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[3.5] Crit stacking?
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<blockquote data-quote="Mike Sullivan" data-source="post: 1004671" data-attributes="member: 9824"><p>Well, I sort of am. I'm assuming that whatever AC the target is, you require exactly the same numbers to hit with a scythe as you would with a greatsword -- so it's the same factor on both sides of the equation, so I didn't bother to put it in in the first place.</p><p></p><p></p><p></p><p>Goodness. Feeling demanding today?</p><p></p><p>Sure, whatever:</p><p></p><p>1.15 ( 5 + x) > 1.1 (7 + x)</p><p><em>Explanation: 5 is the average damage on 2d4, the base damage die for a falchion or scythe. x is what we're solving for -- the damage bonus that makes it worthwhile to use the falchion or scythe, in the expected-damage-scenario. 7 is the average damage on 2d6, the base damage die for a greatsword. 1.15 is the multiplier which represents the effects of a critical hit for an 18-20/x2 weapon or a 20/x4 weapon. 1.1 is the multiplier which represents the effects of a critical hit for a 19-20/x2 weapon. So, the inequality that we're solving for is what damage bonus x makes it true that the falchion or scythe's total expected damage per hit is higher than the greatsword's expected damage per hit.</em></p><p></p><p>5.75 + 1.15x > 7.7 + 1.1x</p><p><em>Explanation: I expanded the multiplication on both sides, using the, oh, hell, it's been like ten years since I took algebra, that rule that says: x(a + b) = xa + xb.</em></p><p></p><p>.05x > 1.95</p><p><em>Explanation: I subtracted 1.1x from both sides of the equation, and also subtracted 5.75 from both sides of the equation. If you want, you can expand this out into a bunch of steps:</em></p><p><em></em></p><p><em>5.75 + 1.15x > 7.7 + 1.1x</em></p><p><em>5.75 + 1.15x - 1.1x > 7.7 + 1.1x - 1.1x</em></p><p><em>5.75 + .05x > 7.7</em></p><p><em>5.75 + .05x - 5.75 > 7.7 - 5.75</em></p><p><em>.05x > 1.95</em></p><p></p><p>x > 39</p><p><em>Explanation: I multiplied both sides of the equation by 20 (or divided by .05, whichever you prefer.)</em></p><p></p><p>Thus, as we check out the original equation, we see that it holds true for all x such that x > 39. Since x must be an integer (you can't have fraction damage bonuses), that means that the lowest x for which it's true is x = 40. Thus, if you have a +40 damage bonus (or more), and do not have either keen or improved critical, assuming that your chances to hit are the same in both cases, it's advantageous to use a scythe or falchion instead of a greatsword against opponents susceptible to critical hits. If your damage bonus is +39, then they're exactly the same. If your damage bonus is +38 or less, it's more advantageous to use the greatsword.</p></blockquote><p></p>
[QUOTE="Mike Sullivan, post: 1004671, member: 9824"] Well, I sort of am. I'm assuming that whatever AC the target is, you require exactly the same numbers to hit with a scythe as you would with a greatsword -- so it's the same factor on both sides of the equation, so I didn't bother to put it in in the first place. Goodness. Feeling demanding today? Sure, whatever: 1.15 ( 5 + x) > 1.1 (7 + x) [i]Explanation: 5 is the average damage on 2d4, the base damage die for a falchion or scythe. x is what we're solving for -- the damage bonus that makes it worthwhile to use the falchion or scythe, in the expected-damage-scenario. 7 is the average damage on 2d6, the base damage die for a greatsword. 1.15 is the multiplier which represents the effects of a critical hit for an 18-20/x2 weapon or a 20/x4 weapon. 1.1 is the multiplier which represents the effects of a critical hit for a 19-20/x2 weapon. So, the inequality that we're solving for is what damage bonus x makes it true that the falchion or scythe's total expected damage per hit is higher than the greatsword's expected damage per hit.[/i] 5.75 + 1.15x > 7.7 + 1.1x [i]Explanation: I expanded the multiplication on both sides, using the, oh, hell, it's been like ten years since I took algebra, that rule that says: x(a + b) = xa + xb.[/i] .05x > 1.95 [i]Explanation: I subtracted 1.1x from both sides of the equation, and also subtracted 5.75 from both sides of the equation. If you want, you can expand this out into a bunch of steps: 5.75 + 1.15x > 7.7 + 1.1x 5.75 + 1.15x - 1.1x > 7.7 + 1.1x - 1.1x 5.75 + .05x > 7.7 5.75 + .05x - 5.75 > 7.7 - 5.75 .05x > 1.95[/i] x > 39 [i]Explanation: I multiplied both sides of the equation by 20 (or divided by .05, whichever you prefer.)[/i] Thus, as we check out the original equation, we see that it holds true for all x such that x > 39. Since x must be an integer (you can't have fraction damage bonuses), that means that the lowest x for which it's true is x = 40. Thus, if you have a +40 damage bonus (or more), and do not have either keen or improved critical, assuming that your chances to hit are the same in both cases, it's advantageous to use a scythe or falchion instead of a greatsword against opponents susceptible to critical hits. If your damage bonus is +39, then they're exactly the same. If your damage bonus is +38 or less, it's more advantageous to use the greatsword. [/QUOTE]
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