Luck

Luck is the statistic that determines a character's chance of being inflicted by a status inflicting problem attached to an ability used against you, such as Sleep and Stun.

It does not increase your own chance of inflicting said status effects onto opponents, contrary to common belief. Having a luck rating of 40 or higher provides immunity to Poison, Venom, Haunt, Death Curse, the target's HP being instantly reduced to 1, and being forced out of battle (Like the Djinni Gale's attack would otherwise have a chance of doing).

Boss Luck Ratings
This means that any boss with a luck rating below 40 is in fact able to be affected by any of the above status conditions. All bosses in Golden Sun other than Saturos, the final encounters on top of Venus Lighthouse, and Deadbeard have luck ratings that would somewhat discourage trying to instant-kill them or afflict them with Venom, but it is otherwise quite possible to cause these effects to trigger on these bosses. Though in The Lost Age on the other hand, the only bosses that aren't immune to these status conditions are the Chestbeaters at the beginning, the Sea Fighter minions of the Briggs encounter, the Knight minions of the Moapa encounter, and the Ball minions of the Star Magician encounter.

Ways to increase Luck
Unlike your other Statistics, Luck does not increase as you level up. Luck cannot be temporarily changed during battle, either. The only ways you can change an Adept's Luck are:
 * Using Lucky Pepper on the Adept.
 * Setting certain Djinn to an Adept.
 * Changing your Character class to one with a higher Luck rating.
 * Equipping luck-boosting equipment.