Luck has alot to do with drops, especially gold chest drops.
If you wander in with low luck, you have an extremely low chance of getting that item.
Chapter 9 is gold since its so quick to finish, best get a friend to farm for you on that one.
Chapter 10 is the easiest since you can change your gear to luck gear before opening the chest.
trust me, you best be having luck gear if you wanna get those rares.
Each point of luck increases the chance of a drop or soul appearing by 0.1%. This means that at 30 luck, your chance has increased by 3%. HOWEVER, the thief ring has a MASSIVE effect on this. With 4.1% chance of a item drop due to luck (YES that takes the lck points given from the thief ring into account), the % skyrocketed to 6.9% for ONE ring. I have yet to get two thief rings but I am working on this now. If anyone has doubts, put on the gambler glasses and see for yourselves. Soul ring does the same for souls, 2 increases it even more.
This all sounds like good news........... BUT, the problem with this is that luck brings up the % appearance rate of ALL items and ALL souls in game. Which obviously if applied to ALL the chests drops does NOT work, since the % would then be over 100%. So one might assume that they did something akin to this:
//PSEUDO CODE:
GENERATE RANDOM REAL NUM FROM 0-100
If (Num < (1 * % chance)) {drop rare}
else if (num < (5 * % chance)) {drop soul}
else if (num < (15 * % chance)) {drop semi rare}
else {FUCK YOU! TRASH DROP!}
//end
So while it increases your chances of NOT getting trash... your chance of getting a rare drop, relative to other non purple chest drops (what I call TRASH) is still about the same as before. UNLESS they apply some kind of internal multiplier to rare drops to increase it with a thief ring on.
..................My point in all that babbling above? This is ALL anecdotal, and maybe, sort of, kind of, guessing on our parts. Without a look at the source, we will never know. But so far, most tests done by players on the net have all shown the same results: that luck has a VERY minor effect on rare chest item drops.

And while we would all like to say "logically the programmer would make it so luck would increase the chance of getting a good chest drop" keep in mind that people are not always logical in their actions.
On that note, I should also state that I have 9 ryukotsuki souls from 108 kills with no soul eater rings for 7 of them. And I generally just use my best gear attack and defense wise, ignoring luck. So my % at that time would be only about 1.5% for each to get them. Yet I have a ton of them. I have also gotten a valmanway*2, sonic boots *2, winged boots *6, claimh solais, valmanway+1, kaiser knuckle+1, thief ring, r. count soul, 6 dracula souls, death scythe, yusutsuna+1, and berserker mail, in this same manner.
Yet with luck equips, I NEVER get SQUAT. O_o So I have little faith in them.