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Message: <blockquote data-quote="Ovinomancer" data-source="post: 7530993" data-attributes="member: 16814">You never take 57.6 damage, or 31.7 damage, or 1.4 damage.  You get hit and you'll take d12+6.  Your analysis only works if you're roll an infinite amount of times.  I'm not.  Using your example of 20 attacks, looking at being hit at least 1, at least 5 times, at least 10 times, and at least 15 times at targets of 2, 11, and 20 with and without disadvantage:[TABLE="class: grid, width: 500, align: center"][TR][TD]To be hit at least x times[/TD][TD]@ 2[/TD][TD]@ 2 diad[/TD][TD]@ 11[/TD][TD]@11 disad[/TD][TD]@20[/TD][TD]@20 disad[/TD][/TR][TR][TD]1[/TD][TD]100.00[/TD][TD]100.00[/TD][TD]96.88[/TD][TD]76.21[/TD][TD]22.62[/TD][TD]1.24[/TD][/TR][TR][TD]2[/TD][TD]100.00[/TD][TD]99.96[/TD][TD]81.25[/TD][TD]36.72[/TD][TD]2.26[/TD][TD]0.01[/TD][/TR][TR][TD]3[/TD][TD]99.88[/TD][TD]99.20[/TD][TD]50.00[/TD][TD]10.35[/TD][TD]0.12[/TD][TD]0.00[/TD][/TR][TR][TD]4[/TD][TD]97.74[/TD][TD]92.22[/TD][TD]18.75[/TD][TD]1.56[/TD][TD]0.00[/TD][TD]0.00[/TD][/TR][TR][TD]5[/TD][TD]77.38[/TD][TD]59.87[/TD][TD]3.13[/TD][TD]0.10[/TD][TD]0.00[/TD][TD]0.00[/TD][/TR][/TABLE]As you can see, the best chance to not be hit (and suffer NO damage) is @20 with disadvantage.  If you have a choice of making the enemy need an 11 or 20 before applying disadvantage, then choosing 20 makes the absolute best sense because the effect is the largest effect possible -- you reduce the chance to be hit to effectively 0.This isn't to say that you get to pick what the giant needs to wallop you -- you usually don't.  This is to say that disadvantage maximizes it's value at 20, not 11.  It's still, as shown above, a good bet @11.  It's just not the largest effect.Honestly, I'm not sure what the pushback on this is.  There seems to be an argument that the biggest reduction in income damage between non-disadvantage and disadvantage is the mark of effectiveness, yet if you have 15 hitpoints, it appears disadvantage @11 still kills you with your numbers above -- and I'm not sure what you're doing there for your trials.  Are you generating 100 random numbers for each target number (100 pairs take worst for disad) and then multiplying the # successes times 67.5 and dividing by 20?  That's odd since you seem to be fine averaging out over perfect probability for everything else.  Wouldn't you take each possible roll from  1 to 20 and factor it that way?  Much simpler.  There you have:@2, perfect averages, hit % 380/400, 5 attacks, 13.7 damage each attack (67.5 max) would be 67.5*(380/400)=64.125 damage.@ 2 disad, hit %361/400, that's 67.5*361/400 = 60.919 damage.@ 11 normal, hit %200/400, that's 67.5*1/2 = 33.75.@ 11 disad, hit %100/400, that's 67.5*1/4 = 16.875@20 normal, hit %20/400, that's 67.5*1/20 = 3.375@20 disad, hit 1/400, that's 67.5/400 = 0.169So, @2, the disadvantage difference is that I take approximately 5% less damage from normal.  @11, the disad difference is 50%.  @ 20, the disad differnce in damage is 95%.  But, again, at not point will I take these damages.  Using the average damage optional rule, all my damage is quantized into 13 point lumps.  So, the odds I take 65 damage (hit 5 times) is above in the table for each value.  There's a 3% chance I take 65 damage from 5 attacks @11, and a 0.1% chance I take that @11disad.  But @20, either case, you need a lot more zeros after the decimal to estimate your chances.  The actual chance @20disad of being hit 5 times is 6.59EE-12.  That's a huge chance to take NO damage at all, not 1 point less (which I cannot actually take 1 point less).This is the problem with math -- it leads to overconfidence because you've done math and math is right.  The real question that's forgotten is "have you done the right math."  I contend you have not, which is why you think disadvantage works best when you need an 11, despite the obvious fact that if you had the option between needing a 20 verses needing an 11, both with disadvantage, you'd always take the 11 because you still have a chance of hitting that's reasonable.</blockquote>

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