hi there,
What is the right balance between corner profit and central influence. Is there a general theory that describes what balance one can maintain out of fuseki to get a balanced game?
Are there certain kind of move orders or joseki that one can adopt to get the kind of position (like central influence or corner profit or both) that s/he wants out of the opening?
that doesn’t explain how balance between two can be achieved.
Well, I’m just a weak player but I think the Fourth Line simply IS the line of balance between territory and influence—the more stones in a row there are on the 4th line, the harder it will become for the opponent to live underneath, and the harder it will be to resist it on the outside
Hello nullx002,
My favorite opening is the Orthodox Opening, because I get some territory and some influence.
http://senseis.xmp.net/?OrthodoxFuseki
Humble thoughts, feel free to disagree: A territorial player often needs to invade or reduce an opponent’s moyo, while an influence player can build large moyo or create a daring battle. The right balance seems to have little to do with a perfect game, yet a lot to do with ones strengths and weaknesses.
The right balance is, like, fifty fifty. 
Seriously, this is an incredibly complex question I can’t answer. I doubt that anyone can adequately answer this question in general.
My working hypothesis is that there are no fixed order of moves to achieve balance you speak of applicable to every situation. I can strive for it, but only creatively.
Moreover, I seek to be balanced with my opponent. He has territory? A want the same amount. He has power? I want the power as well.
See http://senseis.xmp.net/?Balance for concepts that can be in balance.
People have been debating this for thousands of years, and the jury is still out.
A common belief is that the right balance is between 4th line influence and 3rd line territory. However in two recent games against Lee Se Dol, the program AlphaGo proved that you could get a balanced game even when exchanging 5th line influence for 4th line potential territory.
Keeping this in mind, studying joseki will give you more tangible examples of what are considered fair exchanges.