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Your damage x 2
Your sword's damage is most likely 1-8 so It would crit for 2-16(1-8 x 2)
Thus on a roll of 19 to 20 (10% of the time) you will 'threaten' a critical hit. In actual fact, a second roll to-hit must be made to 'confirm' the crit. This second roll need only successfully hit, not be high enough to crit again. If the crit is confirmed, your weapon will do double (x2) its normal damage (not shown here.. it's in the previous line of the weapon description) of 1d8 or 1-8, which would be 2-16.
Base Damage Rating: 7.15
Damage: (3-10) [1d8] + 2 Slash, Magic
Critical Roll: (10%/6-20) 19-20 / x2
The Base damage rating is a mathematical average damage per hit including criticals (I think it assumes all crits are confirmed). However, it does NOT include things like any elemental or other damage that may be listed below, nor feats or enhancements you may have that would increase the damage, crit chance, etc.
Under Damage:, the +2 is the weapon's enhancement bonus, which gives +2 to hit and damage.
The part in [ ] is known as the Base Damage, or [W]. Aside from a few named weapons, the [W] will be the same for all weapons of the same type, but higher-level ones may have a multiplier (e.g. 2.5[1d8] ). Thus the (3-10) is the base damage including the enhancement bonus.
We've already discussed the critical roll above. I'll just note that one number now looks different. the '6-20' is the '3-10' doubled, i.e. it includes (and doubles) the enhancement bonus as well as the [W].
Btw, "19-20 / x2" is known as a 'crit profile'. Aside from some named weapons, crit profiles are also weapon-type specific and consistent. All non-named longswords will have the same base damage and crit profile.
You're very welcome. It's worth understanding how it works, so that you can intelligently compare weapons.
Thank you for this useless piece of information.