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<blockquote data-quote="Ovinomancer" data-source="post: 7618634" data-attributes="member: 16814">Dammit!&nbsp; My thumb keeps hitting the laugh button.&nbsp; Honestly, this is embarrasing.Yeesss... but is this a useful question?&nbsp; I mean, further to the point that I'm pretty sure you can't sum the odds of &quot;kill this round&quot; and have it turn into &quot;average rounds to kill.&quot;&nbsp; Only pretty sure because I haven't worked out if this is one of thise things where it happens to simplify out that way.&nbsp; I don't see it, but I could be missing something.But, back to &quot;average rounds to first kill&quot; being a useful question to illuminate overkill.&nbsp; I don't think it is, because it doesn't address overkill but instead shows that single big hit is swingier (ie flatter) than 2 little hits.&nbsp; This is somewhat obvious if you think about it as PC1 has a much flatter arc over the rounds due to only one variable per round while PC2 is curvier due to doubling the number of tests.&nbsp; This is like showing that a d12 is likelier to roll a 10 or higher than 2d6.&nbsp; You've just shown that, over time, you're more likely to roll a 10 or higher on d12 than on 2d6 (1/4 vs 1/12).I think that an overkill analysis might be better approached as an effective average damage.&nbsp; Say you do damage x, with probability p of hitting.&nbsp; Your target has hp y.&nbsp; The number of hits needed to kill is the ceiling of (y/x).&nbsp; Your effective maximum damage average is then y/(ceil(y/x)), which I'll call z. Note that if x=y, this is just x.&nbsp; Then, your average effective damage is p(z).Example.&nbsp; You do 10 damage (x).&nbsp; You hit 60% of the time against this foe (p).&nbsp; The foe has 8 hp <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f44d.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt="(y)" title="Thumbs up&nbsp; &nbsp; (y)"&nbsp; data-smilie="22"data-shortname="(y)" />.&nbsp; Ceil(y/x) = ceil(8/10) = 1.&nbsp; Z is then 8/1, or 8.&nbsp; Ave effective damage is .6(8) or 4.8 and not .6(10) = 6.&nbsp; 8/4.8 is average 1.67 rounds to kill.Going the other way, if y is 12, ceil(y/x)=2.&nbsp; Z is now 6, and average effective damage is 3.6. 12/3.6 is 3.33 average rounds to kill.</blockquote>

[QUOTE="Ovinomancer, post: 7618634, member: 16814"] Dammit! My thumb keeps hitting the laugh button. Honestly, this is embarrasing. Yeesss... but is this a useful question? I mean, further to the point that I'm pretty sure you can't sum the odds of "kill this round" and have it turn into "average rounds to kill." Only pretty sure because I haven't worked out if this is one of thise things where it happens to simplify out that way. I don't see it, but I could be missing something. But, back to "average rounds to first kill" being a useful question to illuminate overkill. I don't think it is, because it doesn't address overkill but instead shows that single big hit is swingier (ie flatter) than 2 little hits. This is somewhat obvious if you think about it as PC1 has a much flatter arc over the rounds due to only one variable per round while PC2 is curvier due to doubling the number of tests. This is like showing that a d12 is likelier to roll a 10 or higher than 2d6. You've just shown that, over time, you're more likely to roll a 10 or higher on d12 than on 2d6 (1/4 vs 1/12). I think that an overkill analysis might be better approached as an effective average damage. Say you do damage x, with probability p of hitting. Your target has hp y. The number of hits needed to kill is the ceiling of (y/x). Your effective maximum damage average is then y/(ceil(y/x)), which I'll call z. Note that if x=y, this is just x. Then, your average effective damage is p(z). Example. You do 10 damage (x). You hit 60% of the time against this foe (p). The foe has 8 hp (y). Ceil(y/x) = ceil(8/10) = 1. Z is then 8/1, or 8. Ave effective damage is .6(8) or 4.8 and not .6(10) = 6. 8/4.8 is average 1.67 rounds to kill. Going the other way, if y is 12, ceil(y/x)=2. Z is now 6, and average effective damage is 3.6. 12/3.6 is 3.33 average rounds to kill. [/QUOTE]

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