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[UnOrthOdOx]

The only thing I'll add, after looking at the save:

You should be expanding quicker. Whether that means conquering others or building more settlers. (eventually you'll learn to do both by this point in the game)

COTTAGES, as mentioned. But, it cannot be stressed enough. Money is the all important key in CIV.

CATAPULTS. Where money is the all important resource, Catapults (and their successors) are the all important unit. Grab your religion if you must, and Praetorians are all nice and good, but catapults and other artillery are THE unit of CIV warfare.

[BobTheBackpack]

How do I know when I have expanded enough?

[Solver]

It's a skill that comes with time... but early on, it's when there are no more good spots for peaceful city placement or when you're running low on money (like have to lower research to 60% to stay afloat), whichever comes first.

In your save, there was, at least, that city spot to the north, which could have been grabbed peacefully. Americans were faster than you, but Philadelphia is also in a nice location. Anyway, 3 cities are not enough. On Warlord, sure, they're enough to build some Prateorians and conquer the Americans entirely in the above save, but generally, it's not enough.

[Krill]

Actually I'd say the #1 mistake is lack of workers; 2 workers per city is (up to Prince at least) the ideal number. I often get 2 workers before my first city, If I have enough tiles to improve. 2 Workers for 3 cities is just bad.

[Krill]

You haven't built a granary in any city...yet are building courthouses. Courthouses are probably the worst building in the game, apart from when you really need them. Usuaklly just better to work 2 extra cottages instead of building a courthouse.

Start a new game an emphasize building more workers and a granary in every city (before obelisks most of the time), and also emphasize building more cottages. Almost every floodplain ought to be cottaged (and that holds true for MP) except for maybe 1 flood plain if there is no other food resource around.

[guermantes]

Krill, do you really need that many workers? I used to build workers aplenty when I was new to this game but the more I read in these forums the more I understood that the general recommendation is 1 worker per 2 cities. So I started playing like that and am much better now, to the effect that I am trying my luck in my next game on Prince level.

[couerdelion]

Let's split the difference. 1 worker per city is enough to be going on with as a general rule. After you start paying for them you want to make sure they are being used and not all standing idly by.

With war, you can pick up workers from rival civs to supplement your own builds.

In some situations, you may want more (eg lots of jungles to chop)

[UnOrthOdOx]

1/city is what I generally shoot for, but I wouldn't argue with 2/city in some cases, to ensure every tile being worked is an upgraded one in a high food situation, chop jungle, etc.

[Metaliturtle]

2 Workers per city is also helpful for building a road to your newest city in enemy hands (his capital). Praetorians are more effective when they move at 3x speed, and those extra workers can go out with a guard pretty easily.

[zeace]

I think the number of workers you need per city is very different right at the start of the game. 2 worker for your starting city makes sense as there's nothing improved yet. 3 workers for your first 2 cities makes sense too because your new city needs a couple, but your capital probably has most of it's worked squares improved so there's less work to do there.

I usually aim for around 8 workers for 8 cities, 12 workers for 16 cities, and then about 1w/2c after about 25 cities. Also, I'll let my workers ratio drop if I'm starting a war and expect to win a few. Times when I'll increase the ratio include when I have an important worker tech coming (plantations, railroads, etc...)

So I don't think there's a simple rule of thumb.