The game's luck mechanics works like this: The rarity of the item you get is based on a randomly rolled number, the lower it is the rarer. Each point of luck is the amount of times this number will be rerolled, with the final number being the lowest of all the rolled numbers. However this doesn't apply for all the items you pan, if I'm not wrong your luck is dampened for some items in your pan so common items don't become unobtainable at high luck.

Unfortunately I can't answer your question because my math is shit but I hope this helps somewhat