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<blockquote data-quote="NotAYakk" data-source="post: 7889833" data-attributes="member: 72555">The total probability of values from -5 to 1 on the 3d6 curve is under 5%.The total probability of the values from 20 to 25 on the 3d6 curve is under 5%.I'm ignoring the 5% most extreme values on both ends, and looking at the middle 90%.With a d20 on an attack, a natural 1 already misses and a natural 20 already hits; in a sense, it corresponds to a -infinity and +infinity.I talked about the outlying 5% cases already, and now you bring it up as if it was some big gotcha.&nbsp; Those are the crit/auto hit/miss mechanics.I assume we care about &quot;does this attack hit/miss&quot; experience at the table.Given a game played with double-modifiers and d20, and another played with 3d6, I claim distinguishing between those games with a log of hit/misses (and not the rolls) will be a herculean task.You'd basically have to find some creature whose chance of being hit is right on the edge of possible for the 3d6 case (in the &quot;long tail&quot; of 16-18) and tease out if the chance is different than 5%.Suppose we want a 2 SD error bar on the sample.&nbsp; We have some random variable H.&nbsp; Its true value is either 1/20 or 1/216.&nbsp; How many samples do we need to distinguish that?Quick napkin math (I think the right answer involves using student's T?&nbsp; It is basically a polling problem.) gives me about that it would take about 100 samples of &quot;creature we know needs to be hit on an 18 on 3d6&quot; to see a significant (2 SD, or 0.03 P-test) difference between the d20 with double modifiers and auto-hit on a 20 and the 3d6 with normal modifiers.Or, tl;dr, we really don't care about events with really low probability, as they don't happen often enough to care about them.&nbsp; And the entire &quot;tail&quot; you are pointing at adds up to a low probability event.</blockquote>

[QUOTE="NotAYakk, post: 7889833, member: 72555"] The total probability of values from -5 to 1 on the 3d6 curve is under 5%. The total probability of the values from 20 to 25 on the 3d6 curve is under 5%. I'm ignoring the 5% most extreme values on both ends, and looking at the middle 90%. With a d20 on an attack, a natural 1 already misses and a natural 20 already hits; in a sense, it corresponds to a -infinity and +infinity. I talked about the outlying 5% cases already, and now you bring it up as if it was some big gotcha. Those are the crit/auto hit/miss mechanics. I assume we care about "does this attack hit/miss" experience at the table. Given a game played with double-modifiers and d20, and another played with 3d6, I claim distinguishing between those games with a log of hit/misses (and not the rolls) will be a herculean task. You'd basically have to find some creature whose chance of being hit is right on the edge of possible for the 3d6 case (in the "long tail" of 16-18) and tease out if the chance is different than 5%. Suppose we want a 2 SD error bar on the sample. We have some random variable H. Its true value is either 1/20 or 1/216. How many samples do we need to distinguish that? Quick napkin math (I think the right answer involves using student's T? It is basically a polling problem.) gives me about that it would take about 100 samples of "creature we know needs to be hit on an 18 on 3d6" to see a significant (2 SD, or 0.03 P-test) difference between the d20 with double modifiers and auto-hit on a 20 and the 3d6 with normal modifiers. Or, tl;dr, we really don't care about events with really low probability, as they don't happen often enough to care about them. And the entire "tail" you are pointing at adds up to a low probability event. [/QUOTE]

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