Crusader Kings II

Sword of Islam and the Republic DLCs only enable you to play muslims/merchant republics. Everything else was built in with the patch. The only DLC that expands on the default Christian feudal lord experience is Legacy of Rome, which lets you have Retinues (essentially standing armies).

You can outsiege the AI by splitting your army up into smaller units and sieging a bunch of provinces at once.

If a battle will be close, try to have it so you're defending over a river crossing or on hills/mountains (use terrain mode to check). Straights and amphibious landings are similar.

Stacking cavalry will cause massive the enemy to take massive losses in the pursuit phase of battle (when they're retreating).

If you press a courtier's claim and they're either a de jure vassal or of your dynasty, they become/stay your vassal. You can invite claimants to your court, marry them matrilineally to your kinswomen, and press their children's claim when they inherit it, netting you land a full duchy at a time.

Holy wars against infidels and heretics are another good way to nab whole duchies, but those can get out of control if their neighbors join in to defend the faith.

If you're kingdom - or empire-level, it can be very profitable to pick a coastal mayor and turn him into a merchant republic. Grant him the county and duchy he lives in. They won't get more powerful by inheriting other vassal titles, and they pay a big pile in taxes.

You can build additional holdings in a province if there's room. Coastal cities can net you some nice taxes, while baronies (castles) net you more troops.

Scheming isn't a particularly effective way to break up factions. If a vassal likes you (positive opinion), shares your religion/culture, and doesn't want any titles from you (no "desires X" opinion maluses), and isn't a claimant to your titles, they will leave their faction. Solve what you can with handing out titles and bribing people, and kill or imprison the rest.

Character Traits

Certain genetic traits have a small chance of being passed down from parent to child. Most of these are negative, such as Clubfooted or Imbecile, but there's a handful of positive ones (Genius, Quick, Strong and Attractive) that one should keep an eye out for when looking for good spouse candidates.

The Focus and Education systems of the Conclave DLC can have a major impact on character traits. To wit:
- For children, certain childhood traits like Rowdy and Indolent are worse than others as they can develop into Dull and Slothful respectively which hamper further learning. Curious meanwhile is largely a positive childhood trait as it can at best develop into Shrewd and at worst Cynical which is not terrible.
- A child's guardian can intervene with a child's development if they have an appropriate positive trait. As a notable example, a Diligent guardian (a very desirable trait) has a chance to turn a Fussy child into a Diligent one which is not normally possible.
- For adults, in addition to their other effects different Focuses can impact different traits. Theology focus can potentially remove some nasty negative ones such as Slothful or syphilis (Great Pox), Carousing has a chance of removing Stressed or Depressed, War or Hunting can remove Weak or Frail, etc. Focuses also often lead to permanent stat ups and can even upgrade your education, so try out different things.

Good traits for councillors include Content (much friendlier to you) and Shrewd/Quick/Genius (can fire additional positive events for capable councillors). Diligent is also a good trait for Chancellors, Marshals and Spymasters especially. Avoid Deceitful councillors if you can, especially Spymasters.