[The Panther]

The heavy cavalry provinces are one of the hardest ones to take, especially early in the game. There are three level of HC provinces where they have increasing levels of armor. The only way to know which you are up against is to attack with a scout on retreat and examine the armor on the cavs during the battle.

The lowest level of armor is not that much harder than the standard Heavy Infantry province. The middle level is getting very tough, and the highest level is even tougher than the knight provinces.

On the other hand, tribal warriors and tribal archers is quite easy. They suffer from the usual low morale problem of barbarians. Try to get them to retreat with your own archers guarded by high protection infantry spaced around the battlefield as targets for the enemy arrows. It is not unusal to take such provinces with 0-2 troops lost, especially if your infantry comes equipped with a shield (which protects from incoming arrows).