The defender's advantage
In this game the defender has various advantages over the attacker:
- The defender gets an advantage in combat, in particular a 30% advantage when defending in a city, which is the normal situation.
- The defender's forces are all there to start with. The attacker has to order his forces to march into combat; maybe not all of them will arrive.
- The attacking forces arrive tired after marching; the defender is rested.
- Between each round of fighting, the defender can top up his brigades with recruits and may be able to bring in other reinforcements by rail.
- The defender can be Encamped, which uses fewer supplies than Depot.
- The defender in a city is normally in supply; the attacker may go out of supply due to the weather or enemy action. In some cases, the attacker may be inevitably out of supply because the battlefield is too far from any friendly city.
To make a successful attack:
- You need a significantly bigger or better force than the defender has. This should be obvious enough. If the defender has a high entrenchment/fortification level, in my experience you need odds of at least 4:1 to succeed; preferably more.
- The defender shouldn't have easy access to reinforcements. If he can get substantial reinforcements next turn, he'll try for a skirmish on the first turn and hit you with the reinforcements next turn.
On the eastern front, both sides can get reinforcements relatively easily, making successful attacks difficult. Exception: Strasburg is difficult for the Confederacy to reinforce.
On the western front, reinforcements tend to be fewer and further away, so attacks can work better.
Cotton has great strategical importance to this game. If the Confederacy can ship all its cotton abroad, it can get almost as many supplies as the Union. Without those cotton shipments, it's at a great disadvantage.
Both sides start the game with plenty of unused shipbuilding capacity. Both sides should plan to use that capacity immediately and build as many ships as they can. They should also probably increase their shipbuilding capacity later so that they can build more ships.
Basically, the Confederacy should build transports to ship cotton (this works best with single-ship fleets), and the Union should build warships (in fleets of at least three ships) to sink the Confederate transports. However, the Confederacy might decide to contest the seas by building warships, and the Union might want to build some extra transports for invasions by sea or river.
Kentucky and Missouri
In most cases, if you take an enemy state by taking its capital city, the enemy loses access to the manpower and supplies produced by that state; but you gain nothing yourself (unless you sack the cities).
The exceptions are Kentucky and Missouri, which will provide manpower and supplies to whichever side controls the state capital. This makes both states more valuable as they would otherwise be; and in the Confederacy they're already the second and third states by population (after Virginia).
Even in the Union, they're larger than average states, coming seventh and eighth by population.
But note that both states continue to provide a proportion of their recruits to the Confederacy even after joining the Union. These recruits appear as Arkansas and Tennessee brigades, so I suppose they stop coming if the Confederacy loses Arkansas and Tennessee.
You should be aware that cities in Kentucky and Missouri (and captured cities in hostile states) can revolt and change ownership spontaneously if there's little or no military force around. So guard the capital cities in particular to avoid major embarrassment. A mere garrison won't necessarily stop a revolt; to be safe, use a mobile unit (a corps or division). I don't think the quality of the leader matters for this purpose.
If the Confederate player has the chance to offer Sabine City to the French, doing so brings a significant advantage: he can then send cotton shipments to Sabine City, as it becomes French territory. This makes the city a more important to both sides than it would otherwise be.