Exercises
Naval Excercises are practice matches where you combat the fleets of other Admirals.
Benefits of Participating
The first and most obvious benefit of exercises is that participation is required for several quests. The exercise list is updated twice daily, so you get ten chances total to complete all your daily quests.
Exercises are also a very safe way of gaining experience for your ships. Ships cannot sink, and are automatically repaired back to their pre-exercise status after a battle has concluded.
Finally, winning exercises generally results in your ships becoming sparkly. This can be useful if you wish to run long expeditions, or run repeated sorties.
When to Run Exercises
Generally, if the sum of the levels of the ships in the top two slots in the enemy fleet is roughly fifty or more, you can expect a base experience of about 500.
At low Admiral Levels, players have very low level ships, so the experience gain from exercises tends to be bad (sometimes far lower than running sorties). Simply put, it may not be worth running many exercises until you reach higher levels. However, there is usually one admiral in your list that is three or four times your level. Even though you will likely be slaughtered by a superior force, the high base experience still means that you come out with a great deal of experience.
Fleet Composition
As always, the flagship receives bonus experience. Thus, it makes sense to place a ship you wish to level in the flagship slot.
Running carriers in exercises is not recommended. Any competent Admiral will equip their fleet with lots of anti-air, which can utterly decimate your planes. A fleet equipped with type-3 ammunition can easily cost you 200-300 bauxite in planes. If you wish to level a carrier in exercises, consider equipping guns on them instead of planes.
Battleships should form the backbone of your fleet. Their high HP and armor means that they can take a beating, and their firepower makes them effective against all ship types. The number of battleships you use should depend on the number of battleships and carriers in the enemy fleet.
The air combat phase and the opening torpedo salvo can often determine who wins the fight. To this end, make sure you equip sufficient anti-air to neutralize your opponent's carriers. Fielding Kitakami and Ooi is also generally a good idea, as they can very easily oneshot ships.
If the enemy has many light carriers, light cruisers, or destroyers, consider using a sub. As in sorties, anything that can target the sub, will, so you can effectively divert a significant portion of the enemy's firepower to the sub. Light cruisers and destroyers will continue to target the sub (if it is still alive) in night combat, so use this to your advantage.
If the enemy fleet has a sub supported by a fleet, consider running Kitakami and Ooi. Their initial torpedo attack will prioritize enemy ships over the sub, and they have reasonably high ASW. Adding another good ASW ship such as Isuzu Kai 2 is not a bad idea as well. If the enemy fleet has two subs, this strategy still applies, but you may need some luck to get an S rank.