I think the role of BB and CV are just like marksman and forward obsever in combat.
Here explain the meaning of them:
marksman:this job is different from "sniper".The main difference between a marksman and a normal sniper is that a marksman is usually considered an organic part of a team of soldiers, whereas regular snipers tend to work alone or with other snipers. In the military, marksmen are sometimes attached to an infantry squad where they take accurate long-range shots at valuable targets as needed, thus extending the reach of the squad.
forward obsever:an observer with forward troops trained to call for and adjust supporting fire and pass battlefield information. In the absence of a forward air controller, the forward observer may control CAS strikes.
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Forward obsever can searh where the enemy who out of the marksman's sight exactly is,and then maksman can go to a clear area take out the target.And forward obsever also can call air force to apply a long distance attack,and clear enemy's air support,protect marksman from enmey's air strike when bashing.In the other hand,marksman can protect forward obsever from the sneak attack of enemy's marksman.
Perhaps I used a sunk metaphor.But what I mean is,whatever which one is the king of battle,if CVs don't searh for their BBs and blind the enemy BBs,their BBs will down,and enemy BBs kill the CVs at last.If BBs don't rush back to help CVs which are attacked by enemy BBs/CA/ SS,u can imagine what's happen......
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In additional,your exp in a battle is not just depend on your "personal attack",and mainly depend on "team attack".So the way for CVs to get more exp is help your BBs make more attack by send your fp.During the time for a CV from lauch one wave DBs to attack or sunk ONE enemy BB,our BBs can sink 2 to 5 enemy BB(and some small ships) if have good sight.During CV's DBs coming back to their mother,BBs are still sinking enemy ships......
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My way to play CV is,FP or FP+DB/TP.When FP is low level,I will keep stay around a BBs group and use local fp to sweep up the aircraft overhead.When our team is in adventage then a will load some bombers to bomb enemy BB/CV/SS.I usually can get at least 10thousand attack,that's enough if u also shoot some aircrafts down,because that also can gain your exp.
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Finally,this is a game,if u are about to enjoy it,then u should enjoy the cooperation and communication between u and your teamates.And I really enjoy it.