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<blockquote data-quote="NotAYakk" data-source="post: 7889704" data-attributes="member: 72555">Have you looked at the graphs I've been linking to, or not?How math works is you do steps and results come out.Do I have to take a screen shot?&nbsp; I have to take a screen shot.&nbsp; naughty word.[ATTACH=full]117346[/ATTACH]So here we have the CDF (cumulative distribution) of 1d20 and the CDF (cumulative distribution) of 3d6 with different averages and standard deviations normalized.The 1d20 curve is a line.&nbsp; The 3d6 curve is the set of black points.&nbsp; Notice how the 3d6 curve is close to, but not exactly on, the 1d20 line.&nbsp; It only differs significantly at the 5% &quot;critical hit/miss&quot; cases that correspond to 1 and 20 on the d20 roll.I horizontally scaled 3d6 by a factor of 2, which corresponds to &quot;bonuses and penalties are twice as large, conceptually, in a 3d6 based situation&quot;.So yes, that is how that works.&nbsp; The distributions are similar&nbsp; in CDF, because you can see it.&nbsp; Yes, one is a flat distribution and the other is a normal(ish) one, but we aren't playing &quot;can you roll a 7&quot;, we are playing &quot;can you roll a 7+&quot; when we play D&amp;D.&nbsp; And &quot;can you roll a 7+&quot; corresponds to the CDF (the integral) of the distribution.And when you integrate things, the differences between a flat distribution and a curved one fade away pretty fast.This isn't &quot;mathturbation&quot;, because I actually checked my results.&nbsp; I even shared links to those results being checked.&nbsp; I am not sure why I expected people to actually click on those results before saying &quot;this is naughty word&quot;.Anyhow, here is the results inline.Quite possibly a slightly different value than &quot;2&quot; would be more correct once we neglect tails -- a different value than &quot;2&quot; would correspond to a change in the slope of the 3d6 part of the graph, and making it slightly less steep might improve the match (except for the tails).&nbsp; But 2 is so close I really don't care.</blockquote>

[QUOTE="NotAYakk, post: 7889704, member: 72555"] Have you looked at the graphs I've been linking to, or not? How math works is you do steps and results come out. Do I have to take a screen shot? I have to take a screen shot. naughty word. [ATTACH type="full" alt="3d6vs1d20.png"]117346[/ATTACH] So here we have the CDF (cumulative distribution) of 1d20 and the CDF (cumulative distribution) of 3d6 with different averages and standard deviations normalized. The 1d20 curve is a line. The 3d6 curve is the set of black points. Notice how the 3d6 curve is close to, but not exactly on, the 1d20 line. It only differs significantly at the 5% "critical hit/miss" cases that correspond to 1 and 20 on the d20 roll. I horizontally scaled 3d6 by a factor of 2, which corresponds to "bonuses and penalties are twice as large, conceptually, in a 3d6 based situation". So yes, [B]that is how that works[/B]. The distributions are similar in CDF, because [B]you can see it[/B]. Yes, one is a flat distribution and the other is a normal(ish) one, but we aren't playing "can you roll a 7", we are playing "can you roll a 7+" when we play D&D. And "can you roll a 7+" corresponds to the CDF (the integral) of the distribution. And when you integrate things, the differences between a flat distribution and a curved one fade away pretty fast. This isn't "mathturbation", because I actually checked my results. I even shared links to those results being checked. I am not sure why I expected people to actually click on those results before saying "this is naughty word". Anyhow, here is the results inline. Quite possibly a slightly different value than "2" would be more correct once we neglect tails -- a different value than "2" would correspond to a change in the slope of the 3d6 part of the graph, and making it slightly less steep might improve the match (except for the tails). But 2 is so close I really don't care. [/QUOTE]

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