So the game's been out a while, and it's pretty easy
I was never better than Emperor in Civ IV, and only then just barely (Monarch was pretty easy, Emperor was tough, and Immortal impossible, without cheesing with Inca or something anyway).
I can safely say, Emperor is pretty darn easy in this game
My first strategy involved mass companions and breaking things. That worked pretty well. However, it sorta fizzles at higher difficulties when computers have masses of spears that can stop your cavalry hordes. That's when, along with my friend, we discovered ways to use part of the acoustics slingshot in order to power through a rifle (or a couple, if possible) to completely dominate the computer(s).
This is played with Babylon (non-optional) on Emperor difficulty, standard map size, Pangaea (continents or anything really is fine), Marathon speed (i'd assume it should work on virtually any speed though, definitely Epic as that is my base speed), and everything else standard settings. NO SAVE LOADS WERE USED AT ALL as it crashes my computer, so nothing is abused. You can choose to put one city challenge as an option if you wish; it changes nothing (we'll never build a settler, and we'll raze everything).
This strategy depends heavily on your start. A weaker start is still viable, but will slow you down, probably by a couple hundred years. I'm not ashamed to admit that I restarted a whole bunch, and ended up with 2 calendar luxuries, a marble, and 2 cows, near a river with a bunch of grassland. Any similar start should achieve results like mine (it took 4 restarts to get that start, fwiw).
The basic idea is this: Researching gunpowder tosses you into the Renaissance, and if you saved up 4 social policies, you can immediate push through Rationalism and get 2 free techs, for metallurgy and rifling, to get your first riflemen. This immediately gives you a 25 strength ub3r unit, that takes essentially 0 damage from everything and 1 shots all units and towns. Give it blitz (I usually go shock 3 blitz) and it'll firing-squad computer armies no matter how many they have.
The key really is timing. I achieved Riflemen at 1100 BC, but I believe 1300 or even 1400 BC is possible. You are literally fighting warriors with a 25 strength monster, that 1 shots cities. Once promoted, nothing will even damage you, and you can hit cities twice if needed.
The basic build is as follows:
1. Look at your initial start, and figure out what techs to research/improvements to build. GOLD IS MEANINGLESS (you'll be selling luxuries to computer at roughly ~1k per luxury, you keep nothing). In that event, Wheat > Cows > Grassland~Horses. You want 3 luxuries total to sell (for 3k gold).
2. Your starting build order is basically always worker/monument. Always. The monument will build you (eventually) 3 social policies with some random culture thrown in from cultured city states that you befriend in the course of your encampment rampage. You'll never build any military units (obviously). Keep your initial one alive, you cannot lose it.
3. I like to go honor with my first social policy to get more gold from camps and to level my little spearman (he usually gets promoted by a ruin at some point). He can also take out encampments targeted by city states, which is important. I do think that Honor is suboptimal, though.
4. You need to ally all maritime city states, since you'll be running 2 scientists in capital at all times. And it's VERY important that your city grows. Also, BUY A LIBRARY ASAP. As soon as you can, buy a library.
5. After researching basic techs (remember, your goal is gunpowder, so you need all preqs to that), while researching pottery- > writing for your first scientist (horde all scientists, if you get writing at a normal time, you'll have exactly 3 total scientists to pop techs). The computer will race you on great library, so you MUST use great library for metal casting, so you must time your iron working research to be slightly before great library finishes, so you get immediately bulb metal casting.
6. Note that I get honor, so I'll never have enough culture for 5 total policies (you only get enough honor income for 4 policies). This means that you must build oracle if you want the missing policy, or skip honor. Make sure to steal a worker from a city state, you can usually do one ~100 turns in
7. In general, this means if you go oracle, you might as well get calendar luxuries. I did in fact go oracle. I think that's not necessary, and slowed me a few centuries. Regardless of what you're doing, you should chop trees like crazy, as forests are useless to us.
8. So let's say you skip honor. You're basically running around with your spearman taking down encampments (75 each on marathon, 37 on epic), and in general sitting on 1 city (that should have grown very large by now), while befriending as many maritime city states as possible.
9. Build science improvements, like national college (+50% science). You have to chop for them. ~at roughly 1500 bc or so, you'll have 3 scientists.
