civilization-5civilization-5-gods-and-kings
When you set up a game, you can choose which victory types you want enabled.
Will the AI ever attempt to achieve a victory type that is disabled?
For instance, if the only victory type that is enabled is domination, will every AI player attempt to go the military route and crush all other players?
My singleplayer gameplay experience suggest that all of the AI players aren't trying for all-out war.
The question you're really asking is "When does the combined culture / turn of an additional city outstrip the increase in social policy cost incurred by founding that city?"
We know that adding another city increases the culture costs by approximately 30% of the base cost (that of 1 city). Therefore:
If your maximum potential culture / turn won't increase by at least 30% due to the new city, you are hurting, not helping, the time till your next social policy.
(This may be slightly hard to calculate, and if you take too long to reach your "maximum potential culture / turn" you're actually wasting turns.)
It depends
To begin with, we need to make some assumptions:
When you found a new city, you can get its culture / turn maximized within a single turn by buying the necessary building improvements (monument, etc).
Ignore city-states, leader specific abilities, +culture social policies, and wonders. These all help produce culture, and will shift the "ideal city count" down, but do so inconsistently. To produce an "ideal" city count, we limit ourselves by era and improvements alone.
This list of social policy costs is accurate for the given parameters: medium map and normal speed.
And now, some math.
The 1st social policy costs 25 points with a single city. In the ancient era, your cities can generate 2 culture / turn due to the monument. (Remember, we're ignoring the palace for now)
This means that it will take 13 turns (Ceiling(25/2) to enact the policy, or 9 turns (ceiling (45/4) with two cities. We can continue this extrapolation -- 8 turns with 3 cities, 7 turns with 4 cities, 6 turns with 5 cities, and we finally reach diminishing returns at city 6 (also 6 turns).
For the second social policy, the ramifications of the # of cities gets magnified due to a larger starting value: One city takes 23 turns, two cities take 15 turns, three cities take 13 turns, four cities take 12, five cities take 10, and again, we run into diminishing returns cap out at at six cities (10 turns).
It is not until the 4th social policy that this trend is broken and diminishing returns end at the NINTH! city.
Remember -- this assumes that each city has a monument the minute it is founded.
Now let's say we've reached the classical age, and have temples in addition to monuments. Each city is now generating 5 culture.
The first policy takes 5 turns with a single city, 4 turns with two, and 3 with three.
What (hopefully) becomes clear is that we reached diminishing returns (4 cities as opposed to 6 cities) much faster when each individual city's contribution is higher. The more culture any one city is capable of producing, the more incentive there is to produce more cities. Even if you don't manage to build every +culture improvement immediately, you're still likely to come out ahead (as long as you're pre-diminishing returns).
So while the optimal number of cities changes due to any number of factors, you can probably safely not shoot yourself in the foot if you stay between three and six cities, with six being on the high end.
I would say that the only reason not to build on a hill is because there is a better spot. That might seem like dodging the question, but I guess the point is that while hills are good, they are not so good that there aren't plenty of situations where something else would be better. Maybe building off the hill gives you access to a resource you would otherwise miss. Maybe building on the hill keeps you away from the coast when you want to be able to build naval units. Or maybe you play a very Great Person heavy strategy and want to be by a river to build a Garden.
I almost always build my capital in the location that my settler starts, regardless of whether it is on a hill or not. Generally the starting location is dead center with a bunch of resources, and even that one turn of not building your capital does have a multiplied effect over time. So I would say that you should definitely take hills into account when planning city locations, as they are quite nice, but don't get so focused on them that you miss out on other locations that might be better.
Best Answer
Technically speaking, disabling most victory conditions makes even attempting them impossible. Turning off space race makes it so the Apollo Program is no longer buildable. Likewise turning off cultural and diplomatic vortories will disable the Utopia Project and UN respectively. Simply put, the AI will not attempt it because it cannot.
Victory conditions aside, the science, culture, and diplomcay mechanics still provide useful advantages, and the AI will pursue them based on what it perceives to be the best strategic option at the time. The personality of the leader is also a factor, which is why some civs may not seem to be gearing up for battle, or why an aggressive nation will still go to war even if domination is turned off.