Spend GS or save like always?

@Gabriel
No offense taken, I just felt I had to explain why I wrote a mini novel in a mainly maths based discussion :)

As for ruins, I built a scout with US and did some extensive save-load rounds.
Took Tradition, first 40 rounds I took every ruin I saw instantly, managed to get 6, wrote down the turn numbers, reloaded initial autosave.
Next time I picked ruins at the same turns, results were the same, regardless of which ruin I took.
Next reload I took Liberty and from then on they were different.
Next I changed building order, ruins didn't change, same for research.

So it seems your policies influence the results, nothing else of your decisions does.

Also there seems to be a 10 turn interval in variables, I picked none in turns 11-20, and the ones from 20 on were different from when I took one in turn 17. Did this with many turns.

Also, their results seem to be depending on previous finds, rolled 2*culture, didn't get an other culture one until turn 50something, same with gold and map. If you roll 4 good ones first, eg. culture, tech, population, faith, you'll get tons of money, map and camps.
 
@Txurce
I am actually working on a diplomacy expose for G and K. About 80% through it (research wise), and 20% through it (writeup wise).

If you are interested (and much has changed since my initial article) I will post that after I finish up this thread. Probably in a fortnight.

If you by chance want to help a little, I need some info regarding peoples gameplay experiences with the Warmonger penalty.
I have a post in the strategy forums that is more then a little lonely (read completely ignored :) ) and could do with some input.
Testing diplomacy stuff requires a large test bed to make sure your assumptions are sound.
I am trying to confirm my formulaes from peoples gameplay experiences. If you can help, and have the time (it will not take very long) just a couple of notes to make next time you play Civ, I would greatly appreciate it. But noe worries if you do not have time, perfectly understand.

Also thanks for the vote of confidence, :goodjob:

@Nikae

Hmmm very interesting. Sort of confirms my hunch (anecdotally of course) whilst adding a few other factors into the mix. I will look into this at some point in the next few days. Thankyou for your assistance and observations, it is really helpfull and insightfull.

@iffinem
Well you should hear me explain the soccer offside rule, metaphors vs similies vs analogies, australian rules football or the higgs boson. Not enough confused smilies in CFC to cope with the reception :) I will do better to explain it all come D-Day as I am sure the fault lies with me and not your perception. Be thankful you do not have to endure my accent as well.

@All
I actually have a whole heap of articles about the various game mechanics, from basic to more advanced concepts, that I have written, or worked on over the past year or so.
Never really posted any (except the diplomacy one) and a few short ones on the Steam forums.
Some are just references for newbies, ie what buildings are enabled/disabled by city plot(s), civ default start terrain (with explanation for how it works), civ default religion etc etc, as well as others which are more advanced ie how the AI decides to build what it builds, how ther AI decides to pursue a GS, how the AI decide to pursue a cultural policy etc. I never really posted them as some are incomplete, and I really didn't think people would be interested.
I just looked into them for my own interest and or gameplay. Some are handwritten (don't ask why) and I will have to transcribe, others are good to go. Anyway if anyone is interested in some of these concepts then let me know and I will endeavour to create a new thread in the future to address them. I don't really want to clog up the forums with a dozen articles on stuff only I am interested in :) Of course this is all assuming that I can still find them.
 
WORK IN PROGRESS - THIS POST IS INCOMPLETE AND IS BEING UPDATED. PLEASE FORGIVE ANY INCONVENIECE (EXpect it to be incomplete for a few days).

First things first. I am being seconded for th next 48 hours (off site) for work and won't be back till Sunday, so I will not get much time to work on the forumales. That said the RA compounding secton is now complete but I still have to double check eveything. Will post these results when I get back. Apologies for anyone who is awaiting results from me, via PM or this thread, I wish I could provide it all sooner.

In the meantime I should hopefull get the time to outline my method in more detail (for those who asked), and explain each of the factors involved (both complete and yet to be undertaken). I will use this a a bassis for part of the final writeup.

THE PREMISE

The amount of TECH progress (ie Beakers) attained from PLANTING an ACADEMY can be approximated, with minimal error, by calculating the total turns saved upon reaching the BULB DATE that stem from the ACADEMIES beaker contribution. NOTE : This date is set at 8 turns after Research Labs are constructed, and will vary between players.

