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Message: <blockquote data-quote="billd91" data-source="post: 6169654" data-attributes="member: 3400">I'll reiterate that the formula won't work. The denominator (20^2) works for d20 because there are 400 outcomes of rolling two d20s - 20 for the first x 20 for the second = 400. For 3d6 rolls, there are 216 outcomes for just one set alone. When comparing two sets of 3d6 rolls, there are 216^2 (or 6^6) or 46,656 distinct outcomes for those dice. Clearly 18^2 won't cut it. That would work if you were rolling a pair of 1d18 dice that had a uniform probability of every result coming up.To illustrate a bit more, if you were to list all of the outcomes of a 3d6 roll, you could roll 1,1,1 for a value of 3; 6,6,6 for a value of 18; 1,2,1 or 1,1,2, or 2,1,1 for a value of 4, and so on. If you were to actually figure out the numbers, you'd get a table something like this:Value__#_____probability of rolling that value3______1_____0.004629634______3_____0.0138888895______6_____0.0277777786_____10_____0.0462962967_____15_____0.0694444448_____21_____0.0972222229_____25_____0.11574074110____27_____0.12511____27_____0.12512____25_____0.11574074113____21_____0.09722222214____15_____0.06944444415____10_____0.04629629616_____6_____0.02777777817_____3_____0.01388888918_____1_____0.00462963Accounting for all possible outcomes of rolling 3d6, there is exactly one way of getting a 3. There are three ways to get a 4, six ways to roll a 5, ten ways to roll a 6, and so on. At the highest point on the bell curve, you've got 27 ways to come up with a 10 or an 11. So you can see how rolling multiple dice to generate a number really changes the distribution compared to rolling a d20 in which there is exactly one way to come up with any outcome on that die and they all have the same probability of 1/20 = .05.</blockquote>

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