Luck

Luck is a measure of a creature's destiny. Some creatures are more bound by the weave of time to experience fortunes and prosperity, while others are forced by fate to squalor and despair.

High luck scores are represent those who gamble and never lose, gain opportunities few can dream of and creatures that may survive incredible odds stacked against them.

Low luck describes those who may have lost their family fortune, who have a major problem of freak accidents or those who never really can catch a break in life.

Lucky

Whenever you make a roll, you can spend one Luck point to roll an additional roll. You can choose to spend one of your Luck points after you roll the die, but before the outcome is determined. You choose which of the rolls is used.

Maximum number of Luck points = your Luck modifier

You can also spend one Luck point when an attack roll is made against you. Roll a d20, and then choose whether the attack uses the attacker's roll or yours. If more than one creature spends a Luck point to influence the outcome of a roll, the points cancel each other out; no additional dice are rolled.

You regain expended Luck points when you finish a long rest.

Random Rolls

Whenever a random die roll is called for that does not use any proficiency bonus or ability modifier, and where your personal skill, Background or History has no bearing on its result, you may add or subtract your ability modifier to the roll.

However, when your ability modifier is negative, the DM chooses whether to add or subtract from the roll. For example, if you have a luck modifier of +2 and you roll on a loot table, you may add or subtract +2/-2 to the roll. However, if your luck modifier is -2, the DM make the addition or subtraction, always in the most unfavorable way.

Other examples include: directional d8 rolls, random encounter tables, random loot tables, monster targeting, etc.