Starting as dumb as they come when I first played Civ 5 I found Rome to be a really strong civ for beginners esp after the patch moved iron working earlier in the tree - build warriors, find iron, mine it, research to iron working, upgrade warriors to legions, research to math, build ballistas, upgrade promoted ones to Trebuchets when you open physics (, run down the honor tree, go out and conquer as soon as you have a few legions and a balista or two. Take your promoted legions and upgrade to longswordsman for a unit that can handle early gunpowder units. And you can save some gold as your ballistas are almost as strong as Trebuchets so don't need early upgrade. Raze and build cities or annex, add buildings you have in your capital. Or puppet if that's your style. Simple and effective
Before you master stuff like how to be sure to bulb astronomy before the sixth policy opens so as to get rationalism early - with the GS you got from the PT which you completed with the GE you got from the HS which you were able to open quickly with a GL/NC start plus the liberty finisher - (which you accelerated by allying early with a cultural city state) or whatever - well Rome is a civ you can handle and win with using basic principles to king and beyond (well beyond - I think Madjinns first or second deity victory video is Rome).
Agree with the other commentators to win taking advantage of Romes UU you have to strike early and hard and expand your civ early to get a dominant position while your UUs gives you the military advantage against other melee units and cities. Once you get the early advantage use the UA to get the cities up and productive and hope you have got your civ so big and the others so small that you can maintain your dominant position as your UUs become irrelevant.
To beat Rome - take away their iron if you can, play defensive early - even the not too smart AI can carve you up if you go after Ballistas and legions offensively with weak units in the early going. If you have horses and are playing against the AI you will have opportunities to pick off poorly defended ballistas with mobile units - and by the time you have Chivalry/machinery open you can handle anything Rome has got. Rome is like a heavyweight boxer in the early going - if Rome can get close - a few legions adjacent to your city and a ballistas one more space away - it will knock you out. Ranged and mobile units to keep it away
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