Does luck affect the drop chance of Living hat, Garbage hat and or Tiger hat?

[Plura]

I've been grinding for those exact hats for so long, and the wiki doesn't say anything about luck having an affect. Which may mean that luck doesn't have any affect, but I just wanted to be certain.

[BahamaLlama]

I'm pretty sure luck affects the Living hat and the Tiger hat, as they're both drops from mobs (Or fiber in the case of Living hat). The garbage hat isn't though, as each morning is when the items from the garbage cans are chosen, rather than every time you click on the. Exactly the same as dig spots

[Jigain]

https://mouseypounds.github.io/stardew-predictor/

This one will predict the garbage hat.