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Luck positively influences all your dice rolls. For instance, if your attack can deal 50-80 damage, with high Luck you're more likely to roll numbers closer to 80 than 50. On the opposite, if you have a 34% chance on a Willpower save throw - so the system rolls a d100 and you have to score less than 34 to pass, with high luck you're more likely to get lower numbers on the roll.