Here is the last one of the videos about the SPECIAL system used in Fallout 4, which is about luck.
More information.
More information.
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In FO3, Luck affected the quality of loot and increased the likelihood of finding more ammo when combined with the Scrounger and Fortune Finder perks. It's unclear from the Fallout Wiki if this is true with high Luck without those perks.
Those two perks require a base level of 5 Luck and a player level of either 5 or 8.