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Message: <blockquote data-quote="Esker" data-source="post: 7891799" data-attributes="member: 6966824">I'm nearing the end of my patience with you, because you're so quick to fire insults and shoot down straw men without actually taking time to consider what anyone else is saying. You keep fixating on the fact that the probabilities don't actually match, and, no of course they don't match exactly. No one was claiming they were an exact match. But they're close, because we've matched the means and standard deviations of the die rolls.I've only graphed the even target rolls, since 2*3d6-10 can only produce even results before the confirmation correction. Obviously the probability of 1 or higher on a d20 is 1, but that's not on the graph; it's just interpolating between 0 and 2. If the target is an odd value then the confirmation step doesn't matter because you'll either exceed the target or you'll fall below it, so you can use the probability of hitting one number higher without a confirmation correction. I didn't bother incorporating that because it doesn't change the shape, but since you're clearly intent on fixating on any small missing detail, here's the graph with the odd targets added in.<img src="https://imgur.com/erUvLCJ.jpg" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />I don't know what you mean by saying that I've tossed data. Unless you mean that I omitted odd-numbered targets. Well they're there now. Happy?I explained this in my last post: the x-axis shows the target values for the 3d6 scheme. The corresponding targets on a d20 are different because we've changed the bonuses and DCs for that scheme only. If the 3d6 target is X, then the d20 target with rescaled DCs is 10 + 2*(X-10). So the points on the graph at 16 are the probability of getting 16 on 3d6 and the probability of getting 22 on a d20, since these are corresponding rolls. This is a linear transformation and so of course the CDF is still linear. Not sure why you seem to think it wouldn't be.Yes, if you prefer you can think of the modified d20 scheme as altering the roll itself instead of the DC: roll the d20, add 10, and divide by 2, rounding down. So the maximum result is 15 and the minimum is 5 (but you only get 5 when the die shows a 1). And so, as I acknowledged, the adjusted d20 is missing a small chance of getting a 3-4, as well as a small chance of getting 16-18: with the confirmation correction, 3d6 has a 96.8% chance of rolling 5 or higher (instead of 100%), and a 3.2% chance of rolling 16 or higher (instead of 0%).I suggest taking a step back and reconsidering your stance that people who produce results that you don't follow must necessarily be mathematically inept, and instead begin from a place of good faith, reading what they have written and trying to make sense of it to the best of your ability before jumping on any perceived missing or incorrect detail as proof that the whole approach is "horrible math". I acknowledge having made some minor errors here and there, and I originally proposed the confirmation correction in a quick post from my phone with what turned out to be some details that were off before I had a chance to sit down and work out the numbers. But I promise you, my grasp of the underlying math is solid (as I believe I've demonstrated in our previous interactions here, so I figured you might extend some benefit of the doubt).</blockquote>

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