save you quite a bit of work if you're going through and manually filling out the spreadsheet and updating it each time you come to a "building completes" event.

I should point out that the test I gave earlier assumed the same maximum population; if you want to include that, then for case 1 having a production of P1 and case 2 having a production of P2, with A1 and A2 being the approval modifiers, N1 and N2 being the number of tiles used for productions structures, and b1 and b2 being the bonuses to output multiplier not from tile improvements, then the break-even average output bonus per tile is

B = (A1*P1*(1 + b1) - A2*P2*(1 + b2)) / (A2*P2*N2 - A1*P1*N1)

and that if A2*P2*N2 > A1*P1*N1 then for an average output bonus per tile of b > B, case 1 will have a lower maximum output than case 2, while if A2*P2*N2 < A1*P1*N1 then for an average output bonus per tile of b > B, case 1 will have a higher maximum output than case 2. That's half of the picture for the configurations, and you don't even need to know the actual average tile bonuses, just whether or not they're greater than or less than B and whether or not the product of the expected approval modifier, expected base production, and number of available tiles in one case is more or less than in the other case (if you come upon a case where the two products are equal, then the game goes to whichever setup gives the higher unmodified production, assuming that b1 = b2).

I have come to the same conclusion as you... approval is the key to a growing colony (all the time). As long as you have 100 approval you always build one factory first and then whatever structures you think that you need starting with things like a hospital to increase population growth and make sure your approval stays at 100 all the time. You only want more population than your morale can handle on worlds such as super growths planets that you use to move population to other colonies.

If you don't want each planet to become a doctors thesis in logistics you can usually go with the notion that you set aside 40-50% of the space to whatever type the planet are suppose to support, such as research. The rest are dedicated to supporting those structures with population, morale and some industry.

In my last games I have always gone with Interstellar Travel, Xeno Commerce, Supportive Population and then Planetary Improvement.

just curious, did you try entertainment->hospital, then labs? Is seems like growth should be important.

I did, no good:(

Soo... you mean that within a 75 turn period it's not meaningful to build a hospital?

Production is set to 100%  until you built the labs you want on the planet and then you switch to 100% research focus.

I usually start with 100 approval on new colonies...

1. Planet is set to 100% social production.

2. Factory that is rushed (money or colonial trait). A single factory can in the middle of the game easily give about 30 production point on a new planet, just enough to build basic buildings in one turn.

3. Hospital that will immediately provide a growth bonus when built.

4. Three to four labs close to each other.

5. Start producing research by moving the slider to 100% science.

When approval or population start hitting their respective roofs I add the proper buildings so the colony can continue to grow, more labs can be added if there is enough space to allow for meaningful bonuses to apply.

Basically, if you start with 2.5 pop on a Q10 colony and not perfect morale, a hospital is not useful. The growth it provides doesn't pay off compared to the bonus you gain from the entertainment network or a factory...at least over 75 turns.

Ok... yes... that makes sense.

Moral is your first priority, factory second and hospital third... that is how I build my colonies and also why I beeline for approval techs first of all.  

not gonna be bothering with any optimizations like this until the numbers and formulae stay the fuck still for more than a few weeks

While you are right that affect was the correct word to use, both affect and effect can be used as a noun or a verb.

(Sorry, I try not to correct other people's grammar, but if you are going to do it, do it right. )

I can't help but feel it's a bad sign that working out how to build up a planet is this complicated and counterintuitive.

I just wanted to thank you for this thread. I adjusted my improvements strategy and did much better.

I don't know, figuring it out is complicated, but the results seem pretty intuitive to me: If you want a research world, keep your people happy and build research buildings.

Aye, Frogboy is making changes left and right like crazy.

Just the opposite.  It shows that there is lot of interaction and approaches available.  Therefore, intuitive actions work out for intuitive people, and those who need to analyze it down to the smallest point can do that, too.  If it were all obvious and intuitive, it wouldn't be near as much fun to figure out. But nothing forces you to follow the math.  It is just a set of coded observations.  And it is still just one person's analysis, There is likely to be others, possibly many.  Decide for yourself by playing the game and seeing what works for you.  To me, that's the main point of playing a game like this, exploring it and deciding what I think is right.  And being able to have that be different from what other people choose and still be right for me.