1. Contested Rolls
Several statistics in the core Pathfinder game start with a base of 10. These stats are the equivalent of taking 10 on a d20 roll for that stat. For this campaign, those stats will be rolled instead of using that base 10.
Example: A fighter in full plate with no DEX bonus usually has an AC of 19 (base 10 + 9 armor). In this campaign, each time that fighter is attacked, he rolls a d20 and adds his +9 armor bonus. This ends up with an AC ranging from 10 (1 + 9) to 29 (20 + 9).
This rule pertains to the following stats:
- Armor Class
- Spell Save DC
- Combat Maneuver Defense
2. Wounds and Vigor
As the rule from Ultimate Combat (PRD Link)
3. Circumstance Bonuses
In order to encourage role-playing and imagery, any extra description of actions taken can result in circumstance bonuses for any rolls involved in that action.
Example A: The player of a fighter says his character swings his sword at an enemy and rolls to hit. There is no circumstance bonus for this attack.
Example B: The player of a fighter says “He sweeps his sword through the air at the enemy’s head, letting out his aggression with a bloodcurdling scream!” This player will get at least a +1 to his to-hit roll for enhancing the story.