I just did a Luck test to see if Luck affects how quickly you find items, or the quality of items that you find, and it doesn't seem to affect them. One dweller had natural 10 Luck, the other dweller had natural 10 Luck with +5 Luck gear, for 15 Luck, i sent them out within 2 minutes of each other. I frequently checked them, and counted the amount of items each had, and it was roughly the same, within 1-2 items of each other. Luck definitely does affect how quickly they collect Caps though. By the time the 10 Luck Dweller had collected 6,000 Caps, the 15 Luck Dweller had collected 9,000 Caps.

Why wouldn't you try it with 1 luck? Wouldn't that make for stronger evidence?

Not sure why they have all these ways to get more caps anyhow, though. By the time I learned how the game worked, I had hundreds of thousands more than I knew what to do with.

Because i was also trying to determine whether putting Luck gear on your Dweller did any good for gathering items. Who sends out 1 Luck dwellers, other than people who don't have Game Rooms yet?

From what I've read, Luck =Caps, Perception = Loot.

point is, if your 1 luck dweller got a lot less items, you'd have your proof that it matters.

Pretty sure it's just caps though. This game is ridiculous like that. 1 luck would actually be just fine, if that's the case. Why even bother wasting time on building it up.

I also didn't have any 1 Luck Dwellers at the time. I had just finished training up a batch of dwellers to 10 in all SPECIALs.

Although, i do wonder if Luck helps you beat enemies in the Wasteland. Past a certain point with other SPECIALs and Weapon Damage though, extra Luck probably wouldn't help anymore.