FOR EXAMPLE : If an ACADEMY planted early saves you 10 turns by the time you reach the BULB DATE, then the net BC of that ACADEMY is equal your current BPT multiplied by 10. Put another way your ACADEMY saved you 10 turns, so you will have 10 more turns of BEAKER production before you reach the same date you would have BULBED had you not PLANTED.

Those of you who are a little mathematically minded will notice that this method is not really comparing absolute beaker contributions. Instead the benfits of BULBING to PLANTING are compared by which gets you further into the tech tree by the same date. That is the metric that will be used for the coparison. How many BEAKERS do I have at the BULB DATE that stem from, directly or indirectly, the ACADEMY vs how many stem from the BULB. This results in a fair, accurate comparison that takes into account that beakers early are generally worth more then beakers late, as their effects COMPOUND over time.

ROUGH NOTES
WILL NEED TO EXPLAIN WHAT I MEAN HERE WITH EXAMPLES. (Need to show how an absolute beaker contribution is not a fair comparison as it doesn't show the RELATIVE worth of BEAKERS as players progress through the trech tree). For example 1000 BEAKERS in the ancient era is worth more, interms of tech tree progress, than 1000 BEAKERS in the MODERN ERA. One will save you dozens more turns then the other as the TECHS are worth LESS in the ancient ERA. Addittionally SCIENCE MILESTONES will be achieved earlier an thus increase the CIVS BPT ealier. ABC can address the science milestones but not the tech cost factor.​




THE PROBLEM
The problem with accurately calculating a single ACADEMIES beaker contribution [BC], stems from the fact that it varies over time.
EXAMPLE 1: An ACADEMIES BC before SCIENTIFIC METHOD is worth 8 Beakers, after that 10 Beakers.
EXAMPLE 2 : An ACADEMEIS BC after a UNIVERSITY is constructed is worth more than before.​
These affecting factors are called SCIENCE MULTIPLIERS and stem from the following sources :
UNIVERSITY, PUBLIC SCHOOL, OBSERVATORY and RESEARCH LABS.
SCIENTIFIC METHOD and ATOMIC THEORY.
RATIONALISM OPENER.





THE VARIABLES
Science Milestone Dates.
Game Speed.
GS Plant Dates.
Total GS Planted (GS Synergize such that 2 GS Plants are worth more than 2* ACADEMY BC, will show this at a later date)
RA Signing Dates
TOTAL RA SIgned (RA' synergize just as GS's, both with GS and with RA's)

POSSIBLE VARIABLES
MAP SIZE (Might be difficult, might not)

RESULTS
Writeup
Spreadsheet
Graphs
Quick Reference (Possibly)

LEFT IT HERE. ITS LATE. PLEASE EXCUSE THE ROUGH NATURE OF THIS POST. WILL WORK ON IT OVER THE N EXT 48-72 HOURS.
 
Keep it up Gabriel :goodjob:

Very interesting so far. I like maths but not as much as you :D
 
Heh, I'm starting to just use a rule of thumb and plant before Scientific Method, and save them after.

I can tell that this is going to make my head hurt, and I'm pretty good at math :)
 
The science from an academy should be compared to the science from the trading post that you could otherwise build on that tile (and note that the trading post may not be the optimal improvement).

On the other hand, academies can also allow you to start on the Apollo Program a bit earlier. That could be critical. By saving all your GS's you could perhaps generate more science in the end, but what if your production can't keep up?
 
Ribannah: I usually settle GPs on tiles that can't be TP'd like Wheat, Bannanas or Iron, something with an above average tile yield that I would normally be barred from building a TP on so that point really is subjective to whether you build it where you would normally TP. Most places I would rather farm than TP anyways to boost my Pop growth. I mean that would be the same as trying to calculate the gain from an Academy vs the Population growth lost from not farming a tile... but its not. That's just making busy work. Sorry if I sounded mean.
 
In cases where another improvement is better than a trading post, the correction should be larger, rather than be ignored.

The best tiles to put an academy (or landmark, or manufactory) are of course tiles that you are going to work anyway, i.e. not the desert or tundra as people sometimes seem to think.
 
