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<blockquote data-quote="Bacon Bits" data-source="post: 7062083" data-attributes="member: 6777737">d6 = 3.5 because (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5.&nbsp; The mean value of a six sided die is 3.5.d8 = 4.5 because (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) / 8 = 4.5.Single values are used because they're easier to calculate with than ranges.&nbsp; Additionally, over a large number of rolls, fair dice will tend to regress towards the mean because each result is equally likely.&nbsp; Since we're not typically concerned with the behavior of the dice in a single instance but instead care about the most general or consistent result, the average result is the most useful.You can see this by going to anydice.com.&nbsp; Start with &quot;output 5d6&quot; and you'll see that the results are clumped around the middle.&nbsp; Change to &quot;output 100d6&quot;, and you'll see that almost all the values are clumped betwen 290 and 410, even though the range is 100-600.&nbsp; Note that 100 * 3.5 = 350 is exactly in the middle of 290 and 410.&nbsp; So, yes, 100d6 = 100-600, but 100d6 = 290-410 with a probability of 99.93%.&nbsp; Heck, 100d6 = 330-370 with a probability of 76.99%.&nbsp; So ranges can get super misleading.Finally, you can get mechanics that throw a wrench in the works.&nbsp; If you're using a Greatsword with Great Weapon Fighting style, you still deal between 2 and 12 damage.&nbsp; However, the reroll 1s and 2s really changes your average damage.&nbsp; Instead of each die being this:(1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5You have each die being this:(3.5 + 3.5 + 3 + 4 + 5 + 6) / 6 = 4.16666...Since a 1 and a 2 mean &quot;reroll&quot; and you only reroll once, a result of a 1 and a 2 is, on average, 3.5.&nbsp; That way we can say that a Greatsword's average damage is 7 (3.5 * 2), but a Greatsword with Great Weapon Fighting style's average damage is 8.333....</blockquote>

[QUOTE="Bacon Bits, post: 7062083, member: 6777737"] d6 = 3.5 because (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5. The mean value of a six sided die is 3.5. d8 = 4.5 because (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) / 8 = 4.5. Single values are used because they're easier to calculate with than ranges. Additionally, over a large number of rolls, fair dice will tend to regress towards the mean because each result is equally likely. Since we're not typically concerned with the behavior of the dice in a single instance but instead care about the most general or consistent result, the average result is the most useful. You can see this by going to anydice.com. Start with "output 5d6" and you'll see that the results are clumped around the middle. Change to "output 100d6", and you'll see that almost all the values are clumped betwen 290 and 410, even though the range is 100-600. Note that 100 * 3.5 = 350 is exactly in the middle of 290 and 410. So, yes, 100d6 = 100-600, but 100d6 = 290-410 with a probability of 99.93%. Heck, 100d6 = 330-370 with a probability of 76.99%. So ranges can get super misleading. Finally, you can get mechanics that throw a wrench in the works. If you're using a Greatsword with Great Weapon Fighting style, you still deal between 2 and 12 damage. However, the reroll 1s and 2s really changes your average damage. Instead of each die being this: (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5 You have each die being this: (3.5 + 3.5 + 3 + 4 + 5 + 6) / 6 = 4.16666... Since a 1 and a 2 mean "reroll" and you only reroll once, a result of a 1 and a 2 is, on average, 3.5. That way we can say that a Greatsword's average damage is 7 (3.5 * 2), but a Greatsword with Great Weapon Fighting style's average damage is 8.333.... [/QUOTE]

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