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<blockquote data-quote="knightofround" data-source="post: 5263274" data-attributes="member: 27884">I wonder if 2d8 would be a better match for such a system. A 1 in 6 chance of exploding is going to happen almost 2x as often as the 1 in 10 chance you thought worked well with this system.1d20 avg = 10.51d8 avg = 4.52d8 avg = 9&quot;Exploding 8&quot; avg = (1/8) * 4.5 + (1/8)(1/8) * 4.5 + (1/8)(1/8)(1/8) * 4.5 = 0.64162 x &quot;Exploding 8&quot; avg = 1.2832d8 avg + 2 x Exploding 8 avg = 10.283Which is very close to the 1d20 average.And then to apply this function to D&amp;D's crit hit and crit miss system, using the rule &quot;if you get a 7 or 8 on both dice you crit&quot;Chance to get natural 20 =&nbsp; 0.05Chance to get&nbsp; 7 then 8 = (1/8) * (1/8) = 0.0156Chance to get 7 then 7 = (1/8) * (1/8) = 0.0156Chance to get 8 then 7 = (1/8) * (1/8) = 0.0156Chance to get 8 then 8 = (1/8) * (1/8) = 0.0156Chance to get 7 or 8 then 7 or 8 = 0.0625Which is also very close to the natural results...crits (both hits and misses) would happen 20% more often, which I kinda like. &nbsp;If you want it to be less, you could make the rule &quot;if you get an 8 and either 7 or 8 you crit&quot;, so the chance to crit becomes 0.0469, which is closer to the current d20 average.</blockquote>

[QUOTE="knightofround, post: 5263274, member: 27884"] I wonder if 2d8 would be a better match for such a system. A 1 in 6 chance of exploding is going to happen almost 2x as often as the 1 in 10 chance you thought worked well with this system. 1d20 avg = 10.5 1d8 avg = 4.5 2d8 avg = 9 "Exploding 8" avg = (1/8) * 4.5 + (1/8)(1/8) * 4.5 + (1/8)(1/8)(1/8) * 4.5 = 0.6416 2 x "Exploding 8" avg = 1.283 2d8 avg + 2 x Exploding 8 avg = 10.283 Which is very close to the 1d20 average. And then to apply this function to D&D's crit hit and crit miss system, using the rule "if you get a 7 or 8 on both dice you crit" Chance to get natural 20 = 0.05 Chance to get 7 then 8 = (1/8) * (1/8) = 0.0156 Chance to get 7 then 7 = (1/8) * (1/8) = 0.0156 Chance to get 8 then 7 = (1/8) * (1/8) = 0.0156 Chance to get 8 then 8 = (1/8) * (1/8) = 0.0156 Chance to get 7 or 8 then 7 or 8 = 0.0625 Which is also very close to the natural results...crits (both hits and misses) would happen 20% more often, which I kinda like. If you want it to be less, you could make the rule "if you get an 8 and either 7 or 8 you crit", so the chance to crit becomes 0.0469, which is closer to the current d20 average. [/QUOTE]

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