Lots of different answers here, but I'll try to tailor my reply to the Emperor level. I am generally not a fan of very specific and detailed answers when it comes to tips, so I'll try to explain how you might want to start to reason instead, because the value of correct reasoning keeps being valid as you progress further up the difficulties.
As you mention, you struggle with killing your neighbour. This is typical of the experience of jumping from King to Emperor. The reason for this is that one extra city more or less doubles the potential of your neighbour (Emperor AI gets two settlers, not one),
much more so that the other % bonuses they get. This means they tech faster off of two starter cities, they produce twice as fast, and it doubles the chance that you will run into walls (which will come earlier as well). As such, the major difference between King and Emperor is that you will automatically start falling behind your neighbour, you cannot just "wing it" anymore and win. This is the point where you need to start thinking about an actual strategy
Assuming you want to kill your neighbour, you thus have to start thinking about opening strategy. This is because if you fail that rush (which might work at King), you are set back
majorly if you fail to rush your first target. You just wasted all your production for no result, and your target now has more cities than, will out-tech you and and now also has an army. This is obviously not good, and you have to avoid that scenario.
I am not going to tailor a specific opening for you, but rather lay out the general principles you should be thinking about. In order to kill a neighbour successfully and avoid the scenario above where you run into a developed neighbour that has more or better units than you (especially bad if they have walls), you have to consider the central question: How do I ensure that my attack becomes a success in the first place?
There are a few key components to consider here, and they will guide you into choosing the appropriate opening principle for a rush:
- Hit sooner. The goal here is to hit before your neighbour has too many units, a better tech level (which will soon translate into better units than you), and especiallymanages to get walls.
- If you want to do this, you got to look at how much production you can get in the short term. Favourable terrain with lots of production is good, as well as settling another 1-2 cities to have more cities to produce from. Policy cards like Agoge allows you to produce faster as well, if you can get it. Try to cut down on anything that isnt strictly necessary, like Granaries/Monuments etc. Your goal is to overwhelm your target, fast.
- Hit harder. The goal here is signicantly pump out stronger units than what you would ordinarily have at this point in the game. There are many ways to do this:
- You pick a civ with a strong starting combat bonus or early unit (Gaul or Nubia for instance).
- You beeline science fast (only if you have strong adjacencies) and beeline a key unit. Swordsmen with battering rams are very solid, but Horsemen or even Archers can be fine as well.
- Seize a ripe opportunity.This is perhaps the most fuzzy principle, but it's very key. One example of a ripe opportunity (to attack) is when your neighbour has a weak/no army, struggles for some random reason (floods wiped everything, barbs are sieging them), and that they settled their cities on flat, open land with few/no mountains or lakes around it. Especially open cities like these are very easy to run down. Compare it to trying to attack a city with only one tight valley style entrace between mountains, where the terrain is hills and forest. The difference is like night and day.
- Turn on leader icons that show yields! This shows who is vulnerable, as amy strength and science per turn are strong indicators for short- to medium term vulnerability. A target with 5 science per turn and 30 army strength is a cakewalk to mow down (it means he will not get classical era tech anytime soon, and he has roughly a warrior and a half in terms of units), whereas you should be very careful with a target who has 30 science per turn and 200 army strength (about 10 warriors worth) in the ancient/early classical era.
- Use at least one unit to scout your invasion point! You will get to know how the terrain is (very important, as explained above), you know how many units he has and where, and any other important factors.
Teching is the key to the game IMHO ! The faster you get ahead in tech, the easier it will be to overwhelm the other civs, be it military or most other ways. Entering into the fight for a religion sets you back so much on that part.
This is true if you want to speedrun the game, but this is not the case here. Remember that he just made the jump from King to Emperor, which is one of the most rough difficulty spikes to learn to handle, as this is roughly the point in the difficulty curve where you have to start playing somewhat meta in terms of opening strategy (of which there are many viable ones!), and forget about "winging it" like you can easily do at King level without much thought. The reason why religion is good (as mentioned by
@kaspergm ) is because it is one of those opening strategies that is very
consistent (assuming you get the pantheon you desire), and it keeps working consistently into the Deity and Deity++ level (for those who play that mod).
You cannot just blindly tech up at the hardest difficulties, because there might not be enough science available (science adjacencies are the big factor here), and there might be a window of opportunity that you have to or should exploit. That could be a vulnerable neighbour with flat terrain who is struggling, or you are about to get boxed in and risk losing cities on loyalty. You really have to weigh your options here, and as such you can't assume you'll be able to freely play for science. An inland flat plains start with no mountains/geothermal fissures and a vulnerable neighbour is almost forcing a rush over playing for early science (what science?). True, you can often get good science opportunities and it is the fastest way to play, but if either of those are not true, then why limit yourself with such a narrow opening?
The religion opener is not strong on Deity or above due to Work Ethic (though it certainly helps), but due to Crusade. Crusade is the fastest consistent way any vanilla civ can get a "higher tech level" in terms of combat strength, and is faster than science. The combination of speed and consistenty is the thing that allows this rush to work so well on the hardest difficulties. One missionary is often enough to flip the first city, at which point you snowball (you can pillage for more afterwards). There is no reason to focus on religion after the first neighbour is dead if you dont want to, the point is just to mow down the first neighbour with cheap units that act as strong units and set up a strong base from there. This rush hits before you hard tech units through science, which is why it works well if you need a consistent opener. And you can perfectly well transition into a peaceful game after that, as additional cities and more space has more than made up for the religion detour.
For the OP: I do not recommend playing the religion opener until you get a bit higher in difficulty level, because it involves a lot of finer aspects and mandates a bit of min-maxing behaviour.
use the lens filter and settle the cap right next to an AI's cap, DOW and fortify the Warrior appropriately.
