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I didn't really notice any differences though on a run where I had max luck though...
you could have gotten 20 coins or maybe +1 move or +1 puzzledamage or +1 spelldamage or just another 5 coins, ey so , so , so very , very lucky, indeed.
Critical Hit:
(Luck_Level) * 0.05 + (Trinkets) > (Random Value Between 0 and 1)
So you have really random chance to do Critical Hit if you have less than 20 Luck (or 17 luck with Target Trinket).
Room Reward:
It is very simplified version as there are other factors that affect getting a "Jackpot" after clearing a room.
(Luck_Level) * 0.1 > (Random Value Between 0 and 1)
As you can see, a lot of depends on just luck (yours, not Bumbo). So at this state I can say it may be ok to go into Luck stat but there is a chance like you will have 5 Luck and gain absolutely nothing. But hey, it is Luck. so you may gain something or not. Life is tough.