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Message: <blockquote data-quote="Ovinomancer" data-source="post: 7892283" data-attributes="member: 16814">Actually, the graph should look like this:[ATTACH=full]117443[/ATTACH]And that's because you're graphing physical things - the 2*3d6 data DOES NOT EXIST except at certain points.  I graphed the -11 vice your correction for simplicity and to avoid explaining how your correction causes this graph vs the -10 graph to exist half of the time resulting in a bit of a Schrodinger's graph.  It's all bad assumptions.You've still tossed half of the d20 data if you compare where the 2*3d6 curve actually exists.  The 2*3d6 curve DOES NOT EXIST at half the data points you're comparing.  It creates discrete data points spaced 2 apart.  You can't use a model of a physical event non-physically and get coherent answers.Yes, it DOES NOT EXIST, yet you're using it as part of your comparison.This is a game that often hinges on a 5% difference and you're willing to cavalierly ignore the impact of 3% (and it's larger than that) just because you did mathemagic and can't acknowledge that's it's flawed.  This is, of course, ignoring the parts where it's up to 95% different.I bolded the problem in your thinking I've been trying to point out.  If you round down when halving, then rolling a 2 is the same as rolling a 3, rolling a 4 is the same as rolling a 5, etc, etc.  You've tossed half of your unique rolls using this method because you're ended up at the same result for comparison to rolls you aren't tossing on a 3d6.And, yes, [USER=72555]@NotAYakk[/USER] had some small concessions that made their changes to modifiers make those fractions occasionally count (they didn't double attribute bonuses outright, and random die could still produce odd results), but quite a number of modifiers fit the straight doubling model that results in losing half the numbers on the d20 due to rounding.  And the graphs certainly lose the data.You're losing 10% of the possible results, probability-wise.  Not 3%.  Focusing on a single delta as if it stands in for the total fidelity loss is not kosher.Except half the unique die rolls, again.They are not.  I provided an example earlier, a very slightly modified version of the OP example, that resulted in an infinite difference because it was still possible on 3d6 but wasn't possible at all on the modified d20 scale.  I also showed how moving in the other direction (and following the maths as presented in the OP) we encountered ~10% deltas between outcomes.  This is because you're moving up and down the probabilities at twice the rate -- it's not one for one from a giving comparison start point.  This is due to the scaling invalidating half of the die rolls possible by treating them functionally the same.Absolutely, I can do that.  What I can't do is do that and get a result of 11.  That's impossible to do by rolling 3d6, doubling the amount rolled, and subtracting 10.  So, a model that does that an includes 11 in it's comparison is unphysical.Sure, I can use your method, but by doing so I can only get half of the results you're saying correlate to the full range of the other method.  That's what's unphysical.  You aren't actually fully  understanding the data you're creating because the program you're using draws a line between the data points, and you've confused that line for data.</blockquote>

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