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Message: <blockquote data-quote="Ovinomancer" data-source="post: 7892022" data-attributes="member: 16814">I haven't given any justifications?!  Well, I guess repeatedly explaining exactly how you've taken two things and compared a narrow range after arbitrarily adjusting one of the data sets (including changing scale, center, and tossing out inconvenient data points) could be construed as not providing justification.  I mean, if you're going to immediately discount those points to get to the claim I haven't justified anything, at least.I sense a pattern -- you toss data points to make your comparison and you toss data points to claim I don't have any.The 3d6 probabilities do not, yet you've truncated them and ignored them to assume that the part you kept is similar.And that claim is incorrect.  It is wrong.  For the reasons I keep reiterating:  you've tossed data and rescaled data and recentered data.  What you've done is like zooming in on a small part of the arc of a circle and note that, zoomed it, it corresponds to a line.  But the whole is not the part.:headdesk:22 DOES NOT EXIST!  There is NO mapping 22 on a d20 to ANYTHING!!!When you model physical things, your constraints are the same as the physical thing.  That you can do math on non=physical things doesn't make them suddenly exist.And yet, you've compared a 0% probability for getting a 22 on d20 to a non-zero probability of getting a 16 on 3d6.  You've tossed data and made comparison end-points nonsensical.I am flabbergasted by this argument.  You haven't limited the d20 roll to 5 and 15, you just get a 5 if you roll a 1 and a 15 if you roll a 20!  All so very clear, now.I mean, I make this argument to try to show that you're arbitrarily constraining data to a narrower range and not accounting for this fact in your conclusion, and you tell me that no, I don't understand, what you've done is arbitrarily constrain the data into a narrow range and, look, when that's ignored you get your conclusion!  Then claim is that a scaled version of a d20 is the very similar to 3d6.  To do this, you half the d20 roll and recenter it (this is, mathematically, the same, as you've acknowledged) so that it only covers part of the 3d6 roll, and note that, when this happens, the lines look similar.  What you can't seem to grasp is that you've tossed at least a 1/3 of the data points to do this, meaning scaled d20 isn't similar to 3d6, it's similar to the range of 3d6 outcomes between 5 and 15 ONLY.  And then only when you discard all of the fractional results of a halved d20 (there are no fractional results on 3d6, so I cannot compared to non-existent data points).So, sure, if you scale a d20, toss half of those results, and compare to the center part of 3d6, you get some similarity.  Yay?  This is totally not saying that scaled d20 corresponds to 3d6, though.The... actual range of possible rolls... doesn't matter when comparing actual rolls?  :headdesk:This is why I said mathturbation early in the thread.  This is ignoring the physical limits of the system being modeled and claiming that the model of unphysical results is true.  This is the greatest sin in using statistics -- that of reification or mistaking the model for reality.Your assumptions are wrong, which makes the statistics wrong.  You've swapped an unphysical model for reality and claimed victory because the math worked out.  ALWAYS examine your assumptions when doing statistical analysis.  You can run a model on just about anything and it will give you an answer, but it is often not the right answer.  Your error is in conception, which makes your math wrong before you even start.</blockquote>

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