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Yea, either way with FTs it's something to consider - try to make most improvements divisible by 2x/3x/4x (or all, if multiple former power levels). The main goal is to just get the ridiculous number of formers down, modders can do what they like for the forest vs farm/solar debate I think that formula may slightly off what the game gives in practice - seems to overestimate.
By what others are saying and my own experiences, I would say L production ends up being somewhere around (X^2.5)/16 per turn, where X is the # of techs you have.
@Yitzi: I always play my games at Librarian because I just don't like the upper levels. I get too frustrated too quickly and go play something else entirely. In the past week, though, I've been watching how things work out with your patch, and think observations at Librarian are warranted.
Actually I think the L production curve starts a bit lower, and is a bit steeperUsing L=0.02*TECH^2.7+TECHTECH ~LABS1 15 710 2020 8530 22540 46350 82360 1,32570 1,98880 2,83090 3,870100 5,124This is probably a decent estimate for a normal sized map. Assumes fairly average infrastructure for the tech at hand, and perhaps a few pacts. I'll have to play some games to test all this out - it may help to have others post their typical labs at various points in the game.
Yea, satellites might not even need a major nerf. At least if you put Sky Hydro further up the tree.
What I'm more interested in seeing is how a faster early game tech rate will influence the game. As evidenced in my pacifism game, I am only 1/4 through the tech tree after 100 turns in an ideal situation of no war and pacting everyone. This means the early techs are currently very slow (which you would expect since the curve is linear-ish). The early techs will have to come a lot faster if the later ones take longer, is what I'm getting at.
This may end up requiring lower M costs on early facilities, although that could cause even faster teching. Something to think about - it's not as though the curve is perfectly balanced vs M costs of facilities and SPs as it is. Ascent probably being the worst since it's at the end.
What, actually, is the actual unedited research cost formula? I have the Prima guide, and it has what they say is the formula, and it's pretty complicated. In particular, they talk about WORLDSIZE. I'd love to know exactly how it's calculated. I'd like to know for sure, as I'm a bit OCD about research, and so I might be able to contribute to this discussion.
Ok, I looked at the code and got the actual formula (there are a handful of missing pieces, though.) So here's the formula; notable changes from the given formula are in bold:TECHS: Techs you've discovered already (including trading/pods/artifacts, but not the ones you started with). However, there's one variable that is added, and another that's subtracted; I'm not sure what they are, as I haven't found where they happen, but I think they're just discovered techs that are counted differently by the program (I think the one that's added is techs previously discovered this turn). Minimum of 1, maximum of 4999.MOSTTECHS: Highest number of techs discovered by anyone. The same variable as before is added, but the one that was subtracted isn't here.DIFF: This is 1 on citizen difficulty, 2 on specialist, 3 on talent or librarian, 4 on thinker, 5 on transcend.The formula is then:1. Find (DIFF*4)+8. AIs instead use 29-(DIFF*3). Apply to this a minimum of 12-TECHS, and a maximum of 12+TECHS.2. Take TECHS, and subtract TURNS/8 (or TURNS/12 with tech stagnation), to a minimum of 0 and a maximum equal to the result of step 1 (or 1.5 times the result of step 1 with tech stagnation). 3. Add the result of step 2 to the result of step 1.4. Take MOSTTECHS-TECHS and divide by 5, rounding up. Subtract this from the result of step 3, but no more than 30% the result of step 3 (rounding normally) plus 1. AIs instead divide by a number dependent on difficulty, ranging from 3 on Transcend to 8 on Citizen, and the maximum percentage ranges from 0% plus 1 on citizen to 50% plus 1 on transcend.5. Take TECHS, and add 1 for factions with a natural penalty to research, or subtract 1 for factions with a natural bonus to research. Apply a minimum of 1. Multiply this by the result of step 4.6. Modify by WORLDSIZE and faction and alpha(x).txt tech cost modifiers, and add 50% with tech stagnation.
Yitzi have you confirmed the formula to the in-game results? For example I had tech 20 at 828 cost, if year 2101 and in the tech lead. Transcend game.1) 5*4+8 = 28, add 12+20 = 32, sum is 602) 0 turns so = 03) 60 + 0 = 604) mosttechs - techs = 0, so nothing subtracted, so = 60 - 0 = 605) techs = 20+1 = 21 * 60 = 12606) worldsize = 1, cost modifier 1, no tech stag 1, so 1260*1*1*1 = 1260If anything that formula would seem to imply quadratic, since techs is later multiplied by techs. But when I graphed out the points in a game where I gave myself the techs 1 at a time, it was linear. I do agree that techs of opponents and/or mission year are factors, this was just taking them out to simplify.
Now with regard to the actually formula it looks like intervening in Step #4 would be the way to go, before TECHS is multiplied by the result of step 4 you can take TECHS and raise by a power, or possibly just multiply it by itself to introduce a quadratic progression. The Step 4 result looks to be introducing a bonus for lagging factions and this looks to be a good thing, we may want to look at expanding the room for this effect.
Your observation that the cost curve moves from quadratic to linear is quite interesting, I wonder if the designers intended this to follow a similar change in the players growth curve. When the player is expanding vertically and horizontally they will be seeing quadratic growth, but once empty territory is exhausted the player will only be expanding vertically and growth will slow down to linear. Unfortunately the formula as written ignores World-size when placing this quadratic/linear 'knee' in the progression, it should come later the larger the world size, and I think most people play on maps bigger then the intended size for the formula.
What are your plans for modification at this point?, and if your interested in more testers for this I would like to volunteer.