The incremental benefits from settling first scientist are hard to work out but will be big. ID guess settle first 3/4 and then keep anymore :)
 
I support this thread greatly. But the simplifications hurt my brain. The random terrain makes calculations like this a pain in the butt. Even if you classify things as a grassland start, plains start, tundra start, ocean start, there are a random number of urban resources like cow or fish at your capital, a random number of riverside tiles, etc. A perfect objective measure of all this is nearly unfathomable to me.

Because Growth, culture, and happiness all directly affect BPT, so there are more milestones than simply universities/public schools/research labs as it relates to science. Population is your main source of BPT and it is terrain and happiness dependent. Just looking at settled GSes, if you settle a GS instead of saven'bulb you hit fertilizer X turns early. That is worth Z science, because you gained Y population from the extra food. Similarly, hitting Colosseum/Theaters/Stadium Θ turns early is worth Φ population due to growth. Here's a more thorough list of breakpoints:

-The turn differential (TD) on when you unlock civil service, Chemistry, Fertilizer for bonus growth and production.
- TD on strategics: animal husbandry, iron working, industrialization, electricity, biology, and atomic theory for bonus production yield, sales, and factories/hydros.
-TD on railroads is worth ∩ production.

-TD on PT (breakpoints at RA completions) and LT wonders (turn count here is bloody important since deity AI seem to beeline PT every darn game)
-TD on National Intelligence Agency is worth φ stolen techs.

-TD on Scientific Theory and atomic theory are each worth (2 BPT * settled scientists * citymodifiers * TD).
-Obviously, the TD on University, Public School, Research Lab.

Many of these things compound as well. An earlier university leads to an earlier public school, which leads to a significantly earlier research lab, which ends up starting the bulbfest say, 4 turns early (arbitrary example).

Some additional considerations:
-The pyramids can be extremely potent for a peaceful game as you can keep up with growth with fewer workers (saving GPT), and hook up new strategics faster and finish railroads quicker (more GPT and fewer turns with the valuable tile in changeover with no improvement, faster railroads is more production). The hammer cost for the wonder itself is quite low. Petra can be insane for similar reasons (just finished a t257 domination victory on deity after finishing the whole tech tree circa 230 because I felt like visiting a few jerks with A-bombs:) and Petra broke the game open for me on an 11 desert hill city.)
-Oracle for a rationalism policy? (rarely an AI skipped wonder on deity, though in my petra/rome game I got lucky and got the oracle SP into rationalism)
-Likewise, culture buildings allow you to complete each rationalism policy Ω turns sooner, and in that discrete time period you gain δ science. I've found that if I prioritize culture as #2 behind science buildings I do better, though I never go production focus for them. Totally experiential though, I have no hard data to back this up.
 
When you plant an academy, you will lose 2 :c5production: or 2 :c5food: in the capital because you don't work a farm or a mine.
 
Uh, you guys make it sound so confusing. It does require some math, but I think you are overcomplicating things. Maddjinn does it properly and I use the same method.

The only thing that research agreements and bulbs care about is 8 TURN AVERAGE TOTAL OF SCIENCE PER TURN, or the average between Tx and Tx+8 of the listed blue number in top left corner of your UI. Nothing else matters for this calculation.

I'm on vacation so I don't have access to tech costs, but to be able to calculate how effective bulbs or RAs are you need to calculate the inflation rate of techs, by era. It might be 50, 100, 150% I'm. It sure. It's a lot, in any case.

Thus, to keep the tech pace the same (X turns for tech), you need to up your listed BPT by the inflation requirements.

The RAs and bulbs shave off turns not from the total turns you need to finish the tech tree, but from the number of turns you need to get to the next inflation point. Thats the main difference. It doesn't matter that much if you had 16 RAs in the early game if you hit a brickwall at prohibitive tech costs in industrial or later.

To truly quicken the tech pace you need both BPT that can keep up with the inflation AND Bulbs/RAs.

****

Academies are not a tech booster for research agreements. It's wrong to look at them as such. They are boosters for BPT. And if you look at them from this perspective, you'll realize that calculations become much easier.

It is also wrong to compare academies to jungles, universities, research labs or specialists. There are two reasons for this:
First, Academies are a focused science yield tile, meaning they always benefit from National College. it is foolish to build them in any other spot. What this means is that their yield is 50%, 83%, 100% or 200% higher than their listed beaker value. Academies should always be the first science generators that benefit from science multipliers. If you deny yourself a rush-bought university and if you already have an Academy, you lost 4 beakers per turn right there.

