Each forum has an predetermined inventory of .moar files each with a set drop percentage. Increasing or decreasing Luck has a direct effect on the drop percentages. An offsite spreadsheet has details on this.
Furthermore, like Charisma, it raises the value of the junk received daily. It appears that 4 points of Luck are equivalent to a single Charisma point as far as value is concerned, but this is both unconfirmed and uncertain.
See How Attributes Work for more details.
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