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Message: <blockquote data-quote="Esker" data-source="post: 7893227" data-attributes="member: 6966824">Not sure what you mean here. The properties of the model follow directly from the basic assumption that we have fair independent dice. That's the connection between model and reality. If that holds, then the model is the reality, because everything else is derived using mathematical laws.This also doesn't make any sense. The probability of the event is the probability of the event. If it couldn't happen it would have a probability of zero. If there's an error in my math, please point it out, but again, the probability of the event follows from the assumption that when we roll a die, every side is equally likely, and that multiple dice rolls don't influence each other. That's all the reality check we need for the math to match the reality.Well, halving d20 rolls and bonuses both, but yeah.Yes, that's true, but the impact of this is only that we're coarsening the granularity of the DC scale by, essentially, ignoring the differences between (adjusted) DC 3 and DC 6 checks, etc. and similarly between (adjusted) DC 16 and DC 19 checks. But we already mostly do that by switching to 3d6, since the difference between the chance of rolling a 2 or better vs a 6 or better is small (about 4.6% total over a 4 DC range), as is the difference between 15 or better and 19 or better. Even though we only have 10 useful steps to work with, we allocate those to distinguish within the most useful part of the DC range: i.e., between 6 and 15.Keep in mind, the comparison here isn't between RAW and anything else, it's between a 3d6 system and a 1d20 modified system, so we've already upended the system. So we need to be careful not to fall into the trap of using our intuitions about how granular D&D normally is, since that's thrown out either way.Again, keep in mind that there's no need to compare the actual roll distributions; just the success vs DC curves, since the roll distribution only matters to the extent that it affects success chances. We can compare those curves at any point, not just the middle 10 values. As I've said, if you think it makes a big difference for gameplay that the d20 version equalizes DCs that would otherwise differ by a little less than the equivalent of 1 point in the vanilla system, that's fine. It doesn't particularly bother me, except for special case crit mechanics, which we set aside from the start since they have to be dealt with separately.Where have I engaged in special pleading? I don't believe I've forgotten any of the points I've made. I presented two pairs of systems (one of which is vanilla d20) and showed that within each pair of systems, the two methods produce nearly identical outcomes in practice.Where did I do that? If I'm comparing one method to a different scale of DCs using another method, then I'm clearly not using the same DC scale for both. But what I am doing (which is only a slight modification on what [USER=72555]@NotAYakk[/USER] originally proposed) is preserving the same range of difficulties, even if I use different numbers to describe them. It doesn't matter if a "moderately difficult" task is described as DC 15 or DC 20, as long as the other elements (rolls and bonuses) are altered correspondingly to keep the success chance about the same across a range of possible characters trying to succeed at those tasks.</blockquote>

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