Spend GS or save like always?

S.K.

Ok I have a spreadsheet to calculate all the deltas I just need some data from your example, namely the dates you gained you 13 GS's and your bpt at turns 150,170,180 and 230 ?

If you can get back to me with that I can let you know how the deltas turn out.

PS I will just linearly interpolate the bpt between turns for the sake of simplicity. I will also include observatories in the calc at turn 180 (as you mentioned from your example).
 
Haven't done any math myself to back up, so could be off, as the difference in turns might be negligible, but in my head I'd probably side slightly with Gabriel's thought regards variables.

Higher BPT in the earlier game via settling, allowing you to advance "ages" earlier; thus yielding higher culture per turn from cultural CS, thus allowing to unlock Secularism, Free Thought, Scientific Revolution at an earlier stage etc. Hitting Humanism earlier, might help with maintaining growth and not running into a happiness issue. Equally Maritime increasing yield earlier granting higher population quicker (and thus BPT).

Might be small differences, not sure.

edit: Again, might be negligible but advancing ages earlier would yield spies earlier too, if possibility exists for tech stealing.
 
Gabriel Pyyrhic said:
S.K.

Ok I have a spreadsheet to calculate all the deltas I just need some data from your example, namely the dates you gained you 13 GS's and your bpt at turns 150,170,180 and 230 ?

If you can get back to me with that I can let you know how the deltas turn out.

PS I will just linearly interpolate the bpt between turns for the sake of simplicity. I will also include observatories in the calc at turn 180 (as you mentioned from your example).
Click to expand...
It'll take a while to get the dates. If you feel like crunching numbers you can manually calculate each cities GP points, adding in a 2 GP spike just before scientific method due to Pisa/PT.

Edit: My bpt at T150 is typically around 220, T170 around 350, T180 400 and T230 is 700. Also I just got done doing a game as Spain. Getting the universities out promptly and keeping all scientist slots up I got scientists around T115, T140, Pisa(GE)->PT (T150), T180, T200, T215, T230 and T250

Hubble ended being pointless as I actually finished the whole tree before I was done building it. And only had 1 piece left of the ship to build, go figure. It's amazing how much a city can produce when it's starving... I miss the slavery civic :D Also Yay for my first Deity win (T265) that didn't involve a Duel Marathon map.
 
OK I will plug in the numbesr for your bpt.
As far as the GP go, if I get time I will have a go at calculating the GS spawn times but I might be off so I will get you to have a look at them when I am done.
I will try to find time tonight but I am up to my ears in damned segmentation faults at the moment, so it might end up being a rather long night :( Which doubly sucks as it is friday night! I am currently taxing work with occasional (read bi-hourly) Civ Fanatics posts :)

Congrats on your Diety win, stick it to the Zergling AI.
:goodjob:
 
Look forward to the results at which point I will try to understand the line of thinking expressed so far :lol:
 
How many RAs you got, how many BPT you got and how many B you got left on the techs you need should be the deciding factors for what to do with your GS. If you got many RA parterns you should settle longer in the game. The more BPT and the less B needed the more you should consider to use GS for breaker bomb.
 
S.K

Worked most of it out. I needed your bpt at T130, I just guessed at 150 but a more accurate number would help.

Currently the math includes 5 things.

1. [COMPOUND EFFECT] : Per turn saving up to research labs (T230) * bpt at research labs agreements (ie the 700 you mentioned). For example if 5 turns are saved then 700*5 gives the net science gain, or a close enough approximation to it. I have decided to include 100% Observatories so as to ensure a maximum is obtained. They are a big multiplier, so I feel we should include them. BTW what turn would you say you would get these in ? At the moment I am only guessing.

2. The beaker remainder from the above calculation.

3. 8 turns worth of a single academy after research labs (to account for the 8 turn bulbing buffer). Small contribution but worth noting.

4. The bonus per RA that a single academy brings.

5. [COMPOUND EFFECT] : Per turn saving from RA's up to T230. This metric accounts for only the academy contribution to RA's and the beaker contribution that comes from it causing science milestones to be achieved earlier. To calculate this accurately I need to have some idea when you sign RA's after T115 ? How many RA's we can leave as a variable, but the timing of them needs to be set or it will make my calculations too complex.NOTE : 4 is used to calculate 5 , but only 5 is used in the final calculation or it would mean counting the contribution twice.

6. The number of turns saved prior to turn 230 (from Academy Raw Science and Acdemy RA Science) multiplied by the academy science contribution at T230, ie if 5 turns are saved then 5 * 10(Academy base) * 2.15 (Science multiplier). Also need the Observatory percentage multiplier which I cannot remember off hand (Isn't it 50% ?). This is to account for the fact that your bpt at T230 does not include the worked academy.

