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Message: <blockquote data-quote="eamon" data-source="post: 3833655" data-attributes="member: 51942">Well, calculations with variance are simpler (for this kind of thing).  Standard deviation is simply the square root of variance, and variance is just the average of the square deviation.So, for a single d6, with average 3.5, the variance is [ (1-3.5)² + (2-3.5)² +(3-3.5)² +(4-3.5)² +(5-3.5)²+(6-3.5)² ] /6 which is exactly 17.5/6 and roughly 2.92 (and the std. dev. is thus about 1.71).The variance of the sum of independent random variables - say, Var(2d6) - is the sum of the variance of the the independent random variables - say, 2*Var(d6), which is about 5.83.So, by reducing the number of d6's you're always reducing "randomness".Why then is it generally perceived that the more d6's you roll, the less random the result is?Actually, the std. deviation rises as you add more d6's, but since the std. deviation is the sqrt of the variance, which is directly proportional to the number of d6's and thus the average roll, the std. deviation as a percentage of the average drops when you add more dice.So at 1d6 the std. deviation is about half the average, but for 10d6 it's already less than a sixth of the average, and by 20d6 it's less than a ninth.Since we're dealing with distributions that are roughly normal, about 70% of all die-roll's will be within one std. dev. and 95% within two.Conclusion: if you're just using d6's and just adding them, you can't simulate higher-d6's increased std. dev. just by using fewer dice and adding them.  However, you could multiply the d6's, or you could use dice with more sides.And of course, it's questionable how important damage variance really is anyhow, since the effective randomness is largely determined not by these minor fluctuations in damage, but but the far more major factor of whether you actually hit at all (or, for spells, whether the opponent saves)In game, that means that I'm not too worried about the reduced randomness of damage - any minor changes in d20 rules are liable to outweigh it.  Frankly, you could probably just use average damage almost everywhere without big in-game effect, and leave the randomness to hit-n-miss (and criticals...) instead, especially once you're rolling more than a few damage dice per combat.</blockquote>

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