Sneak Dice and Luck

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Would Tymora's Melody or the Luck spell raise sneak dice? So for each 1d6 of dice you would roll one dice higher :2, 3, 4, 5, 6, 6

If so it would help Bard/Wizard/Sorceror synergize with a Sneak Dice rogue build. I am thinking of making a character with very high sneak dice by using the method of creating new party members throughout the story and start with a rogue so that character gets high level.

If it works then if you have one of those for every sneak dice that is 4.33 per dice and if Tymora Song and Luck spell stack (3,4,5,6,6,6) then you get 5 damage per dice. You would end up stronger than a pure rogue in sneak dice because this would give you multiplicative interaction between luck and each extra sneak dice.

 

iirc luck helps only base damage (and crit range) but not extra damage, so I do not expect it to help sneak dice