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Message: <blockquote data-quote="Ovinomancer" data-source="post: 7891214" data-attributes="member: 16814">Because the relationship is accidental and selected, not by analysis and correct math, but by selection of values that cause parts (PARTS!) of the curves to look similar.No, rescaling, arbitrary centering, eliminating 1/3 of the data points of one distribution, and then comparing 10 data points to 20 data points makes those look similar.  The only decision made here that is remotely based on actual characteristics of the curves was the rescaling, which is questionable (because multiplying the 3d6 distribution gives data points spaced 2 apart which you then compare against data spaced 1 apart).  After that it's literally making choices to achieve the goal of making the curves look similar.Technically, what's been discussed is 1 - the cumulative probability function.  Is this the point where we actually start using proper terminology in this thread?  I figured having that argument wouldn't help understanding, so I've been working informally using the language similar to what's been previously used.So, using probability density function is technically correct, if imprecise.Typo.It points out that the stretched distribution distributed very different behaviors due to being stretched, which makes relying only on the visual similarity in that range even less good.Huh.  The OP (and later posts) have relied on the fact that there's a similarity that supports the argument that stretching the d20 line is functionally similar to a stretched 3d6 line, therefore 3d6 and d20 aren't much different.  My point is that the math suggested by such stretching and skewing is very badly founded and an improper use of math.  The point that you can alter the math of 5e to move some breakpoints on the d20 is orthogonal to my point that the math of the graphs is absolutely wrong.  The justification that relies on bad math is what I'm arguing against.I mean, the first point the OP makes is that using 3d6 is the same as rolling a d20, if you change the target numbers and the bonus to the roll.  What that example shows is really only that the likelihood of rolling at least a 16 on a d20 is close to the likelihood of rolling at least a 13 on 3d6.  Cool, I guess.  The reason this schema works isn't any real similarity in the curves of the d20 and the 3d6 but instead skewing the inputs to the d20 to stretch it.  What the OP did was change the math of the bonuses so that you need a 16 instead of a 13 on a d20 to hit the new math AC with the new math attack bonuses.</blockquote>

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