10. The last tech you have to research manually is Engineering. At this point you will have bulbed metal casting, researched engineering, with 4 social policies saved up (oracle or not), and 3 great scientists.
11. Using your 3 scientists, bulb steel, physics and gunpowder. Bam you're renaissance.
12. Burn your 4 policies (starts a free golden age, although you should already be in one given your high happiness at 1 city) and go to rifles.
13. Upgrade your starting troop if you can to rifle. If not, just buy one (costs 1500 in marathon, 750 in epic). You can sell luxuries/etc to buy it if necessary (but I sell my luxuries as soon as I have them, in general).
14. Make friends with military city states, as they have a chance of GIFTING YOU RIFLEMEN (lol). Maritime city states become useless near the end of your tech run.
15. Send rifle to nearest civ, and burn it down.
16. Using the money gained from looting, buy another rifle.
17. Repeat until everything is burned down.
Note the animations are pretty funny, it's basically firing squad. Oftentimes the computer units won't be allowed to move; they just get mowed down. Within 200 years of rifleman spawning, my score was higher than the combined scores of all other computers.
You've sorta 'blown your load' so to speak by doing this, so you can't really tech or build things afterwards. Just send your superunits around the map killing everything; there's nothing they can do to stop you.
I'm going to try it on deity, but I have every reason to believe it will stomp deity just as hard as any other difficulty, as the computer literally has no way of stopping a 25 strength upgraded blitzing city killing monster that 1 shots everything and attacks twice per round
This is strictly better than the acoustics slingshot, as the former doesn't help you at all against computer military, and immediately makes just about everyone declare on you, as you are high tech with no units. In this strategy, the time that you jump ages is the same time your superhero units come out, which slaughter anything the computer can throw at you (free exp baby).
The timings and pops are really tight, so you don't have much leeway to get other techs/buildings here. The problem really is that you will ONLY get 3 great scientists (including your freebie from writing) in this time, so Babylon is forced. You will only get 4 social policies from culture, so you're sorta stuck there too. And you're forced to ally maritime states since you're essentially down 2 workers in order to create more great scientists.
Please let me know any improvements or insights anyone has. If anyone wants to try the slingshot on a lower quality start, let me know how it goes (I don't know how to solve the gold problem from no luxuries. That's the trickiest).

I can safely say, Emperor is pretty darn easy in this game

This is played with Babylon (non-optional) on Emperor difficulty, standard map size, Pangaea (continents or anything really is fine), Marathon speed (i'd assume it should work on virtually any speed though, definitely Epic as that is my base speed), and everything else standard settings. NO SAVE LOADS WERE USED AT ALL as it crashes my computer, so nothing is abused. You can choose to put one city challenge as an option if you wish; it changes nothing (we'll never build a settler, and we'll raze everything).
This strategy depends heavily on your start. A weaker start is still viable, but will slow you down, probably by a couple hundred years. I'm not ashamed to admit that I restarted a whole bunch, and ended up with 2 calendar luxuries, a marble, and 2 cows, near a river with a bunch of grassland. Any similar start should achieve results like mine (it took 4 restarts to get that start, fwiw).
The basic idea is this: Researching gunpowder tosses you into the Renaissance, and if you saved up 4 social policies, you can immediate push through Rationalism and get 2 free techs, for metallurgy and rifling, to get your first riflemen. This immediately gives you a 25 strength ub3r unit, that takes essentially 0 damage from everything and 1 shots all units and towns. Give it blitz (I usually go shock 3 blitz) and it'll firing-squad computer armies no matter how many they have.
The key really is timing. I achieved Riflemen at 1100 BC, but I believe 1300 or even 1400 BC is possible. You are literally fighting warriors with a 25 strength monster, that 1 shots cities. Once promoted, nothing will even damage you, and you can hit cities twice if needed.
The basic build is as follows:
1. Look at your initial start, and figure out what techs to research/improvements to build. GOLD IS MEANINGLESS (you'll be selling luxuries to computer at roughly ~1k per luxury, you keep nothing). In that event, Wheat > Cows > Grassland~Horses. You want 3 luxuries total to sell (for 3k gold).
