coming from an expansionist background, I've found OCC actually easier than TCC/FCC/SCC. The main reason for that is that in OCC, you have several special condions that don't apply in any other games. The main one of course is Shakespeare's Theatre eliminating any possibility of
ever having an unhappy citizen in your civilization. Remove the unhappiness factor and OCC on diety actually becomes somewhat easier than in other levels because of your reliance on AI gifts. Other factors involve more skewed demographics so that you appear weaker or stronger than you should to the AI.
Anyway, to take a stab at a difficulty relationship, i would say it is parabolic (quadratic), at least from the perfectionist standpoint, with the most difficult being around 2-3 cities since you no longer have the OCC special advantages, and yet don't have the power and flexability of larger civs.
From an expansionist/conqueror standpoint, i would venture that it is logarithmic, since it is very difficult to conquer with only 1 city, but there is a lot of diminishing returns for each new city after a while.
Of course since there are so many different ways to play and win the game, you really have to stick to a single approach, or your hardness graph will turn out to be rather flat (linear)
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April Cantor: Sire, in order to expand further we must first gain favor of the King
SCG: darn, I've never really got the hang of that tribute thing, guess it will be a long time until i make prince
*goes off and starts gifting gold and techs*