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Message: <blockquote data-quote="Ovinomancer" data-source="post: 7893101" data-attributes="member: 16814">Earlier in the thread I cautioned against reification of the models, as that's a trap that's easy to fall into when using models, statistical or probability.  And, largely, we're doing a good bit of both, here, with mean shifting, discussion of variance, discussion of deviation, and looking at how closely two probability models match, none of which true probability math cares about.  What we're doing is building a model of a physical system where we plan to use the physical system.  Thinking that we can look at the maths in the model and that tells us what reality is, or, even worse, thinking that truth exists because the models tell us something without validating it in the real is the sin of reification, which you latch onto here.Because you're determining the probability for an event that cannot happen and pretending that, because you can do the math, it does.  Again, you're believing the model and not reality. As you said above, scaling d20 DCs by 2 is mathematically the same as halving d20 rolls.  If this is true, the either we use the original DCs and the half d20, which means that half of the results on the D20 are in-between DCs, or we expand the DC range and use a normal d20 in which half the results on the d20 are in-between available DCs.  Both of these approaches shrink the useful d20 range by half, meaning the d20 range is half as useful as it was.  Essentially, we're taking the d20 from 20 useful steps to 10 useful steps.This halved d20 is then being compared to 3d6, but not the full 16 step range of 3d6, but the central 10 values.  Only, the comparison ignores the fact that the d20 range has been effectively halved from 20 to 10 steps, and you get a pretend game that every step on the d20 now matters against the more spaced 10 steps of the central part of 3d6.  Various reasons why is is okay are presented -- we can find probabilities, we can pretend those DCs exist, the part of the 3d6 we toss isn't that big, etc -- each brought up and levied independently to defeat an objection and then forgotten when those become a challenge for another excuse.  It's a circle of special pleading, always ignoring that the transformation of one of the die methods fundamentally alters the function of the game just in time to compare to a truncated but unaltered other method.In simpler words, when you scale the die method, you change the steps size for DCs in that scale.  You cannot compare to a different scale of DCs using a different die method and pretend you can use the same DC scale for both.  This is the core failed assumption to the whole endeavour, and I've shown it to be so with the OP examples -- examples that have so far been ignored.  The DCs scale differently in the different scales of die and that matters.</blockquote>

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