http://gotm.civfanatics.net/saves/sgotm4/Grayarea_SG004_AD0850_01.SAV
Pre-turn: I raise the science to 30%, PP in 12 at -3gpt.
IBT
A Roman settler/spear is coming out of Ravenna.
760AD (1)
Re-position troops.
770AD (2)
Greece knows Printing Press now.
780AD (3)
Nothing.
790AD (4)
I give Theology to the Ottomans for 91g +9gpt, since they'll soon know it(Greece, Babylon and Persian already have it).
800AD (5)
Nothing new.
IBT
Our Furs deal with Persia ends: I give them Ivory for Furs.
810AD (6)
The Roman settler/spear pair, decides to return home, as it can't settle anywhere
820AD (7)
I "extend" the palace pre-built in Hippo to 12 turns, and I hope that we can make it and build Leo's there. Anyway, the shields can be "re-arranged". Of course, we'd have to follow the tech path to Invention at full speed.
830AD (8)
Nothing.
840AD (9)
PP next turn. Everyone is progressing slowly and that suits us for the Wonder Race(even if we don't win Culturally, it's good to keep the Wonders for ourselves).
IBT
The Germans begin Sun Tzu's.
We lost one galley on the ocean.
850AD (10)
Nothing new.
Summary
1) We can research Engineering in 4 turns at -118gpt(that's where the slider is, but you can change it) and after that go full speed for Invention in less than 7 turns(that's when our palace pre-built in Hippo will end by then: currently at 11 turns, after some more "extending"). We could also starve Hippo for 1-2 turns if needed(make taxmen), so we get Invention first.
I'd say to go full speed to the bottom of the tree, until the GL is made obsolete. When Education comes in, I'd immediately start a palace pre-built for Bach's Cathedral, since it requires a lot of shields, and I'd of course go for Music Theory full speed, switch the palace pre-built to Bach's, then start another palace pre-built elsewhere and full speed for Astronomy(Copernicus Observatory).
Then I'd aim for Economics(Smith's) with a palace pre-built and maybe research/buy Navigation for Magellan's.
Then we need ToG for Newton's University and if possible, build it in the same city that we'd have Copernicus(if the city it's not building something else by then).
Anyway, let's hope that Greece won't learn Invention sooner than 4 turns, since we need 4 turns for Sun Tzu's, and it won't cascade Thermopylae's Sun Tzu's to Leo's.
Since the tech pace is not especially quick, I'd say that we can research at full speed, so we have the time to build our Wonders, without the fear that someone else will claim them.
2) I'd say to have
a) 1 city to built Hoplites until we have 3 Hoplites in all of our cities,
b) 1 city to build catapults to have an equal number as Hoplites in the cities and keep producing them to bombard possible enemies if needed, so we take them out with horses and without any loses,
c) 1 city to built horses.
Of course, Leo's will help big time if we get it, since the upgrades for our Hoplites/horses/catapults will be very expensive. If we're lucky and get Leo's we'll save money for science.
3) I have troops and workers fortified in such way, that no one can settle more cities on our island, so be careful not to take them from where they're.
4) We can begin to road all our island now, and I already begun doing it. Steam Power is WAY far, at the moment, so we can concentrate on roading.
We may need to "extend" a palace pre-built/Wonder, so I'd leave those tiles in Utica only with roads. Sanitation is still far to come, and we can wait.
5) When we have the troops we need, I'd stop producing anymore, so we invest more money on science.
EDIT: Better to send horses down to Rome (I have some fortified in Carthage and Utica), in case the Persian city in our island culture-flips to us, so we can occupy those tiles.
Of course, it's a question of give the city back to the Persians(after we move the regular unit from there) so we won't get possibly attacked or risk it and see what happens?