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Message: <blockquote data-quote="pawsplay" data-source="post: 5196915" data-attributes="member: 15538">While each of the 20 rolls is a an even distribution, the actual die roll is not meaningful. There are actually only two results, hit or miss, and they are not the same probability in every scenario. The idea of normalizing attack bonuses and defenses in 4e is actually a way of creating a more bell-like distribution. The bell curve was not invented to model 3d6 or a dice pool or whatever. It's what happens when you sample multiple times from a random distribution. Even though many things in nature, like the d20, begin as a completely random distribution, as the results are aggregated, the bell curve magically appears. As I said before, the d20 and 3d6 are functionally identical in the amount of "randomness" they posses. Both are ultimately ways of deciding what fractional probability you will have to succeed. Using a 3d6 does not create a "bell curve." Rather, it just changes the graduations of probablity from bite-sized, 5% chunks of the entire distribution to chunks that vary in size. The result is not a change in the bell-curved of the distribution, but a transformation of the modifiers and target numbers from a proportion of the variance to a curve, with the highest slope near the normal target numbers and the lowest slope at the extremes. Thus, even small differences become large ones, but very large differences are only slightly more meanginful than large differences. The 3d6 is more predictable but also more stratified, with the extreme values being fatter strata. Even though 3d6 is more mathematically predictable, the high shifts in probably that come from situational modifiers are not predictable. As long as there are no modifiers to the rolls, the 3d6 is a lot more predictable. But if the situation is such that you may get +1, +2, or no bonus from round to round, the probability will actually swing wider. Further, you will want to compare the usual range of skill or attack modifiers to the usual range of DCs, and compare the shift in % between d20 and 3d6 within those values to see if perhaps you are making high, but fairly common DCs out of reach.</blockquote>

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