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General Tabletop Discussion
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Fixed damage per attack
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<blockquote data-quote="CapnZapp" data-source="post: 4585813" data-attributes="member: 12731"><p>Are you trying to determine the average result of <em>roll a d6; if you "don't like the result", roll again and keep the new result</em>?</p><p></p><p>Let's assume you'll want to re-roll all 1s, 2s and 3s (because the average result of a d6 is higher than that) but that you'll never want to to re-roll any 4s, 5s or 6s (again because you've already rolled higher than the average). Obviously, in some cases where you "only need one more point of damage" and your current result is effectively worthless this won't necessarily be true. But in general, this will allow us to compute the highest new average of this kind of roll.</p><p></p><p>And it is very straight-forward:</p><p></p><p>1 => 3.5</p><p>2 => 3.5</p><p>3 => 3.5</p><p>4 => 4</p><p>5 => 5</p><p>6 => 6</p><p></p><p>The average of this strange beast of a die roll is 4.25. An improvement upon the standard d6 with 21.4%.</p><p></p><p>A quick check confirms that this increase is relatively constant for all die sizes, increasing very slowly with bigger dice. (It's +23% for the d12, for instance).</p><p></p><p>From a purely statistical standpoint, it would stand to reason to have Pray For More give +25% more damage once per encounter. </p><p></p><p>However, this doesn't take into account the fact that you might want to use Pray For More only when you roll really badly. To mimic the choice you have with the original power, upping the damage to +50% doesn't seem unreasonable in practical play.</p></blockquote><p></p>
[QUOTE="CapnZapp, post: 4585813, member: 12731"] Are you trying to determine the average result of [I]roll a d6; if you "don't like the result", roll again and keep the new result[/I]? Let's assume you'll want to re-roll all 1s, 2s and 3s (because the average result of a d6 is higher than that) but that you'll never want to to re-roll any 4s, 5s or 6s (again because you've already rolled higher than the average). Obviously, in some cases where you "only need one more point of damage" and your current result is effectively worthless this won't necessarily be true. But in general, this will allow us to compute the highest new average of this kind of roll. And it is very straight-forward: 1 => 3.5 2 => 3.5 3 => 3.5 4 => 4 5 => 5 6 => 6 The average of this strange beast of a die roll is 4.25. An improvement upon the standard d6 with 21.4%. A quick check confirms that this increase is relatively constant for all die sizes, increasing very slowly with bigger dice. (It's +23% for the d12, for instance). From a purely statistical standpoint, it would stand to reason to have Pray For More give +25% more damage once per encounter. However, this doesn't take into account the fact that you might want to use Pray For More only when you roll really badly. To mimic the choice you have with the original power, upping the damage to +50% doesn't seem unreasonable in practical play. [/QUOTE]
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