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Are Composite longbow adjusted with +1 STR Bonus considered masterwork and if so do they give the +1 To hit that masterwork weapons usually haves ?

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No, they aren't masterwork by default.

Nothing in the composite longbow's statblock says it must be masterwork (same for a composite shortbow). Compare this to magic weapons:

All magic weapons are also masterwork weapons, but their masterwork bonuses on attack rolls do not stack with their enhancement bonuses on attack rolls.

Additionally, a composite longbow costs 100gp (a composite shortbow is 75gp) and each point of strength rating costs an additional 100gp (or 75gp for the shortbow). The total cost of a composite longbow with a +1 strength rating is only 200gp, less than the 300gp cost — on top of the base price of a weapon — to get a masterwork version.

If you were to get a masterwork composite longbow (starting from 400gp, plus 100gp x strength rating), you would get a +1 enhancement bonus to attacks as per usual, independent of the bow's strength rating.

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    \$\begingroup\$ Further evidence is that the +1 and +2 STR variants' STR component are less than the 300 gp masterwork component of a weapon. \$\endgroup\$
    – minnmass
    Commented Apr 14 at 3:05
  • \$\begingroup\$ @minnmass Good point. The entire cost of a +1 strength rating bow is less than 300gp; I'll add that to the answer. \$\endgroup\$
    – Shivers
    Commented Apr 15 at 16:53

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