2. Your starting build order is basically always worker/monument. Always. The monument will build you (eventually) 3 social policies with some random culture thrown in from cultured city states that you befriend in the course of your encampment rampage. You'll never build any military units (obviously). Keep your initial one alive, you cannot lose it.
3. I like to go honor with my first social policy to get more gold from camps and to level my little spearman (he usually gets promoted by a ruin at some point). He can also take out encampments targeted by city states, which is important. I do think that Honor is suboptimal, though.
4. You need to ally all maritime city states, since you'll be running 2 scientists in capital at all times. And it's VERY important that your city grows. Also, BUY A LIBRARY ASAP. As soon as you can, buy a library.
5. After researching basic techs (remember, your goal is gunpowder, so you need all preqs to that), while researching pottery- > writing for your first scientist (horde all scientists, if you get writing at a normal time, you'll have exactly 3 total scientists to pop techs). The computer will race you on great library, so you MUST use great library for metal casting, so you must time your iron working research to be slightly before great library finishes, so you get immediately bulb metal casting.
6. Note that I get honor, so I'll never have enough culture for 5 total policies (you only get enough honor income for 4 policies). This means that you must build oracle if you want the missing policy, or skip honor. Make sure to steal a worker from a city state, you can usually do one ~100 turns in
7. In general, this means if you go oracle, you might as well get calendar luxuries. I did in fact go oracle. I think that's not necessary, and slowed me a few centuries. Regardless of what you're doing, you should chop trees like crazy, as forests are useless to us.
8. So let's say you skip honor. You're basically running around with your spearman taking down encampments (75 each on marathon, 37 on epic), and in general sitting on 1 city (that should have grown very large by now), while befriending as many maritime city states as possible.
9. Build science improvements, like national college (+50% science). You have to chop for them. ~at roughly 1500 bc or so, you'll have 3 scientists.
10. The last tech you have to research manually is Engineering. At this point you will have bulbed metal casting, researched engineering, with 4 social policies saved up (oracle or not), and 3 great scientists.
11. Using your 3 scientists, bulb steel, physics and gunpowder. Bam you're renaissance.
12. Burn your 4 policies (starts a free golden age, although you should already be in one given your high happiness at 1 city) and go to rifles.
13. Upgrade your starting troop if you can to rifle. If not, just buy one (costs 1500 in marathon, 750 in epic). You can sell luxuries/etc to buy it if necessary (but I sell my luxuries as soon as I have them, in general).
14. Make friends with military city states, as they have a chance of GIFTING YOU RIFLEMEN (lol). Maritime city states become useless near the end of your tech run.
15. Send rifle to nearest civ, and burn it down.
16. Using the money gained from looting, buy another rifle.
17. Repeat until everything is burned down.
Note the animations are pretty funny, it's basically firing squad. Oftentimes the computer units won't be allowed to move; they just get mowed down. Within 200 years of rifleman spawning, my score was higher than the combined scores of all other computers.
You've sorta 'blown your load' so to speak by doing this, so you can't really tech or build things afterwards. Just send your superunits around the map killing everything; there's nothing they can do to stop you.
I'm going to try it on deity, but I have every reason to believe it will stomp deity just as hard as any other difficulty, as the computer literally has no way of stopping a 25 strength upgraded blitzing city killing monster that 1 shots everything and attacks twice per round

This is strictly better than the acoustics slingshot, as the former doesn't help you at all against computer military, and immediately makes just about everyone declare on you, as you are high tech with no units. In this strategy, the time that you jump ages is the same time your superhero units come out, which slaughter anything the computer can throw at you (free exp baby).
The timings and pops are really tight, so you don't have much leeway to get other techs/buildings here. The problem really is that you will ONLY get 3 great scientists (including your freebie from writing) in this time, so Babylon is forced. You will only get 4 social policies from culture, so you're sorta stuck there too. And you're forced to ally maritime states since you're essentially down 2 workers in order to create more great scientists.
Please let me know any improvements or insights anyone has. If anyone wants to try the slingshot on a lower quality start, let me know how it goes (I don't know how to solve the gold problem from no luxuries. That's the trickiest).