From the rules you gain a +1 luck bonus on attack and weapon damage rolls for every three caster levels you have (at least +1, maximum +3).
We're sort of in disagreement as to which caster level the +2 and +3 bonus kicks in.
Is it: +1, +1, +1, +2, +2, +2, +3. Meaning caster level 1, 4 and 7?
Or is it: +1, +1, +1, +1, +1, +2, +2, +2, +3. Meaning caster level 1, 6 and 9?
Both make sense, but there are many other spells with similar caster dependent powers which are better defined. This is not one of them.
A thread search left it unanswered and our cleric is currently 7th level and want to use it with Imbue with Spell Ability on the monk.
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It's 1, 6, and 9. It used to go up t +6, making the spell much more useful throughout play, but they changed it to cap at +3, like a lot fo other Cleric spells, it tends to cap out quickly.
If it said you get a +1, +1 every 3 caster levels after 1st, it would be @4 th and 7th like you said in the first example.