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Message: <blockquote data-quote="orsal" data-source="post: 1322340" data-attributes="member: 16016">That's true about the Central Limit Theorem only if by "closer to the average" you mean "proportionally closer to the average". If you're talking about absolute difference, the more dice you roll the farther from the average you'll generally be. If you roll four times as many dice, you'll generally get results about twice as far from the mean, but since the totals will be four times as high, twice as far (in absolute terms) is only about half as far (proportionally).To clarify: If you roll 10d6, the standard deviation is about 5.4. The standard deviation is a convenient measuring stick for about how far from the "expected" result (35 in this case) you typically get. As a rule of thumb, about 2/3 of the time you will get a result within one standard deviation of the "expected value" (a misleading technical term). Thus about 2/3 of your 10d6 rolls will be in the range 30-40.Now suppose you roll 20d6. The expected value is now 70, and the standard deviation is about 7.6. About 2/3 of your totals will be between 63 and 77.How do you measure how far you are from that theoretical average? If you measure it in absolute terms, 7.6 is higher than 5.4, so with more dice you'll tend to be farther from the average. But if you measure it in relative terms, a range of 30-40 is comparable to a range of 60-80, so you get less variation with more dice.In general, if you roll twice as many dice, multiply the standard deviation by the square root of two, which is greater than one (hence the larger absolute variation), but less than two (hence the smaller relative variation). If you roll four times as many dice, multiply the standard deviation by two (the square root of four). Nine times as many dice, multiply standard deviation by three, and so forth.</blockquote>

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