I entered the middle ages fairly soon after my last post, and went straight for Education, to deny India most of the benefits from the Great Library. After looking at the world's situation, I decided to either a) get Domination with Sipahi or b) get a larger second core in Carthage with Sipahi and go for diplomatic/space race victory.
I started building horsemen early on, and later knights. Errant AI behavior helped, as Rome decided to conquer a Celtic city when I had eight knights nearby...
I grabbed the city, and shortly after acquiring a few more knights (and upgrading my spare warriors), I eliminated the Celts to one city in the space of 4 turns, and waited for the last one to expand its borders as I didn't have a spare settler. My cities all had libraries, or were about to finish them, making my science powerful enough to place me in bargaining position tech-wise.
Carthage was the perennial 2nd power during the Middle Ages, the Pyramids boosting growth, and until Hannibal found Gandhi I had the best of both worlds- Hannibal went the bottom half of the tech tree, and the other AI the top half. (The other AI together only researched about 1.5X the speed of Hannibal- a testament to the power of the Pyramids, Hanging Gardens, and industrious workers). Rome kept squabbling with first the Celts, and then Carthage, and generally blew its massive lead at the start of the era due to not researching Republic- Caesar spent half the Middle Ages in Monarchy, and suffered as a result.
Late in the Middle Ages, Egypt declared war on India, but until then the 4-civ continent was relatively peaceful. Eliminating the Celts didn't hurt the AI's opinion of me that much, as I razed no cities, hitting Brennus with a knight blitz to knock out any potential cultural challengers faster than the cities could flip. I also had a culture second only to Rome, and equal to India, as a lot of early libraries to expand cultural boundaries helped.
Wonder-wise, I grabbed Sun Tzu's, Leo's, and Smith's by careful prebuilding, as I knew that I would a) go to war where free barracks to heal quickly would help enormously and b) need lots of cash for Sipahi upgrades, as they cost as much as a tank.
In 710 AD, I discovered Military Tradition, traded that plus about 80g to Egypt for Physics, and turned off research. Trading this set off a chain reaction of MT discovery, causing several major wars on the 4civ continent. In 800 AD, after Hannibal stopped paying me for a tech I had sold him, I entered the Industrial Age, drew Steam Power as my free tech, and sent 28 Sipahi into Carthage, starting my Golden Age. In 840 AD, I captured Carthage, with the Pyramids, Hanging Gardens, and Copernicus' Observatory. 880 AD marked the disappearance of Carthage from the original continent, as I captured the last Carthagnian city. Despite many elite victories, no leaders appeared during this war.
900 AD marked the belated building of the Forbidden Palace in Iznik. Given the AI tech pace, and that I would have to conquer part of the 4-civ continent to trigger domination in any case, I decided to bite chunks out of the AI on that continent first, leaving backward Rome, the least likely to get Nationalism quickly, for last. Spain lacked horses or iron, and so was my first target. The first attack in 980 AD with 40 Sipahi produced a great leader, Orhan, who moved the Palace to Carthage's former capital. In 1000 AD, Isabella gives up her throne. The turn afterwards, Cleo gets Nationalism.
Leader #2, Murad, arrived in the first turn of the assault on India in 1020 ad, and in 1090 ad India perished. The same turn, I attack China and take on an MPP with Egypt to avoid getting backstabbed, giving me time to rushbuild libraries in my new acquisitions. This worked out nicely- Egypt sent single cavalry units out front, luring the counterattacks and allowing my Sipahi to attack without much harassment on the way.
China falls in 1200ad, and I send my Sipahi back to prepare for Rome, which I attack in 1250ad. Rome had veteran rifles, but no cash or legal trade tender to rush more, and conquering Roman territory while rushing libraries nets me domination victory in 1305 ad with a Firaxis score of 6088.
Although I reached a few techs into the Industrial Age, nothing beyond Steam Power and Nationalism made any difference. Having rails speeded conquest, as well as troop organization, and rifles delayed the acquisition of Roman cities slightly. I tried to strike before the AI targets I chose would have either the time to build rifles or the money to upgrade them, and I largely succeeded: India never fielded a non-conscript rifle that I saw, and China only had a few regulars around. Rome's vets gave my Sipahi the most trouble, but still fell to sufficient force. This game reinforced the lessons of HOT3 about the awesome power of Sipahi.
Grabbing Sun Tzu's, Leo's, and Smith's was key to this strategy, once I formulated it- free barracks, cheap upgrades to start off the Sipahi ride, and a continuous flow of money to rush culture and defenders in new cities far away from home. With the amount of luxuries present on the home continent, even in the original radius before I went to war, almost all native citizens and most foreign nationals behaved themselves. I had a 7-turn revolt to Republic shortly before hitting the Middle Ages, and never left it.
Here are some pictures of the minimap from the military advisor, to highlight my progress:
880 AD & 1000 AD:
1090 AD & 1200 AD:
Endgame: