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*Pathfinder & Starfinder
Vorpal Uber Weapons?!?
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<blockquote data-quote="DracoSuave" data-source="post: 4343751" data-attributes="member: 71571"><p>Yes but the weapon damage rolled goes up. In the end, that's what we're concerned with is multiple dice being involved with damage, which comes up -often- at epic tier.</p><p></p><p>Often enough you -could- call it 'every single damage roll'.</p><p></p><p></p><p></p><p></p><p>I just did the algebra on the average weapon damage for individual die rolls that don't explode vs. die rolls that do explode.</p><p></p><p>Like right now.</p><p></p><p>Let d = the number of sides on that die.</p><p></p><p>Average die roll for a singular die that does not explode on a max roll is 1+d/2.</p><p></p><p>Average die roll for a singular die that -does- explode on a max roll is d.</p><p></p><p>The increase in damage then is equal to d - 1+d/2 = d - 1/2 - d/2 = d/2 - 1/2.</p><p></p><p>So... the increase in damage from vorpal on a single die is d/2 - 1/2.</p><p></p><p>What does this mean? This means that the larger the die size, the greater the advantage from vorpal.</p><p></p><p>For a 1d12 weapon, this turns out to be 12/2 - 1/2 = 5.5 extra damage per die.</p><p></p><p>For a 2d4 weapon, each die is individually exploding, so you get 2 X (4/2 - 1/2) = 2 X (1.5) = 3 average damage difference.</p><p></p><p>To -truly- compare, a 1d8 damage weapon's difference is (8/2 - 1/2) = (4 - 1/2) = 3.5 average damage difference.</p><p></p><p>Seems that this mysterious fear of exploding d4 damage becoming out of hand is completely unfounded based on the math.</p></blockquote><p></p>
[QUOTE="DracoSuave, post: 4343751, member: 71571"] Yes but the weapon damage rolled goes up. In the end, that's what we're concerned with is multiple dice being involved with damage, which comes up -often- at epic tier. Often enough you -could- call it 'every single damage roll'. I just did the algebra on the average weapon damage for individual die rolls that don't explode vs. die rolls that do explode. Like right now. Let d = the number of sides on that die. Average die roll for a singular die that does not explode on a max roll is 1+d/2. Average die roll for a singular die that -does- explode on a max roll is d. The increase in damage then is equal to d - 1+d/2 = d - 1/2 - d/2 = d/2 - 1/2. So... the increase in damage from vorpal on a single die is d/2 - 1/2. What does this mean? This means that the larger the die size, the greater the advantage from vorpal. For a 1d12 weapon, this turns out to be 12/2 - 1/2 = 5.5 extra damage per die. For a 2d4 weapon, each die is individually exploding, so you get 2 X (4/2 - 1/2) = 2 X (1.5) = 3 average damage difference. To -truly- compare, a 1d8 damage weapon's difference is (8/2 - 1/2) = (4 - 1/2) = 3.5 average damage difference. Seems that this mysterious fear of exploding d4 damage becoming out of hand is completely unfounded based on the math. [/QUOTE]
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