The factotum class gains brains over brawns. Does this apply to initiative? To attack rolls?
Brains Over Brawn says this:
At 3rd level, you gain your Intelligence bonus as a modiﬁer on Strength checks, Dexterity checks, and checks involving skills based on Strength or Dexterity, such as Hide, Climb, and Jump.
So we have four qualifying categories:
Strength ability checks
Dexterity ability checks
Skill checks for Strength-based skills
Skill checks for Dexterity-based skills
If a check is one of these four things, Brains Over Brawn applies; if not, it doesn’t. Therefore:
d20SRD > Combat > Initiative
At the start of a battle, each combatant makes an initiative check. An initiative check is a Dexterity check. Each character...
An initiative check is a Dexterity check, and therefore benefits from Brains Over Brawn. The factotum adds his Intelligence bonus to initiative checks (in addition to his Dexterity bonus and any other bonus that might apply, e.g. Improved Initiative).
d20SRD > Combat > Attack Roll
An attack roll represents your attempt to strike your opponent on your turn in a round. When you make an attack roll, you roll a d20 and add your attack bonus. (Other modifiers may also apply to this roll.) If your result equals or beats the target’s Armor Class, you hit and deal damage.
This says nothing about attack rolls being checks of any kind, much less specifically one of those listed in Brains Over Brawn. Skill checks involve a bonus equal to the ranks bought with skill points in the skill; that clearly doesn’t apply to attack rolls. And attack rolls include base attack bonus; you don’t add that to any ability check. An attack roll is, in fact, its own, separate thing. Since it is not any of the four things that Brains Over Brawn applies to, it gets no benefit from that class feature.