There may be occasions when a completely random event is called for. For example, if the characters all draw straws, who gets the short straw could reasonably be established by assigning everyone a number and rolling an appropriately-sized die.
For a more generic system for determining how fortunate a given character is, just roll 2d10 and consult the below chart.
Example: when the party starts travelling cross-country, the GM decides to randomly roll to see how good the weather is. He rolls 2d10. A really low roll will indicate bad weather (with a roll of 2 indicating that travel has to halt completely until the bad weather clears) while a higher roll indicates better conditions. A roll of 20 could indicate a really pleasant, nearly perfect day that gives them bonuses for any travel rolls that they have to make.
Don't overuse luck rolls. They should be a source of inspiration for your game, not a way to compensate for lack of direction.
Optional Edge: Lucky
Your character is unusually lucky. Fortune favors them. Whenever the GM asks you to make a luck roll for a random occurance, you get a bonus die for the roll.
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