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General Tabletop Discussion
*Dungeons & Dragons
Cost/Benefit Analysis of True Strike
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<blockquote data-quote="fuindordm" data-source="post: 6440451" data-attributes="member: 5435"><p>Valid point above about the relative benefits of casting TS vs casting another cantrip.</p><p>And yes, it is also generally better to go nova and cast one's most powerful spells as often as possible.</p><p>The scenarios above are only indicative, as a real combat has many more variables and possible choices.</p><p></p><p>Let's run the numbers on a slightly more concrete situation:</p><p></p><p>The party is fighting a gnoll captain plus several mooks, and the mooks are holding the line thanks to the captain's leadership. The wizard wants to hurt the captain, but doesn't want to go nova since it's just the first encounter of the sortie. So the option of spending two spell slots is off the table due to PC preference.</p><p></p><p>Let's compare these 4 scenarios:</p><p>S1: TS followed by Acid Arrow (average 15 damage)</p><p>S2: Fire bolt (average 5 damage, not 5.5, to make the math a little easier), followed by Acid Arrow.</p><p>S3: as S1, but with disadvantage (for example, because the captain is invisible)</p><p>S4: as S2, but with disadvantage</p><p>Let's say the wizard needs a 11 to hit. </p><p>Define ED = expected damage</p><p></p><p>S1: ED = P(hit)*15 = 15*[1-(11-1)^2/400] = 15*300/400 = 11.25</p><p>S2: ED = 0.5*5 + 0.5*15 = 10</p><p>S3: ED = 0.5*15 = 7.5</p><p>S4: ED = [(21-11)^2/400]*5 + [(21-11)^2/400]*15 = 0.25*20 = 5</p><p>So in both cases casting TS is better than casting a cantrip for damage to set up your high-level spell, under the assumption that you only want to spend one high-level slot.</p><p></p><p>What if captain is easier to hit? Let's make the roll to hit 6 (75% chance) Then:</p><p></p><p>S1: ED = 15*[1-(6-1)^2/400] = 15*375/400 = 14</p><p>S2: ED = 0.75*5 + 0.75*15 = 15</p><p>S3: ED = 0.75*15 = 11.25</p><p>S4: ED = [(21-6)^2/400]*20 = 11.25</p><p></p><p>What if the captain is very hard to hit, for example because he has cover? (target roll is 16)</p><p></p><p>S1: ED = 15*[1-(16-1)^2/400] = 15*175/400 = 6.56</p><p>S2: ED = 0.25*5 + 0.25*15 = 5</p><p>S3: ED = 0.25*15 = 3.75</p><p>S4: ED = [(21-16)^2/400]*20 = 1.25</p><p></p><p>So the trend is pretty clear: if you want to conserve spell slots, and have time to set up an attack, TS compares pretty favorably to leading with a damaging cantrip. Yes, you need to balance that against the need to finish the combat earlier rather than later to mitigate damage to the party, and so on.</p></blockquote><p></p>
[QUOTE="fuindordm, post: 6440451, member: 5435"] Valid point above about the relative benefits of casting TS vs casting another cantrip. And yes, it is also generally better to go nova and cast one's most powerful spells as often as possible. The scenarios above are only indicative, as a real combat has many more variables and possible choices. Let's run the numbers on a slightly more concrete situation: The party is fighting a gnoll captain plus several mooks, and the mooks are holding the line thanks to the captain's leadership. The wizard wants to hurt the captain, but doesn't want to go nova since it's just the first encounter of the sortie. So the option of spending two spell slots is off the table due to PC preference. Let's compare these 4 scenarios: S1: TS followed by Acid Arrow (average 15 damage) S2: Fire bolt (average 5 damage, not 5.5, to make the math a little easier), followed by Acid Arrow. S3: as S1, but with disadvantage (for example, because the captain is invisible) S4: as S2, but with disadvantage Let's say the wizard needs a 11 to hit. Define ED = expected damage S1: ED = P(hit)*15 = 15*[1-(11-1)^2/400] = 15*300/400 = 11.25 S2: ED = 0.5*5 + 0.5*15 = 10 S3: ED = 0.5*15 = 7.5 S4: ED = [(21-11)^2/400]*5 + [(21-11)^2/400]*15 = 0.25*20 = 5 So in both cases casting TS is better than casting a cantrip for damage to set up your high-level spell, under the assumption that you only want to spend one high-level slot. What if captain is easier to hit? Let's make the roll to hit 6 (75% chance) Then: S1: ED = 15*[1-(6-1)^2/400] = 15*375/400 = 14 S2: ED = 0.75*5 + 0.75*15 = 15 S3: ED = 0.75*15 = 11.25 S4: ED = [(21-6)^2/400]*20 = 11.25 What if the captain is very hard to hit, for example because he has cover? (target roll is 16) S1: ED = 15*[1-(16-1)^2/400] = 15*175/400 = 6.56 S2: ED = 0.25*5 + 0.25*15 = 5 S3: ED = 0.25*15 = 3.75 S4: ED = [(21-16)^2/400]*20 = 1.25 So the trend is pretty clear: if you want to conserve spell slots, and have time to set up an attack, TS compares pretty favorably to leading with a damaging cantrip. Yes, you need to balance that against the need to finish the combat earlier rather than later to mitigate damage to the party, and so on. [/QUOTE]
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