The game states that:
"Luck is about a ninja's odds. The word is that ninjas with high luck values tend to get more breaks during battles."
It also increases your chance of encountering fortunate events during missions.
Most items do not increase your luck. Ninja tools are more likely to increase your luck than weapons and armor. Some items that increase luck are:
Novice Compass - (training mission award)
Fallwind Scarf - (challenge award)
Dragon Kite - (treasure award)
Sorcerer's Bells (mission award)
Crescent Kunai - Bronze quality or higher (Obtainable only during Jiraiya's Last Dance event)
Reef Nunchuk - (Obtainable only during Jiraiya's Last Dance event)
Think of Tomorrow - (Only obtained if you have been playing since prior to Events)
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