Second, Academies are not multipliers like University. They provide base science like population, libraries, public schools do. The larger the empire, the less effective Academies become.

***

The logic behind "bulb or academy" thus becomes quite simple.
1. Take your current BPT, count the number of turns you need to reach the next inflation level at current BPT. (to do this shift-select all techs in the current era, add the turns up)
2. Count the number of turns you would loose in that timeframe by (in other words, by how many turns will you shorten the current era)
3. Calculate the loss you will suffer in the next inflation phase in BPT by not having the Academy.
4. Count the number of turns you would extend the next inflation phase by not having thee Academy up.

If the number of turns you extended the next inflation level is greater than the number of turns you shortened the current inflation level, the bulbing was a waste.


Let me give you an example. Lets say you just hit renaissance and you know that at current tech pace you need 40 turns to complete all renaissance era techs.
Let's say that by bulbing you would shave off 8 turns from this calculation. Thats 32 turns to finish this era.

Now you select all the industrial era techs and you realize you would need 75 turns to complete all industrial era techs at current BPT rate.

If you save your game now and plant an academy, check how the total numbers changed. Maybe by a tiny bit, maybe by a lot.

If the planted academy saves you 10 turns in renaissance, the bulb is still worth it because population levels will grow enough to compensate for the 2 turn difference.

To do the calculation for industrial is a bit trickier, because you have to add more population AND account for social policies and public schools. The more public schools you have, the less effective the academies become. BUT, perhaps the public schools won't be enough to compensate for the inflation rate.

Let's say with bulbing at current rate you would shave off 5 turns in industrial era. At any point, if an academy would shave off more than 5 turns in industrial, the bulb isn't worth it.

This is where the compounding effect of Academy really shines and why on the long run, early academies can shave off more total turns for research than other sources of tech.

****

There are two moments where Academies become obsolete, or when bulbs become definitely more powerful:
1. When your empire is large and well developed enough so that it provides much much more BPT than a new academy would provide.
2. When growth starts to stagnate and all cities have public schools built. (Because academies will still profit from research labs.)
 
Here's an even simpler calculation, but to make it exact, I'd need access to civ. The exact percentage should be easy to get once I get back home.

IF a new academy would add less than 10% to your empires base science output, don't build it.
 
Here's an even simpler calculation, but to make it exact, I'd need access to civ. The exact percentage should be easy to get once I get back home.

IF a new academy would add less than 10% to your empires base science output, don't build it.

What if my new academy will add 5% to base science output on turn 130? Given that i am planning to launch 100 or so turns later .. I would bulb for Public schools in that case.
 
Moriarte said:
What if my new academy will add 5% to base science output on turn 130? Given that i am planning to launch 100 or so turns later .. I would bulb for Public schools in that case.

Each public school is basically an academy waiting to be built, so yes :)
 
Ribannah said:
The academy will still be there after you enter the next age, build the public school, etc. so no, you cannot calculate like that.

Depends on the number of public schools. Obviously if only one then no. But often you can build six, seven public schools. At that point its worth to look at population increase methods that will yield more and more BPT.
 
Depends on the number of public schools. Obviously if only one then no. But often you can build six, seven public schools. At that point its worth to look at population increase methods that will yield more and more BPT.

i get that but i almost never have more than 4 cities in a science rush. 3 or 4 is all i usually do. a rare 5th is settled but mostly for a late game resource like coal for the factories. also on occasion i'll take a city but i usually puppet it unless they have some serious production value.
 
I think the first thing people need to look at is the following questions:

What is the 'maximum' planned output of a GS or RA in the end game?
What is the Assumed last turn of RAs/Bulbs?

Without that, all comparisons are moot, given that you're fighting against a strawman argument without specific numbers involved.

For the "last turn of RAs', We can assume turn 240 if people want. It's a relatively safe number, and not too early or too late.

Thankfully the tech tree provides:

Before we get there, let's assume a few things -

1) You wait until 8 turns after both Research Labs and Atomic Theory before using GSs for bulbs.
--- Primarily as you max your bpt this way, at least for the boosters (population changes aside).

