In my opinion this is the best single thread on this subject:
https://www.matrixgames.com/forums/tm.asp?m=3939691
(Note post #2) and very good advice on AA and BB’s in the thread as well.
As Alfred has stated there is not a correct answer.
For me the question about how many carriers should be in an Allied task force is not mainly about
the coordination penalty. As stated in the thread it is not really a penalty just the chance of
A penalty. I agree it is not a real big deal. The word “penalty” seems to scare some players.
The computer makes a random die roll for a percentage chance of penalty.
A configuration which might be good in one situation may not work well in another.
There are a large number number of factors involved other than coordination.
Weather, Task force leader, detection level, pilot experience, Air group set up, Search settings,
Plane types, Cap percentage, Task force total AA, Reaction settings, Air group leadership, etc…
You need to evaluate your situation, the enemy, and the year you are in.
I agree with Bullwinkle that in 1942 your main concern is defense not offense.
Don’t worry so much about offensive coordination just don’t stick your neck out unnecessarily
and reducing your cap in 1942 by using just one CV can be fatal as noted in post #11.
As the Allies if you lose your carriers in 1942 you are at the total mercy of the Japanese.
Another major factor for me is the size of the task force footprint.
The more ships you have in a task force the greater the chance of detection.
Also the chance that if the enemy gets that good detection he may get a more
accurate spotting report on your task force composition.
This can be good or bad depending on the situation because it can be a major factor
In whether he will accept combat in a PBEM game. Fog of war ever present.
In other words, if he sees multiple carriers in your task force he may decline combat and run away.
(This factor more important after you start getting the Essex class carriers in 1943)
But in 1942/early 43 he may also come after you in a big way depending on the situation.
He could win big and sink multiple Allied carriers.
1942 is a critical year for the Allies. Going with one CV per task force can be fatal.
Going with multiple CV’s in a task force can also be fatal in a large way.
Welcome to the Pacific War.