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General Tabletop Discussion
*Pathfinder & Starfinder
Careful Attack/Sure Strike: A mathematical analysis
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<blockquote data-quote="eamon" data-source="post: 4489883" data-attributes="member: 51942"><p>Whoops, I didn't see this post, so I missed replying.</p><p></p><p>It is <strong>NOT</strong> the case that Careful attack and Twin strike are inextricably linked such that upping Careful Attack's bonus will simply either leave Careful attack worse or make it absolutely better. Even in terms of expected damage, there exist bonuses such that high AC creatures will be more usefully hit with careful attack and low AC creatures with twin strike.</p><p></p><p>Image a creature you hit on all attacks unless you roll a one. Against such a creature, and arbitrary Careful attack bonus would not suffice to make careful attack competive with Twin Strike. Conversely, consider a creature which twin strike cannot hit (i.e. a natural 20 is a non-crit hit). Clearly, a +20 careful attack bonus would make careful attack <u>much</u> more attractive against such a creature. In other words, if careful attack's bonus is high enough, then vs. difficult to hit creatures it will deal more damage than twin strike, and vs. low-AC creatures twin strike will deal more damage.</p><p></p><p>Where is the crossover point? Well, that depends on a number of factors.</p><p>Without hunter's quarry it's pretty readable:</p><p></p><p>P = B - cM * C</p><p></p><p>where P is the non-crit hit probability (excl. careful attack's bonus) such that careful attack is balanced with twin strike, B is the bonus granted by careful attack, cM is the crit-multiplier (i.e. crit avg damage divided by non-crit avg damage) and C is the crit chance.</p><p></p><p>This formula assumes that the bonus B+P+C < 1, i.e. that natural 1 rolls don't need to be taken specially into account for careful attack and that similarly the critical chance for careful attack and twin strike are identical (per strike), which is the case when twin strike and careful attack both hit the AC on any critical roll (20,19-20,18-20 depending on the situation). In short, this formula assumes that twin strike hits normally at least on a crit and careful attack misses normally on a 1.</p><p></p><p>The formula gets a lot more complicated when you take hunters quarry into account, but it's not truly relevant; the conclusion remains the same.</p><p></p><p>It is possible to balance careful attack and twin strike by raising careful attack's bonus sufficiently far; if you do so, careful attack will be good vs. high-AC targets and twin strike vs. low-AC targets (which seems to make sense to me).</p></blockquote><p></p>
[QUOTE="eamon, post: 4489883, member: 51942"] Whoops, I didn't see this post, so I missed replying. It is [b]NOT[/b] the case that Careful attack and Twin strike are inextricably linked such that upping Careful Attack's bonus will simply either leave Careful attack worse or make it absolutely better. Even in terms of expected damage, there exist bonuses such that high AC creatures will be more usefully hit with careful attack and low AC creatures with twin strike. Image a creature you hit on all attacks unless you roll a one. Against such a creature, and arbitrary Careful attack bonus would not suffice to make careful attack competive with Twin Strike. Conversely, consider a creature which twin strike cannot hit (i.e. a natural 20 is a non-crit hit). Clearly, a +20 careful attack bonus would make careful attack [u]much[/u] more attractive against such a creature. In other words, if careful attack's bonus is high enough, then vs. difficult to hit creatures it will deal more damage than twin strike, and vs. low-AC creatures twin strike will deal more damage. Where is the crossover point? Well, that depends on a number of factors. Without hunter's quarry it's pretty readable: P = B - cM * C where P is the non-crit hit probability (excl. careful attack's bonus) such that careful attack is balanced with twin strike, B is the bonus granted by careful attack, cM is the crit-multiplier (i.e. crit avg damage divided by non-crit avg damage) and C is the crit chance. This formula assumes that the bonus B+P+C < 1, i.e. that natural 1 rolls don't need to be taken specially into account for careful attack and that similarly the critical chance for careful attack and twin strike are identical (per strike), which is the case when twin strike and careful attack both hit the AC on any critical roll (20,19-20,18-20 depending on the situation). In short, this formula assumes that twin strike hits normally at least on a crit and careful attack misses normally on a 1. The formula gets a lot more complicated when you take hunters quarry into account, but it's not truly relevant; the conclusion remains the same. It is possible to balance careful attack and twin strike by raising careful attack's bonus sufficiently far; if you do so, careful attack will be good vs. high-AC targets and twin strike vs. low-AC targets (which seems to make sense to me). [/QUOTE]
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Careful Attack/Sure Strike: A mathematical analysis
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