In combat, an actor's luck factor is a number determined by the LUK difference between them and their attacker/target. This number's minimal value is 0.5 and its maximum value is 2. Luck factor is computed this way:
Actor's luck factor = min(2,max(0.5, 1+ (Actor's LUK - attacker or target's LUK) * 0.025))
Luck factor in combat
Luck factor determines evasion when attacked. The target's base evasion is multiplied by their luck factor.
Luck factor has a role in inflicting status effects. If the base probability of inflicting a status effect is not 100%, this probability gets multiplied by the attacker's luck factor.
Finally, luck factor intervenes in the random part of damage.