Things not considered yet :

1. I have not factored in any gains made from working through the Rationalism tree quicker due to cultural buildings/wonders gained earlier. I guess this depends on where your culture is coming from post Rationalism opener ? I can factor this in relatively accurately (that is if it makes a difference) if you can pinpoint any cultural buildings/wonders that you target during this time frame.

2. I have not factored in any gains to GPP generation due to tech advancement coming earlier. This one is very diffcult to approximate, but you could assume that some of the scientists would come a turn or so earlier. May not come quick enough to make any difference.

3. Any other science multipliers ie Korea, Babylon, Sweden, Maya.

Final Question : How quickly do you get through the rationalism tree and how much do you prioritise culture after the rationalism opener ? Is there any leeway for further cultural aquisition ?

ATM the net science gain from the T115 scientist is looking considerably higher then your estimate. I don't want to comment further without factoring everything in, and double checking my spreadsheet for formulaic errors.

Will try to post tommorrow sometime, if you can get me the info on your T130 bpt, and cultural strategy post rationalism opener.
 
@Denkt I agree with you, but this thread (S.K is the OP, not me) is trying to compare raw science output from bulbing to planting, considering all of the factors that are calculable, and enumerating those which are not. The HOW to compare is just as important as the WHAT to compare.

The result will tell you which is more efficient for raw science, tech progression and the science VC. It is very hard to compare the benefit of planting a scientist at an arbitrary turn date just by looking at the factors you mentioned, without a compariosn to what you would get by bulbing at a later date.

@iffinem Yeah thats probably my fault, hijacking and obfuscating the thread. Probably will result in me proving S.K is right anyway :)
 
S.K. Ren said:
Now when saving GS for a Science VC you want to bulb 8 turns after you've finished all your Research Labs and are running full science. On 4 city Tradition I get around 700 bpt w/o any academies. 700*8= 5600:c5science:... so why do I want to settle GS again?
QUOTE]

Beacuse of 2 things one is RAs which benifit acadamies and the second is that GS as far as I know cost gold like other units do and less gold means less RAs.
Click to expand...
 
@Denkt Good point about the gold/maintenance. Completely forgot about this. Playing devils advocate though - RA's may not end up being limited by gold but rather time and available partners.
 
Gabriel Pyyrhic said:
@Denkt Good point about the gold/maintenance. Completely forgot about this. Playing devils advocate though - RA's may not end up being limited by gold but rather time and available partners.
Click to expand...

I nearly allways do get all civs as my friends by giving gifts which cost me gold. The biggest problem is gold for me to keep a active RA with all civs at same time because the farm feels more usefull then the TP for a science game. I have sometimes gotten GM to get more gold.

We should probably compare GM for gold for RA vas GS for science because getting GM for that purpose could actually be a valid strategy if it can give you more RAs then you normaly get. We shouldn't limit ourself to GS for science game before we do now how the other GPs effect our science, GM for gold for RAs, GA finish rationalism faster and can give you more gold, production and polcies and great enginner for wonders and better production which allows you to finish the spaceship faster.
 
One thing I'm not seeing really weighed explicitly (but is being mentioned indirectly) is the concept of BPT inflation and the percentage increase of overall tech progression a single academy or bulb has.

Factoring in things like "reduced turns toward Research Labs" has a similar effect in a vacuum but is not the same.

Explaining further what I mean, I think everyone here generally accepts that 500 beakers are not equally valuable at turns 25 and 225, and thus a formula that simply finds the intersect between total beakers over time of a settled academy and total beakers gained from a saved end-game bulb, while useful, is not by itself a fair assessment. But how to quantify this?

It's worth at least considering the concept of what % of total current BPT a settled academy or bulbed tech represents, both currently and over time. In obvious examples, if you're at 16 bpt early in the game, an extra settled academy (+8) immediately increases your tech progression by a whopping +50%. On turn 150, with say 160 BPT, that extra academy could be a 5-7.5% depending on modifiers. Obviously this means an academy's impact over time (marginal product, if you will) is a diminishing value (with rare one-time bumps when academy yield bonuses or a city's +science modifier change).

In less obvious examples, it's worth noting that a mid-game settled Academy could be worth an average per-turn BPT*** of, say, 6% of your total science production over the course of its existence (I made 6% up as an example). Then you can compare that apples-to-apples with the % of total science your end-game bulb will produce (starting at the point you produced the GS). I'm not implying this single comparison should dictate what you should do in a given scenario, but it could be a useful perspective when comparing the relative value of beakers many turns apart.