2) RAs are 'dirty', unless signed after the above turn point for GS bulbs. Ie, you're not already working on maxed bpt when you sign them.

As per targets -

Particle Physics: 9680 beakers

That requires a maxed bpt of 968 for RAs (with PT/SR and for both you+partner) or 1210 for a GS bulb. Neither of which is 'normally' attainable in a fast non-aggressive game.

Advanced Ballistics: 8470 beakers

- 847 maxed bpt for RAs and 1058 maxed bpt for GSs. This works for RAs, but not for GSs. But it's a better plan if you're finishing Rationalism for the two free techs (Particle Physics and Nanotechnology).

So let's assume you're maxing out around 850 bpt. That gives a maximum GS bulb boost of 6800 beakers.

An Academy, maxed out, will give: 12*(50%+50%+50%+15%) = 12*165% = 31.8 beakers/turn.

So an Academy gives out 254 beakers for every GS bulb and ~159 beakers for every RA (only affects your side, so only 5*bpt) after the max beakers point. But that's just the Academies portion of the beakers used on bulbs.

Let's also assume you saved 8 GSs and signed an extra 4 RAs AFTER the max bpt point. That gives you 2035 beakers for the Bulbs, 636 beakers for the RAs AND 30*31.8 = 954 beakers while you worked the Academy during the RA cycle. For a grand total of 3625 beakers per Academy.

Now you just need to work out the details on the 6800-3625 = 3175 beakers left over.

To start that, let's assume you also stopped founding Academies two RA cycles earlier. This won't be 'maxed' bpt, so the numbers will be 'fuzzy'.

Assume - (so we're now 90 turns back from the end of the last RA, or turn 150 - give or take just after finishing Scientific Theory).

no Research Labs or Atomic Theory, but the rest of the buildings are in place, along with the Social Policies/PT.

10*(50%+50%+15%) = 21.5 bpt for Academies.

Let's assume two more cycles of 4 RAs again, that adds: 21.5*5*8 = 860 beakers + 60*21.5 = 1290 beakers = 2150 beakers on that cycle. Bringing the 'left over' amount down to 3175-2150 = 1025 beakers.

Depending on timings for getting into the Renaissance, adding universities and Rationalism (3 policies), that 1025 beaker number gets dropped pretty rapidly over ~50 turns.

Now... that still seems wasteful, but you need to either mass expand/grow or drop Academies to hit the 850 beakers/turn mark.


(this part gets very messy - written in a hurry, so some 'fuzzy math may be involved')


Assuming 850 bpt, you would need a population around:

850 - 165% (research labs, universities, Rationalism opener, National College) = 320 bpt /2 (Public Schools/Libraries) = 160 population in a single capital without Academies.

Ok, that's not plausible and the national College skews things a bit. Some linear algebra (or even basic maths) should be useable though (assuming all tech buildings in all cities and all academies are planted in the capital with the National College.

x = pop in non-capitals
y = pop in capital
z = number of Academies

x*2*2.15 + y*2*2.65 + z*12*2.65 = 850

So.. we can conclude that one academy is worth 6 population in the capital (straight population and no jungle/TP questions involved - leave that for the 'fuzzy' math later).

Let's also assume that a 30 pop capital is the highest you're going to get. That reduced the calculation to:

x*4.3+z*31.8 = 850-159 = 691

As well, we can conclude that one Academy is worth ~7.4 population outside of your capital.

691 bpt/4.3 = 160 population

So x + 7.4z = 160

16 10 pop cities is doable if you're mass puppeting/expanding. Even less if those cities go over 10 pop.

If you keep small, and only have 3 cities outside of your capital, each would need to be massive to get to the 160 population requirement - which means you need more Academies, even if a few are 'lossy' for some of the game.

This seems obvious after the fact, but the 160 pop gets dropped by 5 for every science specialist you run (normal+rationalism booster). That's 4 specialists/city by the end of the game (or 20 pop equivalent).

So that concludes a rather long post to say:

TL;DR

Get to needed bpt mark any way you can, and don't skimp on the Academies if you're not expanding/puppeting!

Stop dropping Academies around the time you finish Scientific Theory.

Aim for 850 bpt as the mark AFTER research labs/Atomic Theory kicks in.

Each Academy pays for itself IF you sign a lot of RAs and save a number of GSs for late game bulbs.
 
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