Well, not quite.
I picked up from a 620 AD savegame to replay the game for a cultural victory instead. An earlier start would have left me a bit too subject to spoiler information. I don't want to go back and found the early religions since that wasn't part of the original game plan. This isn't an academic exercise to prove fastest possible cultural finish in this scenario, it's a real-world execution of whether culture could succeed from the point at which I might have chosen to go for it.
The three culture cities will obviously be Karakorum, Beshbalik, and Ning-hsia.
Fortunately, this is a small map, so that my six core cities will be sufficient to build enough temples to qualify for three of each religious cathedral. With Free Speech forbidden by variant rule, we're going to need to get our hands on as many religions as we can. I've founded Taoism, but only Islam is still available. So I am planning on one little bit of conquest: to eventually capture Yakutsk, just to get access to Christianity.
And my tech plan is this. Instead of beelining to Astronomy, Knights, and Grenadiers, the game plan is now to snag Music for the Great Artist, then beeline to founding Islam. Along the way, Notre Dame and Spiral Minaret will be critical wonders, both for their effects and for the raw culture. In the longer term, I plan to never shut off research in favor of the cultural slider. Rather, I'll rely on wonders for the culture, including the late-game prizes of Broadway and Eiffel Tower. I've long wanted to see what they can do for culture; they rarely come into play since a well-played cultural victory shuts off research long before Electricity.
This savegame was from just when my second Great Person popped, as a Scientist, for the Academy in Beshbalik. I was still in Pacifism from having done that. In the real game, I revolted to Organized Religion now, but in the cultural replay, I stuck with Pacifism for a while longer, in order to put out at least one more Great Engineer from my capital (from Pyramids + HG), to go for Notre Dame.
So Music came in as planned, and the Great Artist settled in Beshbalik. This city clearly needed the most cultural help; Ning-hsia and my capital both had tons of hammers to build wonders. And the economic production from the super-specialist would be largest in Beshbalik too.
I continued with the beeline to Divine Right, founding Islam in my third cultural city (nice), and kept building.
In 1208 AD, Gandhi scares me -- apparently he didn't get the memo that the AIs can't do naval invasions. BTW, I have not gotten any of Archery, Feudalism, Construction, Horseback Riding, or either component of Macemen. The best I've got to fight this off is spears, axes, and swords. But fortunately, that stack consists of mostly easily-countered mounted units. Two whipped spearmen, a sword that was hanging around, a warrior upgraded to axeman, and a couple cleanup garrison chariots took care of that at a total cost of one axeman and one chariot.
Japan shortly later sent a single galley with two axemen; I lost an axeman (with Shock at 78% odds) and two chariots fending them off, but didn't have to whip anything.
I shut down Karakorum's growth at size 15 due to health, and hired artists to pump Great Artists from there. Leader Four came as my third Engineer, though, against 70% Artist odds. With no relevant wonder to rush, he settled in Beshbalik like his first peer. Leader Five a while later was an Artist who went for Beshbalik too. Leader Six still some time later (after Economics) was another against-the-odds Engineer who did the same yet again.
On the research front, my plan was essentially to play follow-the-leader, paying discounted prices. With Free Speech forbidden by variant rule, there was no rush to Liberalism, or to any other particular technology besides Music. So I followed in the AIs' footsteps on Feudalism, Machinery, Compass, Optics, Construction, Engineering. That last was important to enable better zone defense from my limited number of units. Everybody kept building the usual infrastructure: forges, aqueducts, Taoist temples and monasteries (the latter to benefit from Spiral Minaret), courthouses. Happiness quickly became a non-issue with temples and cathedrals, but health continued to be a problem.
I did adopt Vassalage, mostly so that I could produce naval units with extra experience in order to keep control of my fish resource. I had some fun with this guy, who for quite some time killed everything that dared to approach my precious fish. He ruled the seas for quite some time, as a caravel, then frigate, then destroyer, until he eventually lost against an enemy battleship. Also amusingly, this boat was my first (and only for quite some time) 10 XP unit -- first time I've qualified for the Heroic Epic with a ship.
Then came Guilds, and I struck out beyond the follow-the-leader discounts for Banking to get my critical Mercantilism online. Qin had had Paper for a while, but only him, so I ignored it for a while... when I did go for it after Banking, I found that Qin already had both Education and Philosophy, which means...
dammit. I could've gotten that if I'd been bolder. He took either Astronomy or Divine Right, which were both in possession of other civs anyway, so no big loss. And then next I went for the Great Merchant at Economics, but Qin beat me to that by two turns too.
I proceeded through Astronomy - Gunpowder - Printing Press - Nationalism. Silver popped at Ning-hsia (I got no resource pops in the first game.) That was actually less helpful than it sounds -- Ning-hsia is a hammer city, not commerce, and the silver pop actually hurts hammer production. And the happiness was moot since the religious buildings were covering that. Still, it wasn't unwelcome.
Leader Five came as an Artist from my capital in 1670 AD, who settled yet again in Beshbalik. Leaders Six and Eight were also Artists in 1750 AD and 1820 AD, and they had to balance out the culture production by settling in Ning-hsia. Leader Seven was a Prophet from Ning-hsia, who finally went for the Taoist shrine (even though he'd be more economically productive by settling, I wanted the culture from the shrine.)
So, by this time (1700 AD), my cities had just about finished all the Taoist and Islamic buildings. It was time to get access to Christianity.
At Yakutsk, I landed two Accuracy catapults, one grenadier, one knight, and two chariots. OK, the chariots were kind of a cop-out to support the catapults, since the grenadier and knight were expected to do the work against only the two defenders. Well, the game decided that was to be no skirting the variant like that. The grenadier lost his attack at 90% odds, and both chariots (one suiciding) were needed to kill that last sliver of longbowman.
The city capture also got me two workers - for some reason, a Russian galleon-longbow-settler-worker package moved into the city right before I took it.
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