*** Note that "average per-turn BPT" means you're averaging the percentages--not taking the total science produced by the academy and dividing by the total science generated by your empire over that same time. Otherwise, you're just factoring in raw beakers without respect to when those beakers came, which is already being done above.
 
@Aestis25 I think my calculation covers that (if I am understanding you correctly). Once S.K gets back to me I will plug in the numbers and provide the writeup, then you can then see if it accounts for your concerns.

My calcs basically follow the complete science yield from planting an academy at turn X, until the bulbing date (which for the sake of this thread is 8 turns after Research Labs and built/bought); T238 from S.K example.

It considers all of the benefits that accrue (science wise anyway) from techs being achieved earlier, and RA benefits.

This is all based upon BPT. I am using S.K example for BPT but my calcs will allow any BPT to be plugged in.

If I have time I will provide a graph at the end that should show the relative benefits of planting increasing/decreasing as bpt goes up.

My hunch is we will get a "hump" or upside down saddle, increasing to the point where the bpt gets so high that the academy portion gets to low to provide enough benefit. This is only conjecture at the moment, so we will see I guess.
 
@Denkt : Yes you make a good point. I will have to look at that. It should be easy enough to compare once the science stuff is done.

RA's are easy to compute so long as you know your BPT, and to keep things simple, assuming you are not being averaged with your partner (IIRC that means your BPT is higher then his ??? Could be the otherway as I can't trust my memory).
In my playstyle I tend to keep as many people as friends as possible aswell, so I guess we play the game similarly.

That said I beleive S.K was playing on standard map size so that limits you to 7 RA's at one time, and given they last X turns (hmmm can't rmemeber how long they last, I think it is 30 turns on standard) that puts a hard limit on how many you can get.

Also as you now need DOF's for RA's it will pretty much mean everyone will have to like everyone in order to get the full amount, otherwise you will be friends with one of their enemies which has diplomatic repercussions.

As far as farms go. IMO there are diminishing returns the higher your city population gets.

As the growth amount is continually increasing, each citizen needs to make more per tile to retain the same growth rate (via extra food, policies, buildings etc). Otherwisethe growth rate drops. If the growth rate drops then the net benefit also drops.

Following this line of thought, there will be a tipping point where gold (hammers/whatever) becomes a better proposition to food. No idea where that lies but it will be there somewhere IMO.

In a sense the arguement about more food= more people = more gold is analagous to the more cities = more culture = more policies.
Eventually the policy cost gets high enough that you cant maintain the city culture penalty for a given city. I think (and I stress it is conjecture at this point) that the same holds for growth. Perhaps with buildings/wonders/CS/etc you can keep it in check all game ? IDK.

Personally I love big cities, and try to grow my cities regardless, that said though I do not believe this is necessarily the best use of resources once a certain (albeit unknown) city population is gained. I think the capital is probably an exception to this, given the large multiplier you get to gold via monarchy, and food via (landed Elite I think and Maritimes).

Also trading posts allow you to direct a puppet's citizens effectively whereas farms do not. At the moment I have too many Civ thought experiments on the go :) , S.K Science thread and my own AI diplomacy/strategic project, otherwise I would look more into this to see if there is a calculable tipping point.

There is always a delicate balance in civ between developing a city now for greater future efficiency VS drawing on immediate city benefits, then leveraged for greater future efficiency. Very hard to qualify, let alone quantify :)

Out of interest Denkt what do you think your BPT would be once Research Labs are completed, in a typical science game that you were doing well in ?

I am interested to see how others BPT (and science milestones) differs from S.K. If you feel like providing further info (ie the crucial science milestones (university, rationalism, research labs, etc) and BPT at those times, please do as it would be good to have multiple data sets to draw from). This goes for anyone reading and interested in this thread.

If you are interested, please refer to SK original post for the milestones in question, and provide BPT + Turn Attained at those points.

Hopefully I will get some down time during compiles at work tonight, and can finsih factoring in the RA compound effects.

BTW In your previous post you mentioned RA's affecting Academies, I think you meant it the other way around ?

Apologies for the WALL OF TEXT :)
 
S.K and Denkt et al

Here are the preliminary results, without RA's (which I doing the Visual Basic for tonight hopefully).

I will just use the T115 Scientist for this example and add the others in later. I will also post the spreadsheet once its finished so people can play around with various values (ie science milestone turn time, bpt, GS spawns, RA times etc).

