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Message: <blockquote data-quote="Ovinomancer" data-source="post: 7891751" data-attributes="member: 16814">Not what you say above, and still a really weird, non-mathematical thing to do to correct at a single point in the distribution because your choice of arbitrary centering (to get, recall, a optical match but not actual match in probabilities) to look better.  You're chasing rabbits down the wrong holes and claiming victory because you found an orange plastic cap that you're calling a carrot.I don't know what you're actually graphing, here.  Your d20 line has data outside of the possible range, and the value for 1 on d20 is incorrect.  The rest are correct (2-20), but these obvious issues make me very leery of what it is you're doing.Secondly, you've done exactly what I said the OP did -- you've tossed data from the scaled 3d6.  Here, you've actually truncated the values form the graph which makes it look even more visually similar.  This is bad math. I think you've set yourself up to fail, here, because your next bit is way, way, way off the rails.I have no idea what you've graphed here.  The d20 in your scheme does not display a different CPDF -- it's still linear.  But, here, you have a weird hybrid curve that goes to a 0% probability when you need a 16.  Can you not even roll a 16 on a d20?  Clearly, you can, you can roll all the way up to a 20 (not featured on your graph), so whatever you've done here, it's not the density function of a d20.The best I can figure is that you've graphed a d20 scaled by 1/2 and recentered.  You've increased the slope of the d20 line, but tossed a bunch of data.  Your d20 values go from being able to generate a value of 5 through 16.  This is NOT what a d20 can generate.I also tried to understand your graph as using the expanded d20 roll as graphing likelihood of meeting a DC, but I can't get that math to work, either, even trying out a number of possible mistakes.I was able to recreate your graph, though.  I divided a d20's probability by 2 and recentered it at 10.5, then changed the first and last data points to be an average of the data point before and the data point after (which is why you have those ramps to 100% and 0% on the d20 line).  I then recentered the 3d6 line to 10.5.  I don't really know why we did this, because both lines were centered on 11, but whatever, it's a bunch of arbitrary decisions to make lines look like each other so it's all the same.[ATTACH=full]117417[/ATTACH]<table style='width: 100%'><tr><td>roll</td><td>d20</td><td>3d6</td><td>scaled d20</td></tr><tr><td>1 </td><td>100 </td><td></td><td></td></tr><tr><td>1.5 </td><td>97.5 </td><td></td><td></td></tr><tr><td>2 </td><td>95 </td><td></td><td></td></tr><tr><td>2.5 </td><td>92.5 </td><td>100 </td><td></td></tr><tr><td>3 </td><td>90 </td><td>99.76852 </td><td></td></tr><tr><td>3.5 </td><td>87.5 </td><td>99.53704 </td><td>100 </td></tr><tr><td>4 </td><td>85 </td><td>98.84259 </td><td>100 </td></tr><tr><td>4.5 </td><td>82.5 </td><td>98.14815 </td><td>100 </td></tr><tr><td>5 </td><td>80 </td><td>96.75926 </td><td>100 </td></tr><tr><td>5.5 </td><td>77.5 </td><td>95.37037 </td><td>97.5 </td></tr><tr><td>6 </td><td>75 </td><td>93.05556 </td><td>95 </td></tr><tr><td>6.5 </td><td>72.5 </td><td>90.74074 </td><td>90 </td></tr><tr><td>7 </td><td>70 </td><td>87.26852 </td><td>85 </td></tr><tr><td>7.5 </td><td>67.5 </td><td>83.7963 </td><td>80 </td></tr><tr><td>8 </td><td>65 </td><td>78.93519 </td><td>75 </td></tr><tr><td>8.5 </td><td>62.5 </td><td>74.07407 </td><td>70 </td></tr><tr><td>9 </td><td>60 </td><td>68.28704 </td><td>65 </td></tr><tr><td>9.5 </td><td>57.5 </td><td>62.5 </td><td>60 </td></tr><tr><td>10 </td><td>55 </td><td>56.25 </td><td>55 </td></tr><tr><td>10.5 </td><td>52.5 </td><td>50 </td><td>50 </td></tr><tr><td>11 </td><td>50 </td><td>43.75 </td><td>45 </td></tr><tr><td>11.5 </td><td>47.5 </td><td>37.5 </td><td>40 </td></tr><tr><td>12 </td><td>45 </td><td>31.71296 </td><td>35 </td></tr><tr><td>12.5 </td><td>42.5 </td><td>25.92593 </td><td>30 </td></tr><tr><td>13 </td><td>40 </td><td>21.06481 </td><td>25 </td></tr><tr><td>13.5 </td><td>37.5 </td><td>16.2037 </td><td>20 </td></tr><tr><td>14 </td><td>35 </td><td>12.73148 </td><td>15 </td></tr><tr><td>14.5 </td><td>32.5 </td><td>9.259259 </td><td>10 </td></tr><tr><td>15 </td><td>30 </td><td>6.944444 </td><td>5 </td></tr><tr><td>15.5 </td><td>27.5 </td><td>4.62963 </td><td>2.5 </td></tr><tr><td>16 </td><td>25 </td><td>3.240741 </td><td>0 </td></tr><tr><td>16.5 </td><td>22.5 </td><td>1.851852 </td><td>0 </td></tr><tr><td>17 </td><td>20 </td><td>1.157407 </td><td>0 </td></tr><tr><td>17.5 </td><td>17.5 </td><td>0.462963 </td><td></td></tr><tr><td>18 </td><td>15 </td><td></td><td></td></tr><tr><td>18.5 </td><td>12.5 </td><td></td><td></td></tr><tr><td>19 </td><td>10 </td><td></td><td></td></tr><tr><td>19.5 </td><td>7.5 </td><td></td><td></td></tr><tr><td>20 </td><td>5 </td><td></td><td></td></tr></table>NOTE:  I did some fast and dirty extrapolation for the 3d6 curve for the .5 values by averaging the preceding and following values.  This is because there isn't a probability for rolling, say, 6.5 on 3d6 but it's a pain to get Excel to graph data where values are missing.Sigh.  That makes things easier -- you need a 10.5 to succeed 50% of the time instead of a larger value, 11.  This actually increases the likelihood of success by a small amount.  That is, if what you've done was remotely correct at all.  I point this out because you've not only managed to do horrible things to math, but you've failed to even apply a correct interpretation to the horrible things you've done as if they were okay.Look, no matter what you do to target numbers, the CPDF of a d20 doesn't change.  If you don't get a straight line from 100% to 5% from 1 to 20 with a slope of exactly -1, you've done something horribly wrong.</blockquote>

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