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Message: <blockquote data-quote="orsal" data-source="post: 2486922" data-attributes="member: 16016">19-20/x3 is the equivalent of 2 extra damage roll, 2 times out of 20, meaning 4 extra damage rolls every 20 hits. 18-20/x2 and 20/x4 each give 3 extra damage rolls every 20 hits. Suppose your average damage is X, you have Y numbers in your threat range (e.g. Y=2 if your threat range is 19-20) and your critical multiplier is Z. Then you will get on average Y(Z-1) extra damage rolls from criticals every 20 hits, for a total of 20+Y(Z-1) damage rolls, doing on average X[20+Y(Z-1)] HP damage. You can either replace X with X+2 or replace Y with 2Y. Weapon Specialization: (X+2)[20+Y(Z-1)]=20X+XY(Z-1)+40+2Y(Z-1)Improved Critical: X[20+2Y(Z-1)]=20X+2XY(Z-1)Now solve this inequality:20X+XY(Z-1)+40+2Y(Z-1) < 20X+2XY(Z-1)40+2Y(Z-1) < XY(Z-1)40 < (X-2)Y(Z-1) So calculate (X-2)Y(Z-1). If the number is more than 40, go with Improved Critical; if less than 40, Weapon Specialization. This does ignore a few details. If you are fighting a high-AC opponent, so that you will only hit on a 20, the higher threat range doesn't do a darn bit of good. If you're fighting a bunch of 1-HD monsters, the extra +2 is likely to be enough to kill them, while the critical would be wasted, so you'd rather get the extra +2 with every hit rather than slgihtly more frequent criticals. So on the whole, Weapon Specialization comes out slightly better than this algebra shows. At least, if (X-2)Y(Z-1)=40 exactly, go with Weapon Specialization. EDIT: After posting this I looked over the weapon table to see when you might get (X-2)Y(Z-1)>40. Basically... never. If you use a greatsword with 20 Strength, then X=12, Y=2, Z=2, so (X-2)Y(Z-1)=20. Not even close. If you qualify for Weapon Specialization, it's a lot better.</blockquote>

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