  • By University = 1 turn saving.
  • By Rationalism = 1 turn saving (Total = 2 turns)
  • By Scientific Method = 1 Turn Saving (Total = 3 turns)
  • By Free Thought (+Observatories) = 0 Turn Saving (Total = 3 Turns)
  • By Research Labs = 2 Turn Saving (Total = 5 Turns)
  • By Bulb Date = 0 Turn Saving (Total = 5 Turns).
  • Remainder Beakers = 404.6
  • Total Beakers from Turn Savings = 5 * 726.5 (bpt at bulb date without academies + a single academy) = 3632.5
  • Total Beakers = 4037.1

This is a considerable difference from S.K original estimates which did not take into account the compunding effect of reaching science milestones earlier.

This figure does not have RA's factored in yet, which I believe will push it past the bulb amount.

I have computed values for GS spawning at all the science milestone dates (for simplicty) so we should get a good analysis of how the beakers are falling off over time.

For example a T130 GS (UNIVERITY MILESTONE) only nets 3280.6 beakers. T150 (RATIONALISM MILESTONE) is 2431.3 beakers. Remeber to break even we need slightly less than an 8 turn difference.

For those who want to know how this has all been computed I will write it up later and post the spreadsheet, but so long as I have not made any calculation errors I believe the mathematical method is sound.

The RA calculation is more complex as it depends on when the RA is taken, and the amount needs to be averaged over 30 turns (may make that a variable so other game speeds can be analysed) and then its compunding effect computed. The excel formulae would end up being ridiculous so I will use VB, and post the code when I am done for others to validate.

Anyway thats where the analysis currrently stands.

Comments ?
 
Wow I play [REDACTED: NDA] for a bit and the thread explodes. Looks good, more complete than my original half-assed reasoning. If you want to simplify the RA's calculations the easiest would be to write BPT as f(T)=blah... I think a cubic equation would work best.

Since I already calculated the static value of the Academy to the RA, why not just compare when the RA is theoretically finished to the average BPT at the time and take the ratio as the number of turns saved.

Also about milestones, 1 thing to note is my initial milestones were based around missing the rationalism opener timing by 1 policy so if you do get it as your 7th policy instead of your 8th, everything is about 20 turns sooner in my experience. I've taken to rushbuying the Uni in my capital for expressly this reason.

As for Observatories, I typically get Astronomy right after Scientific Theory if at all mostly because I have at most 1 Mountain city. So for post Sci. Theory its around built around T190. Now if you wanted to calc me getting it right after Acoustics, it would push Sci. Theory up about 25 turns and would be built on T145ish
 
BPT = the summ of all breakers (science) produced by your cities and CS?

RB = rationalism opener bonus which is 1.15 if active and 1 if not active.

RA = resarch agrements which got the formula: ((your last 30 turns breakers/6)+(your partners last 30 turns of breakers/6))(.5+.25*PT+.25*ST) if your partner sum of the last 30 turns of breakers is less then yours otherwise the formula is: (your last 30 turns breakers/3)(.5+.25*PT+.25*ST)

PT = 1 if you got porslin tower otherwise 0

ST = 1 if you got scinifitic revolution otherwise 0

URAA = Rearch agremments active which actually helps you to get the needed techs for scinifitic victory.

BN = The sum of all breakers needed to get the techs for scinifitic victory.

TNTGNTFSV = Turns needed to get needed techs for scinifitic victory.

Forumula to find TNTGNTFSV = BN/(BPT*RB*RA^URAA)

You want to get the TNTGNTFSV as low as possible and now the add the GS to the caculation.

SFBB = science from breakerbomb or bulbing which use a GS and give you the last 8 turns of BPT * RB

A = acadamy which increase your BPT

(BN-SFBB)/(BPT*RB*RA^URAA) = lower value then BN/((BPT+A)*RB*RA^URAA) then the breaker bomb wins and its the opposite if the caculation which got the acadamy gets the lower value.

This is a simple caculation which I haven't goon deep about but it can probably be used to tell which one is more helpfull of GS action. However you should be aware that this caculation do not show how to caculate URAA and other importent things may be missing.
 
@Denkt

I am alittle confused by your formulae ? Admittedly acronym TNTGNTFSV caused me a mild stroke, but after recovering I am still a little confused :)

What exactly do you mean by BPT ? Is this your BPT at the bulb date ? Or an average ? Ignoring RA's for a minute (just for simplicity) I do not see how your formulae can work.

