My opinion, to get the most damage for Card Strike, One Pair + Lady Luck, you must go for 4114 and since the formula for these skills are:
(AP + HV × 8) × m
so it means AP gives more damage than HV since 1 level AP = 4 while 4 levels HV = 1 BUT you don't get a buff that multiplies AP.
While Fullhouse, for me, is more of a skill for 1144 since LK determines its success rate AND LK is already used in the formula for damage so its hitting two birds with one stone. Besides, what's good with 4114 hax damage FH if most of the time it fails and recoils on YOU and you get the hax damage?
Four of a Kind is based on DA so I guess its for 1144. Also need confirmation since I haven't tried if it has to be 4 of the same kind. Wiki only says 4 enemies, NOT 4 of the same type enemies.
Good luck and hope to see your Gambler in action!