Disagree with science penalty. What if I just choose not to build more than 4 cities? Wouldn't liberty be out teching Tradition 4 cities by alot? Even now, with 7 liberty cities properly developed they are already out teching tradition.
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GhostSalsa, re: Liberty Finisher, An academy (w/ NC) is 12 beakers. On t85 (which I usually finish Liberty by) that's usually boosting my science by 25%. (9,7,5,4 pop + NC = 48)
The growth advantage of Tradition+aqueducts isn't all that significant until you finish Tradition, which is usually around that same time, so for a brief moment you can be farther ahead in tech with Liberty, right before Civil Service + Aqueducts leaves you in the dust.
Anyway, regarding the science penalty, and why it IS significant:
A brand new city generates 1 beaker. Let's take a very typical Liberty example prior to turn 100. Your size 10 capital generates ~40 beakers. (10 from pop, 5 from library, 8 from academy, 3 from NC = 26. + 50% = 39, let's pretend 40 for simplicity)
That's how you have to measure your "base" beaker cost. With just this city, if a tech is 200 beakers, it will take 5 turns to research.
If you have one expo, size 6, w/ a library, it generates 9 beakers.
This boosts the tech cost to 210 beakers, but reduces the time to 4.3 turns. (still 5)
Let's say that city started out at size 1, and when it was size 1, you didn't have NC up, and your main city was only outputting 20 beakers, so 20 + 1 is a break-even (+5%)
Now. Your second expo, size 4, w/ a library, generates 6 beakers.
This boosts the tech cost to 220 beakers, but reduces the research time to an even 4 turns. You're generating the *equivalent of 25% more beakers*, (after penalty) but you've *doubled your population to do it*... This is bad, yes?
Your third expo, size 4, w/ a library, generates 6 beakers.
This boosts the tech cost to 230 beakers, and now we're down to 3.8 turns.
I'm intentionally ignoring some factors along the way (mainly that those expos after the first weren't pulling their own weight, tech-wise, at first)
Now, we plant another city. (#5)
It starts out generating 1 beaker. We can't afford to rush-buy the library, because we need that money for other things. (Say, perhaps a university)
Now our cost is 240 beakers, and we're back up to 3.9 turns. Unfortunately, we can't build Oxford until we get 5 universities now, and Oxford will take longer to build. This was the same issue earlier with National College when we had 3 cities. So, we throw a trade route at this city, try to get the library built fast, and rush-buy a university.
We can't place another city now if we build Oxford, but we're going to wait on that anyway for timing reasons.
Sometime around t110 (because we're kicking ass) we have all 5 universities done, and we place our 6th city.
Now let's say our beakers are:
(capital size 14) (14 + 7 + 3 + 8)*1.83 = 59.
(expo size 10)(10 + 5)*1.83=27.
(expo size 8)(12*1.83)=22.
(expo size 6)(9*1.83)=16.
(expo size 4)(6*1.83)=11.
Grand total is 135. If a tech is base 400 beakers, it costs us 500 and takes 3.7 turns.
We drop another city. Total is 136. Now we're at 520 beakers, and it takes us 3.8 turns. We'll break even at 140, when the city hits 3 pop w/ a library, but that costs us 6 happiness.
We drop another city, six now. Total is 141. 540 beakers, and it takes us 3.8 turns again. We'll break even at 4 pop w/ a library, but that costs us 7 happiness. Otherwise, it takes us 6 pop to break even. (9 happiness)
From here on out, it's pretty much the same thing. Each new city breaks even at the cost of 6 happiness and a library or 9 happiness. Until we need to build Oxford, now we need all those extra universities. And it takes longer to build Oxford. And after we build Oxford, our capital is generating even more science.
Now we build public schools. Our more recent expos (unless they have insane production) are kept busy building those schools for a very very long time, or we have to rush-buy them. At which point, the capital is generating an even greater percentage or our total science.
So, it may seem like we broke even, and maybe even eventually generated more science total... but at what cost? Well, for each city, we lost ground before breaking even. With the science penalty, we paid 25% more for technologies than before. Over 125 hundred turns, we research as much as we would have in G&K in 100 turns. Over the course of a typical game, that adds 50 turns.
FIFTY TURNS. And that's only with 6 total cities. The AI usually builds more. This is why the AI in G&K could win by t270, and now doesn't win until t330 or later. It's that simple.
The happiness cost USED TO BE made up for by the faster tech rate. It's now only slightly better than a break-even, and it requires a ton of money and hammers be dedicated to those new cities.
The final factor is internal food trade routes. You can only have so many. There's a fixed-size pool of bonus food, enough to feed a few expos. (or boost a mega-capital)
And you're sacrificing money to use all those trade routes on food in the first place. OCC is impractical because you can't use Trade Routes, and wide is impractical because there aren't enough. So, we're stuck at roughly 3-5 cities being the sweet spot.
Now, Liberty gives us +1 happiness per city, (20% of the breakeven on happiness) but it doesn't help at all with those 50+ turns of extra research. My proposal, droppping it from 5% to 3%, would reduce the effect to 30 turns (over a game) from 50, which would help (somewhat but not completely) compensate. Tradition would still be superior at science because of Monarchy and the limited number of trade routes in a game, but at least early conquest wouldn't *cripple* your science rate... as much. Because you can't afford to annex puppets to build libraries... This is why late-game conquest is so much more profitable than early-game. You're capturing cities with universities and wonders vs adding +15 unhappiness for no benefit whatsoever.
Anyway, I digress. Point is, going "wide", even 7 cities, is nerfed by the science penalty. And my suggestion of reducing it is really not going far enough, but removing it entirely would make Liberty even MORE superior at conquest, and Honor is even more nerfed than Liberty right now. Maybe the Honor closer should remove the science penalty in cities with a courthouse?