You are essentially just dividing the ((SV beaker cost - bulbing beakers) by BPT) vs dividing the (SV beaker cost by (bpt+academy)).
This won't work as it only compares base science accruel and does not take into account the compounding effects from attaining science milestones earlier. This is similar to what S.K did in his OP.

I mean no personal attack in my anaylsis BTW. I know sometimes disagreement can be interpreted as villification and this is certainly not my intent. Perhapas I am misinterpreting you, or have just made a mistake in my reasoning ?

I decided not to use the overall beaker cost of the SC victory (or bulb date) in my calculations as I couldn't be bothered going through and adding it up. In addition it does not allow for any variation in tech choice, map size or game speed. Instead I have used science milestone turn dates as variables (the ones mentioned in SK OP) so that it can be tailored to individual playstyles.

S.K seems like a very proficient player, most people are not, so the relative benefits of planting are likely higher for them. OTOH players like Vexing, Madjinn, Martin Alvito et al probably have turn dates earlier then this. So a variable for this allows the tech tree progression to be variable and therefor the results more individually tailored.

I have pretty much finished the raw science compounding effects, the base results I posted earlier. I am just factoring in the RA's now and fixing any errors.
Once done I will post it all and you can see how I calculated it and decide if you think its a fair estimate or not.

That said, the base premise is thus : If planting allows you reach the bulb date X turns earlier, then net science gain is equal to X multiplied by the BPT at the bulb date. This can then easily be compared to the beaker sum of bulbing. (Obviously RA's are factored in too).

This seems to be the easiest way to calculate IMO, whilst still allowing enough variables to be tailorable to individual playstyles. In the end I might make a graph showing whats going on, so people can just look and see beaker production being affected by bpt, spawn dates, and milestone times. A simple picture is likely to be more helpful (and more used) then a multi-variate spreadsheet :)

If you disagree with this premise please let me know, as it means I screwed up somewhere bigtime :)

Let me know what you think
 
*yawn* God It's too hot in Las Vegas... makes you want to sleep all day. It looks good to me Gabriel. What did you think of my suggestion for handling RAs? If a cubic equation is no good, how about a step function?

Denkt: Looks like we think alike :D
 
Gabriel Pyyrhic said:
@Denkt

I am alittle confused by your formulae ? Admittedly acronym TNTGNTFSV caused me a mild stroke, but after recovering I am still a little confused :)

What exactly do you mean by BPT ? Is this your BPT at the bulb date ? Or an average ? Ignoring RA's for a minute (just for simplicity) I do not see how your formulae can work.

You are essentially just dividing the ((SV beaker cost - bulbing beakers) by BPT) vs dividing the (SV beaker cost by (bpt+academy)).
This won't work as it only compares base science accruel and does not take into account the compounding effects from attaining science milestones earlier. This is similar to what S.K did in his OP.

I mean no personal attack in my anaylsis BTW. I know sometimes disagreement can be interpreted as villification and this is certainly not my intent. Perhapas I am misinterpreting you, or have just made a mistake in my reasoning ?

I decided not to use the overall beaker cost of the SC victory (or bulb date) in my calculations as I couldn't be bothered going through and adding it up. In addition it does not allow for any variation in tech choice, map size or game speed. Instead I have used science milestone turn dates as variables (the ones mentioned in SK OP) so that it can be tailored to individual playstyles.

S.K seems like a very proficient player, most people are not, so the relative benefits of planting are likely higher for them. OTOH players like Vexing, Madjinn, Martin Alvito et al probably have turn dates earlier then this. So a variable for this allows the tech tree progression to be variable and therefor the results more individually tailored.

I have pretty much finished the raw science compounding effects, the base results I posted earlier. I am just factoring in the RA's now and fixing any errors.
Once done I will post it all and you can see how I calculated it and decide if you think its a fair estimate or not.

That said, the base premise is thus : If planting allows you reach the bulb date X turns earlier, then net science gain is equal to X multiplied by the BPT at the bulb date. This can then easily be compared to the beaker sum of bulbing. (Obviously RA's are factored in too).

This seems to be the easiest way to calculate IMO, whilst still allowing enough variables to be tailorable to individual playstyles. In the end I might make a graph showing whats going on, so people can just look and see beaker production being affected by bpt, spawn dates, and milestone times. A simple picture is likely to be more helpful (and more used) then a multi-variate spreadsheet :)

If you disagree with this premise please let me know, as it means I screwed up somewhere bigtime :)

Let me know what you think
Click to expand...

The BPT should probably be renamed to somehing like avarage breakers per turns of the turns remaining before all needed techs are resarched.

As I said before the formula is very simple and lacks many things including not telling the benifit of getting things faster.
 
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