Some thoughts before I started my second attempt...
I'm thinking of a game where I only have 3 cities. Assume I am Elizabeth. (The 'expected' numbers below aren't exact, I kind of adjusted them as I was playing)
Great People
My theory is it requires 36 Great People to fully bomb 3 cities to legendary. Obviously that's not going to work, so tone it down to two cities, and it requires only 24 bombs. This implies that 1 city should get culture by other means. Therefore, I'm thinking one (not necessarily the capital, but would make sense) will be cottaged, the other two farmed.
Now, assuming the farm cities can produce 6000
normally, then I only need 22 GArtists. This costs a total of 26720
(if I've done my maths right - 1st 10 @ 80*N
each, 2nd 10 @ 160*N
each, last 2 @ 240*N
each). Assuming I'm always Pacifist and Philosophical, that requires 26720/3 = 8907 raw
, or 8907/3 = 2649 artist turns.
Assume I'm targeting a T120 (ambitious!) finish, that's an average of ~20 artists per turn. Between two cities, that's 10 per city. Considering 20 artists in the NP city isn't difficult towards the end, and another city could produce a hopefully similar amount... perhaps it's possible??
National Park City
With Biology comes National Park, as well as better farms. In terms of producing specialists, 1 grass farm with 4 food can support 1 specialist, as can 1 forest with a preserve. Happiness and Health aren't issues, so they are pretty much equivalent. SO, it's not really essential to preserve all the jungles like I have been doing. It also means that it is probably good value to chop forests to build the National Park. With Mercantilism and a food resource or two this city could support ~23 artists.
Targetting Biology by turn 50, and ~5 turns to build/chop the park leaves 65 turns. 65*23 = 1495 artist turns. Assuming for the first 50 turns it averaged about 3 artists per turn that's a total of 1645. That's also worth 13,200
, so it might only need 9 bombs.
Second Farm City
This city needs only 1004 artist turns. With a couple of food resources and some farms a size 18 city could easily support ~13 artists. Do that from turn ~40 and it is there. It might use 10 or 11 bombs. Since this city has not much else to do, it would make sense that it is the missionary city, so try to found it 2nd and become holy city.
Cottage City
This leaves the cottaged city. It needs all 50,000 culture from commerce or buildings. Obviously it will have the hermitage and at least 1 cathedral, and free speech for +250%. So that's 14285 raw
. Average over 120 turns is ~120. Not so likely, but, lets say by turn 40 I've gone 100% culture, am working 20 hamlets, and half of them are riverside, and I am financial then that's 70 per turn right there. By turn 46 they are villages (with PP bonus), so now 110 per turn. By turn 78 they are towns (free speech bonus) that's 170 per turn. 70*16+32*110+32*170 = 10080. The palace is worth 2*100+8*80 = 840, a religion, temple, theatre, monastery, library and university (cheap for philo leader) another ~80*12=960. Trade routes worth ~80*4 = 320... err.. I'm running out of sources here and I've only made ~12,200. Can I throw in 2 bombs? We'll see.
Civics
I think the first civic choices are Representation, Free Speech, Caste System, Mercantilism and Pacifism. But, at the start I'm tempted to use Universal Suffrage to rush out some workers, missionaries and other buildings. Since I can changes 3 civics for only 1 turn, what else might be useful? Emancipation for a short time would be nice to more quickly grow the cottages. Without Caste System suggests the first builds in the other cities should be theatres so they can quickly switch to working artists. There is a risk of producing a non-artist here, eg GE or GM, but it's not like these are a total waste, the GE could rush something useful like the NP, and the GM could be saved to found Sid's Sushi. In fact, up to now I haven't even considered Sid's Sushi. Is it worth it?
Sid's Sushi
With only 3 cities, gathering Sid's resources might be difficult. Might have 4 or 5 sources in local area, which only add 8-10
and 3-4
. Is that worth the cost of the GM and teching to Medicine?
Assume you found Sid's on turn 80. Then that's roughly 40 turns worth of 10
, so 400 raw. In the cottage city (place to found it +2
per turn for the wonder itself = 2*40*3.5=280) that's 400*3.5 = 1400, in the others that is 400*2 = 800. Total between the 3 cities of 3000. But wait, there's more! The 4 food is worth at least 2 artist specialists per city, so more
and more
. In the cottage city it could be more if that food allows you to work all cottages if you aren't already. So all up, I think it's a wise move.
Also, teching medicine is good trade bait to get Electricity, which boosts all your windmills
.
Ok, onto the actual game
The biggest problem I had of course was meeting the numbers I said I would
In the end I managed 1968 = T138. 21 GArtists produced + 1 GM. 3 bombed in the capital. 7 Sid's resources producing 14
2
.
My capital wasn't ideal - only 10 riverside tiles, but too many hills and not enough food resources, so took a long time to work all the cottages. I probably should have built some temporary farms at the start to grow it quicker.
The civics gambit worked well I think - I didn't produce any unwanted great people from lack of caste system, and the cash rushing was nice to quickly get workers. In fact, when I started I didn't plan on Sushi, but in hindsight it wouldn't be a big risk to run a merchant for a short time.
Biology wasn't discovered until T56, with National Park built 4 turns later. Not too far off I guess.
Sid's Sushi was founded on T84, so that's on track.
It took a very long time to get to 100% culture, and to build the Hermitage/Cathedral. Perhaps if the capital had more forests to chop.
I only had one religion the whole game, which was founded in my NP city. This city also wasn't ideally green. Only had 20 specialists for most of the game.
What would have made a big difference I think would be 1 extra support city, specced for production. Building wealth here would have helped a lot.
I think I'll try it again and see if I can do better than T120.
Micro management practice though.
prior to medicine, to take advantage of the financial trait. And although Enviro makes the corporation costs higher, it pays that back with a +2 
to the flood plain city with Public Transportation), Steam Power (it came early enough that I made levees useful in two cities), electricity (+ commerce on the windmills; not a big deal, but everything helps), and some junk that I traded back around to other civs for more gold.
instead of -1 
is basically equivalent to 1
I don't actually leave until tomorrow and I am off today... maybe I can get one in after all 
