20 cities in 50 turns is good enough to win you any game.
I think you're slowing yourself down getting horsemen though. That's a lot of hammers or gold that could be used on settlers or archers. Think of each of those horsemen as a settler you could be building, since they both cost 20 hammers and 40 gold to rush in the ancient.
Irrigation in 33 turns (700 BC) is pretty slow actually, and to only have 4 cities at this point of the game is not good for the Romans.
Currency by 37 turns is pretty slow too.
Ususally you want irrigation around 20-25 turns, maybe 30. but currency around that time too. Ususally in FFA, someone is racing to irrigation, and lots of times it's already had by 1500BC.
I'd shoot for at least 10 cities by 0 AD, but preferably about 15, that are well defended with legions and archers.
Give up on those horsemen man. You can take those AIs later with legions if you want, for cheaper, better free techs, and bigger cities, all while building your own empire up. Just think about it. For each horseman you build, that's another city. So you could have in 15-19 turns by your same calcuations:
6 cities all 2 pop
warriros at chokes
100 gold
bronze working
If you don't expand before you get five techs, then settlers are going to cost more gold. If you only have 4 cities by the time you have 6 techs, you're expansion is gonna be slowed down. I usually like to have at least 5 cities, prefferably more by the time I get to 5 techs. But often I'll not go for irrigation at all, just keep spamming settlers at 40 gold, and then get my five techs, saving a few of those settlers to settle after I get 5 techs to get 3 pop in my new cities.
but the main thing is, each horseman you build is another city. So almost to justify making a horsearmy, you'd have to take 3 cities at 2 pop, or 2 cities at 3 pop to make up for the lost expansion. There is some usefulness to horsemen, and they can be good protection after you finish rushing, and they can help you get gold quicker, but I still think it's a big waste of time in the ancient era for the romans, and if your army gets killed, then you've really lost time.
