The Fallen Lands
The Thief gets a Luck Die that goes up with level. On any roll the character makes after seeing the roll, the Thief can spend one or more points of Luck (deciding how many to spend before rolling any of the Luck Dice) and roll a Luck Die per point, with the result being added on to the original roll. The Thief recovers Level * 2 points of Luck per night, back up to the original Luck score. When rolling the Thief’s body, always roll versus the current Luck score, not the original.
Level and Luck Die
Luck die is same as level, e.g. a level 3 Thief rolls a d3