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Message: <blockquote data-quote="Alomir" data-source="post: 773471" data-attributes="member: 6622">Should have 'named my sources': the 3d6 and 4d6 numbers are easy enough to obtain analytically (avg for 3d6 is hopefully pretty clear, avg for 4d6 = 15869/1296).  The others I got from making a few runs of 10 million rolls each using MATLAB, as I was too lazy to figure out the mathematics (really, the interest is there, I just didn't have the time).However, it just dawned on me that it would be more accurate to just zip through all of the possible rolls, and get an exact value (much less than 10 million, except for the 9d6 case, which is just over 10 mil).  Here they are again with standard deviations:dice:__avg:____std:3 --- 10.500 -- 2.9584 --- 12.245 -- 2.8475 --- 13.430 -- 2.6036 --- 14.274 -- 2.3647 --- 14.903 -- 2.1508 --- 15.389 -- 1.9659 --- 15.775 -- 1.804As I said before, this system is somewhat weighted towards people who go for lots of reasonable scores, as opposed to a few big scores.  For example, if I have 18 extra dice, and put 3 into each score (6d6 each), I'd have an average score of 14.27; if instead I put 6 into three scores (3 3d6 scores, 3 9d6 scores), I'd have an average score of 13.14, more than a point less.</blockquote>