I appreciate the question. But you are simply failing to grasp the fundamental concepts of a random number generator at work. All of your "Whys" and "whats" fall into essentially crap results on the RNG. To be more exact, luck doesn't even exist in the real world. Its more or less a delusion brought on by our perception of random events and occurrences we try to reason. There is no such thing as good luck, or bad luck, its for lack of better word, superstitious bull.
But thats another discussion. Regardless I'll rebut your point 1 and 2 for you.
COR isn't luck, you have 6 options, 1 through 6 on a JA activation. These are programmed in a way where it randomly selects 1 through 6. Nothing in the game increasing your odds of hitting 11, its just random. Even abilities like "Snake Eye" have mathematically quantifiable %'s to hit you to 11. Its right in the Merit descriptor. (though I'd bet SE programmed in rolling double 6 to be 99% chance)A: That Thief and Corsair are even in the game. They are nothing but basically luck driven jobs and if luck has absolutely nothing to do with their abilities then they aren't supposed to be a part of the game.
THF is also not even a little luck based since as i explained, luck is little more than a delusion of our attempts to explain random chance. THF works on a % system like anyone else. Drops aren't 100%, so what it comes down too is random numbers. I'll give an example to help explain it.
Gil drops from enemies with a variable of 10-100 gil a kill. Gilfinder adds 50% more gil, so in the end, the game chooses a gil amount through as random as math can make it, and Gilfinder adds 50%. this explains why sometimes a THF gets 150, sometimes they get 15. Its not luck, its math at work.
Also math at work lady. If an item has 20% chance to drop, thats an average, not an absolute. but i'll give you an example.B. Well the fact that some, even thieves, have a tough time getting some things to drop and stealing things while others easily get it to drop/ steal it.
Say obtaining a drop is based on a /random system of rlls. 0-999. Getting a D.ring is rolling 0-50, but with TH, THF rolls 5-12 times depending on their TH proc. They have 12 chances to roll a 0-50, where as any other person has 1. But as with random numbers, each chance is equal in terms of how it will roll. You may have 12 chances, but landing on one of the 1000 numbers doesn't remove it, so your odds are still 50 in a 1000, or 1 in 20. a THF just gets a 1 in 20 shot 12 times instead of 1.
But to make it less complicated. I /random and land on 14, I win. THF rolls 12 times and gets 129, 983, 583, 287, 87, 908, 300, 398, so on... and not a single 0-50... His LUC stat didn't fail, its just the random number generator didn't hit the desired outcome. Its not more "Luck" than tossing a coin and getting heads twice in a row and your friend getting tails twice in a row... Its just chance.
So in the end, no quantifiable evidence of a luck stat exists, so far everything you suggest is easily and well explained through the series of mathematics formula that already exist in the game. It's easy to mistake random chance with luck if you believe luck can actually be a thing, but its not, and most if not all things are easily explained by math, especially things like games and computers which are almost entirely derived from complex or not-so-complex mathematics.
-Also, I remember a Dev response a long time ago, possibly a live letter or even before that back in the Allakhazam days where someone asked about a luck stat. Think they mentioned stuff like always drinking a can of pepsi before fighting Fafnir, and so on. SE almost word for word said "There's no way to program Luck, but that shouldn't stop you from opening your pepsi" or something to that extent. They came out and said "luck doesn't exist"... Where? Idk... I'm sure enough time on Google could bring it up.
Edit: I'd also like to mention most of the discussion on Luck Stats were about the time COR was released, and most if not all in the COR section back when people suspected LUC would be added as a brand new stat. No dice.
Edit:found it - the 2007 Fan Festival!
In regards to items like Four-Leaf Mandragora bud and so forth, items considered "lucky"
Plain and simple.Do the luck items have any effect on drops and do they have to be consumed?
There is no hidden effects programed for these items. But there is no program for luck.

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