Korea is another one of those civs I recommend playing one higher difficulty level, they are that powerful. I also recommend this with Macedon. Of course if you are already a deity player, not much you can do. I stayed same difficulty level as to compare them with other civs I'm playing in civ of the week.
My first game I started a game without reading a description of all their abilities, and I forgot about the mines giving +1 science when adjacent to your campus. I actually started a 2nd game because I was a little disappointed my first game didn't end as early as I was expecting. I only beat my Netherlands game by 9 turns. Kind of shows Korea isn't
that massively overpowered. They are still the best at science (though my Scotland games seemed pretty close, but we'll see when I play them again), but Netherlands sure gave them a run for their money in my game. I feel like I can get their time down more. I'm not the best at fast victories, because I still like to build wonders, but it's something I'm improving on.
My start:
Strategy is simple: Place as many Seowons as you can and don't put other districts next to them. Though pay attention and try to put them in places you can surround with farms and mines. I didn't do this enough in my first game. Also run natural philosophy as soon as you can. I felt like I didn't enable this policy card early enough in my first game, it's why I'm playing them again to get my win time down. I recommend Natural Philosophy and Rationalism (you really should build Forbidden Palace so you can do this with your tier 2 government) as both policy cards work out well for Korea. And don't forget the governors. I went ahead and picked them all up. Though each promotion also gives the +3% so you don't need all of them, but I wanted the boost to as many cities as I could.
Three Kingdoms: As if they aren't powerful enough, you can get even more science (and food) out of them. Worth paying attention to. I forgot about this my first game.
Seowon: Massively powerful district, worth building in every city you can. Try to plan ahead where you want your districts.
Hwarang: +3% science AND culture for each governor promotion: As if Korea isn't powerful enough, they throw in culture as well. Helpful though, as you'll find your science far outpacing your culture.
Leader Agenda: Her agenda is annoying to satisfy. She often has more science than you. But if another AI hammers her and she never expands you can satisfy this without too many problems.
Hwacha: Ended up using this my first game when Khmer attacked me. The not attacking and moving is annoying. And knights can hurt these pretty bad, I almost lost a couple. Honestly, they kind of suck for me. Your best bet is to keep them parked in cities, forts, or encampments. You can upgrade archers into them, so you don't need to hard build them.
Final Grade: A+. Overpowered, what else can you say. Sometimes it's fun to play such a powerful civ. It's why I started a 2nd game with them. I felt like I could get my win time down more and that I didn't build enough Seowons early enough and didn't get enough mines up around them. And I went to war in my first game which may have slowed me down. Other than taking one city from Gorgo in my 2nd game, I stayed away from war.
Final screenshot of my first game
So the question is do you go for a religion with them. I ended up doing it both times. Since the religion race wasn't very active I figured why not. I picked the belief that gives +1 science to cities with campus districts and +1 gold to cities with commercial districts. You could pick the belief that gives +2 science to other cities following this religion, but that would mean building enough holy sites to spread your religion to other civs, seems kind of dumb (that belief would work better with Arabia) since you should be building Seowons instead. I know I delayed getting a Seowon up in my 2nd city by building a Holy Site, but only by a little bit.
edit: I should also note that Casa De Cantratación is a good wonder to build since that gives you 3 promotions and that's an extra 9% science and culture for your cities.
