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General Tabletop Discussion
*Dungeons & Dragons
The Overkill Damage Fallacy
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<blockquote data-quote="Harzel" data-source="post: 7617680" data-attributes="member: 6857506"><p>If you are going to use this reasoning, then you need to give PC 2 "credit" for kills on the half rounds because it is at that point that, as you say, PC 2 gets to start applying damage to the next enemy. For instance, instead of this entry in the PC 2 table:</p><p></p><table style='width: 100%'><tr><td>2</td><td> 0.4608</td><td> (which contributes 0.9216 to the total)</td></tr></table><p></p><p>instead you should have</p><p> </p><table style='width: 100%'><tr><td>1.5</td><td>0.288</td><td>(contrib. 0.432)</td></tr><tr><td>2.0</td><td>0.1728</td><td>(contrib. 0.3456)</td></tr></table><p></p><p>The total of these two is 0.7776, which is 0.144 less than 0.9216. That by itself brings the total for PC 2 down to ~ 1.682. The appropriate adjustments for the subsequent rounds would result in additional small downward adjustments to the total. It's just a guess, but I conjecture that adjusted in this way and carried all the way out as infinite series, the PC 1 and PC 2 scenarios actually converge to exactly the same number.</p><p></p><p>Although looking at your PC 2 table further, I'm not sure I can duplicate the calculation that leads to the numbers you have for Kill Chance on rounds 3 and 4. Could be my hand calculations are off; I will redo and check back later.</p></blockquote><p></p>
[QUOTE="Harzel, post: 7617680, member: 6857506"] If you are going to use this reasoning, then you need to give PC 2 "credit" for kills on the half rounds because it is at that point that, as you say, PC 2 gets to start applying damage to the next enemy. For instance, instead of this entry in the PC 2 table: [TABLE="width: 500"] [TR] [TD]2[/TD] [TD] 0.4608[/TD] [TD] (which contributes 0.9216 to the total)[/TD] [/TR] [/TABLE] instead you should have [TABLE="width: 500"] [TR] [TD]1.5[/TD] [TD]0.288[/TD] [TD](contrib. 0.432)[/TD] [/TR] [TR] [TD]2.0[/TD] [TD]0.1728[/TD] [TD](contrib. 0.3456)[/TD] [/TR] [/TABLE] The total of these two is 0.7776, which is 0.144 less than 0.9216. That by itself brings the total for PC 2 down to ~ 1.682. The appropriate adjustments for the subsequent rounds would result in additional small downward adjustments to the total. It's just a guess, but I conjecture that adjusted in this way and carried all the way out as infinite series, the PC 1 and PC 2 scenarios actually converge to exactly the same number. Although looking at your PC 2 table further, I'm not sure I can duplicate the calculation that leads to the numbers you have for Kill Chance on rounds 3 and 4. Could be my hand calculations are off; I will redo and check back later. [/QUOTE]
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