with each stack of luck you get one item to be rarer
if you have 4 luck rings the rewards from winning battles will always have a legendary and if you have more than 4 you will get multiple things to be not a common
pretty sure it doesn't work like that, the luck rings specifically state that they increase luck after the combat, which would mean that the luck stat is increased permanently no matter if you have that original luck ring or not
also I'm pretty sure thejaspel stated in another comment that legendary items wouldn't be guaranteed based on luck