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Power Attack Optimization
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<blockquote data-quote="Elder-Basilisk" data-source="post: 3338499" data-attributes="member: 3146"><p>In answer to the question about the figures, see the top of the post:</p><p></p><p></p><p></p><p>Unfortunately, I redid the math and it's not entirely correct so you were right to ask me to show my work</p><p></p><p>Against AC 20, Roy hits on an 11: 50% chance to hit. That's part 1. Part 2 is the damage. Roy will stagger the hobgoblin on a 6 (not considered in this analysis) and drop the hobgoblin on a 7 or better. So, that's a 50% chance to drop any uninjured hobgoblin he hits.</p><p></p><p>So, with no Power Attack:</p><p>50% chance to hitx 50% chance to drop= 25% chance to drop a hobgoblin with his first attack.*</p><p>Over two rounds, that comes out to:</p><p>Drops 2 hobgoblins: .25*.25</p><p>Drops 1 hobgoblin and injures a 2nd: .25 (drop 1st)*.25 (injures 2nd)</p><p>Drops 1 hobgoblin: .25 (drops 1st round)*.5 (miss 2nd round)+.5 (miss 1st round)*.25 (drops 2nd round)+.25 (injures 1st round)*.5(hits 2nd round--any hit being a kill)</p><p>Injures 1 hobgoblin: .5 (miss 1st round)*.25 (injures 2nd round) +.5 (miss 2nd round)*.25 (injures 1st round)</p><p>Accomplishes nothing: .5 (miss 1st round)*.5 (miss 2nd round)</p><p></p><p>Answers</p><p>Drops 2 hobgoblins: 6.25%</p><p>Drops 1 hobgoblins and injures a 2nd: 6.25%</p><p>Drops 1 hobgoblin: 37.5%</p><p>Injures 1 hobgoblin: 25%</p><p>Accomplishes nothing: 25%</p><p></p><p>Now the answers actually add up to 100%.</p><p></p><p>On to the Power Attack for three answer which should have much simpler math:</p><p>Power Attacking for 3, Roy is attacking at +6 for 1d12+13. He hits AC 20 on a 14 or better which is a 35% chance. Minimum damage is 14, so every hit drops a 13hp hobgoblin below 0.</p><p></p><p>So:</p><p>Drops two hobgoblins: .35 (drop round 1)*.35 (drops round 2)</p><p>Drops 1 hobgoblin: .35 (drops round 1)*.65 (misses round 2)+.65 (misses round 1)*+35 (drops round 2)</p><p>Accomplishes nothing: .65 (misses round 1)*.65 (misses round 2)</p><p></p><p>answers:</p><p>drops 2 hobgoblins: 12.25%</p><p>Drops 1 hobgoblin: 45.5%</p><p>Accomplishes nothing 42.25%</p><p></p><p>So, the answers are a little less clean cut now, but by power attacking for 3, Roy still manages a 57.75% chance of dropping at least one hobgoblin with a 12.25% chance of dropping two included in the figure instead of a 50% chance of dropping at least one hobgoblin with a 6.25% chance of dropping two hobgoblins included in the figure.</p><p></p><p>That's still a pretty strong shifting of the odds in Roy's favor.</p><p></p><p>*You'll notice that these numbers exclude crits--really it should be a little more than that because if Roy crits the hobgoblin (2.5% chance=5% chance to roll a 20 and 50% chance to confirm) minimum damage will drop the hobgoblin.</p></blockquote><p></p>
[QUOTE="Elder-Basilisk, post: 3338499, member: 3146"] In answer to the question about the figures, see the top of the post: Unfortunately, I redid the math and it's not entirely correct so you were right to ask me to show my work Against AC 20, Roy hits on an 11: 50% chance to hit. That's part 1. Part 2 is the damage. Roy will stagger the hobgoblin on a 6 (not considered in this analysis) and drop the hobgoblin on a 7 or better. So, that's a 50% chance to drop any uninjured hobgoblin he hits. So, with no Power Attack: 50% chance to hitx 50% chance to drop= 25% chance to drop a hobgoblin with his first attack.* Over two rounds, that comes out to: Drops 2 hobgoblins: .25*.25 Drops 1 hobgoblin and injures a 2nd: .25 (drop 1st)*.25 (injures 2nd) Drops 1 hobgoblin: .25 (drops 1st round)*.5 (miss 2nd round)+.5 (miss 1st round)*.25 (drops 2nd round)+.25 (injures 1st round)*.5(hits 2nd round--any hit being a kill) Injures 1 hobgoblin: .5 (miss 1st round)*.25 (injures 2nd round) +.5 (miss 2nd round)*.25 (injures 1st round) Accomplishes nothing: .5 (miss 1st round)*.5 (miss 2nd round) Answers Drops 2 hobgoblins: 6.25% Drops 1 hobgoblins and injures a 2nd: 6.25% Drops 1 hobgoblin: 37.5% Injures 1 hobgoblin: 25% Accomplishes nothing: 25% Now the answers actually add up to 100%. On to the Power Attack for three answer which should have much simpler math: Power Attacking for 3, Roy is attacking at +6 for 1d12+13. He hits AC 20 on a 14 or better which is a 35% chance. Minimum damage is 14, so every hit drops a 13hp hobgoblin below 0. So: Drops two hobgoblins: .35 (drop round 1)*.35 (drops round 2) Drops 1 hobgoblin: .35 (drops round 1)*.65 (misses round 2)+.65 (misses round 1)*+35 (drops round 2) Accomplishes nothing: .65 (misses round 1)*.65 (misses round 2) answers: drops 2 hobgoblins: 12.25% Drops 1 hobgoblin: 45.5% Accomplishes nothing 42.25% So, the answers are a little less clean cut now, but by power attacking for 3, Roy still manages a 57.75% chance of dropping at least one hobgoblin with a 12.25% chance of dropping two included in the figure instead of a 50% chance of dropping at least one hobgoblin with a 6.25% chance of dropping two hobgoblins included in the figure. That's still a pretty strong shifting of the odds in Roy's favor. *You'll notice that these numbers exclude crits--really it should be a little more than that because if Roy crits the hobgoblin (2.5% chance=5% chance to roll a 20 and 50% chance to confirm) minimum damage will drop the hobgoblin. [/QUOTE]
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