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Message: <blockquote data-quote="Ovinomancer" data-source="post: 7893905" data-attributes="member: 16814">You assume too much.  I'm fine with a rescaled system of resolution and targets within that system ONLY.  Once you begin comparisons, the gaps become important.And, the kludge is still a kludge -- it's an grafted on mechanic to correct an failure in the original system.  It's not clever, and adding a kludge is admitting the original system failed so you need another system on top of it to try to correct your failure.  The problem with your kludge is that you're using it to address target numbers that don't exist in the scaled schema, only when you try to compare to a different schema.This, right here, is the error.  You are NOT using the same DCs in each system.  The scaled system uses DCs stepped by 2, because it's scaled.  The d20 isn't.  You cannot compare these thing without making an error, because possibilities exist for one that do not for the other.Yes, you can determine if you roll greater than a 2 in the 2*3d6 system and it's mathematically the same as the probability you roll a 3 or greater.  However, 2 as a target number DOES NOT EXIST in the 2*3d6-10 system.  This is the reification sin -- you confuse being able to create a probability for an event that does not exist in the system.  Here, a target number of 2.  You confuse that comparing a probability of greater than a number is not the same analysis as greater than or equal to, but you mix an match these to fool yourself into thinking 2's actually exist in the 2*3d6 system.2 exists for d20, though, which is why you can't compare these systems.  One has even DCs, the other doesn't (except below 0, which is an artifact of the recentering).When you recenter the mean of the method, you must recenter the mean of the DCs, or your system is very, very much not the same as what you started with.  This is like saying that needing a 3 on 3d6 is the same as needing a 3 on 2*3d6-10.  It's not.  The same value on 2*3d6-10 as a 3 on 3d6 is -4.  This is the other half of the fundamental reason you can't compare the systems as you're doing -- you're comparing values of DC that do not align but, because it graphs, you've fooled yourself into thinking it does.Dear god, but you've graphed two different PDFs on top of each other as if they're the same thing.  You've graphed the PDF for greater than x on the half steps, and greater than or equal to on the whole steps.  For someone that lectured on the basics of probability and made semantic arguments because I haven't gone jargon but tried to keep this jargon free, this must be an embarrassing error -- graphing two different probability questions on the same graph and pretending they're the same thing.  And that doesn't even get to the other system you're graphing and the issues I've outlined above.And, the worst discrepancy is still where I can roll 2*3d6-10 and can't roll a d20.  Surely, this must sink in sometime?  I'm losing hope.  I'm sure the response will continue to not get the problem I've been rephrasing for many, many posts now -- you have different scales of both die outcomes AND DCs, but you're treating the DC scale as if it's the same.  It is not.</blockquote>

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