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The pathfinder core books states:

"Off-Hand Weapon: When you deal damage with a weapon in your off hand, you add only 1/2 your Strength bonus. If you have a Strength penalty, the entire penalty applies.

Wielding a Weapon Two-Handed: When you deal damage with a weapon that you are wielding two-handed, you add 1-1/2 times your Strength bonus (Strength penalties are not multiplied). You don't get this higher Strength bonus, however, when using a light weapon with two hands."

So for those with an odd number for their Strength Modifier do you round up, down or do we actually do 0.5 damage?

E.g: Two-weapon rogue with str mod 1. Does str bonus for offhand damage round down to 0, up to 1 or does it deal 0.5?

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Unless something specifically says otherwise, fractions are always rounded down. See The Basics:

Rounding Fractions

In general, if you wind up with a fraction, round down, even if the fraction is one-half or larger.

Exception: Certain rolls, such as damage and hit points, have a minimum of 1.

So if you have Str 16, a greatsword will add +4 bonus to damage (rounded down from 4½).

Note that this round down, not towards zero. This matters for negative numbers.

For example, negative Strength mods don't get multiplied because the rule says not to, but if they did and you have Str 8, a dagger would add a −1 penalty (rounded down from −½).

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