Do Luck-J and Mug synergise?

Question

I have found a Luck-J scroll using Boko and I have added it to my GF. I am interested if it will work with Mug and allow me to mug rarer items from enemies easier?

What things does Luck effect?

Answer 1

No. Luck will not improve your ability to mug.

Maybe the logic is that mugging is a matter of a character's skill more than luck. If you want to improve your mugging, improve your speed.

Luck affects accuracy, evasion, critical% and Odin/Gilgamesh battle appearances.

According to several sources (final fantasy wiki, a gamefaqs question, and an informative gamefaqs thread):

Luck affects the character's hit accuracy (unless the character already has 255% hit rate), evasion, critical hits, and increases the chances of Odin and Gilgamesh appearing during battle.

The battle mechanics guide is very relevant here:

The accuracy formula is stated as:

Hit% = (AttackerLuck / 2 + AttackerHit - TargetEva - TargetLuck)

Luck will increase your chance to hit the enemy with an attack and since mug is treated as a normal attack, higher luck means you will probably mug in fewer attacks because you won't miss them altogether quite as often. Luck is not known to affect the mug calculations however:

Mug is a normal physical attack that has the added effect of stealing items.

Mug% = (MugDifficulty + (MuggerSpd / 2) + 1) / 256 * 100

MugDifficulty is different for every enemy, but will be 128 or higher most of the time (giving you a base Mug% of 50% or higher, which is further increased by your Spd) If you successfully mug an enemy, the game decides which item slot's item you get:

rnd = [0..255]
if (rnd < 178) Slot = 0
  else if (rnd < 229) Slot = 1
    else if (rnd < 244) Slot = 2
      else Slot = 3

Probability of..

Slot 0           178/256    69.5%
Slot 1            51/256    20%
Slot 2            15/256     5.8%
Slot 3            12/256     4.7%

Higher slots usually contain better/rarer items. If you have the Rare Item party ability, the probabilities are modified:

rnd = [0..255]
if (rnd < 128) Slot = 0
  else if (rnd < 242) Slot = 1
    else if (rnd < 261) Slot = 2
      else Slot = 3

Probability of..

Slot 0           128/256    50%
Slot 1           114/256    44.5%
Slot 2            14/256     5.5%
Slot 3             0/256     0%

Since you can never get values higher than 255 from the RNG, it's impossible to get Slot = 3 with Rare Item.