Reply to thread

Message: <blockquote data-quote="Esker" data-source="post: 7891953" data-attributes="member: 6966824">And yet, you have yet to give any justification for that claim, other than repeatedly harping on the fact (a fact that everyone acknowledges) that the range of 3d6 is not identical to the range of 1d20, and so for extreme DCs in either direction, you have one method giving a small chance of either success or failure and the other giving zero chance. That may or may not be a problem in a game. It's not a mathematical flaw, but a consequence of a particular choice of approximation.There's no missing data, it's just that the d20 probabilities hit the ceiling and the floor. Again, you wind up with one method giving you probabilities very near 0 or 1, and the other giving you probabilities exactly at zero or 1.I did this because that correspondence is the claim. On the one hand, you have a 3d6 roll, with one set of modifiers and DCs, and then you have a translation of those modifiers and DCs to a d20 system. The target value changes when you change the modifiers and DCs, but there's a direct correspondence between one roll and the other. That was the original claimYes, because 16 maps to 22 when you work out the correspondence implied by the modified bonuses and DCs. If you needed a natural 16 to hit some AC originally, then after you double attack bonuses and move ACs twice as far away from 10, you're going to need a natural 22 to hit. For example, if your attack bonus was +5, then needing a natural 16 means you're up against an AC of 21. That AC becomes 32, and your bonus becomes +10. Hence, you need a natural 22. I'll leave other combinations as an exercise for the reader, but they're all the same: any time you needed a 16 with the original modifiers and DCs, you're going to need a 22 now.You don't. That's why there's a 0% success chance if the target value is a 22. I'm not sure what's so hard about that.I didn't limit the d20 roll to between 5 and 15. The 5 to 15 range is the target 3d6 roll. If instead of transforming the 3d6 to 2*3d6-10 you leave the 3d6 alone and transform the d20 using the inverse transformation, which is 10+(1d20-10)/2, then the range of possibilities is 5 to 15, where you get a 5 if you roll a natural 1, and a 15 if you roll a natural 20.No one is saying they are the same thing. We are saying they give very similar success probabilities.I think what you're not getting is that the actual range of possible rolls doesn't matter in and of itself, since we're always comparing the roll to a target. The only thing that affects outcomes is the probabilities of success at different combinations of bonuses and DCs. And we can simplify that further if instead of treating bonuses as something we add to our roll, we treat them as something that reduces the DC; then, the only thing that matters is probabilities of success vs different DCs.You have repeatedly asserted that what I'm doing is wrong, but, apart from some early off-by-one type errors which I have corrected, you haven't actually pointed out any flaws. As far as I can tell, you just don't like the fact that some small probabilities are approximated by zero, and some large ones are approximated by 1. And that's fine as a critique; but don't pretend it reflects a mathematical mistake... it's a property that everyone has acknowledged from the very start.</blockquote>

Verification