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Normalized d20 dice
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<blockquote data-quote="Drawmack" data-source="post: 547461" data-attributes="member: 4981"><p>For easy bell cuvre just roll 2d20 and divide the result by 2, rounding down. Of use 2d10 and loose a number, as mentioned earlier you can loose 1 or one that I saw a while ago rolled 2d10-1 unless you rolled a natural 20 which effectively got rid of the 19. The logic was that 1 is a critical fumble and 20 is a critical pass so 19 was a much less important number then either of those two. It also did something wierd to the average roll</p><p>(1+2+3+...+18+20)/19 ~ 10.05. </p><p></p><p>You can vary the dice find any combination of dice that totals 20 when rolled to max.</p><p></p><p>a) 5d4</p><p>b) 3d4 + 1d8</p><p>c) 2d4 + 2d6</p><p>b) 2d4 + 1d12</p><p>e) 2d6 + 1d8</p><p>f) 1d8 + 1d12</p><p>g) 2d10</p><p></p><p>Then subtract N-1 where N = the number of dice rolled, in all cases except when all dice maxe out. </p><p></p><p>a) - 4</p><p>b) - 3</p><p>c) - 3</p><p>d) - 2</p><p>e) - 2</p><p>f) -1</p><p>g) - 1</p><p></p><p>The number that you eliminate is 20-(N-1). </p><p></p><p>a) 20 - 4 = 16</p><p>b,c) 20 - 3 = 17</p><p>d) 20 - 2 = 18</p><p>e,f) 20 - 1 = 19</p><p></p><p>so you averages become</p><p>a) (1+2+...+15+17+18+19+20)/19 ~ 10.21</p><p>b,c) (1+2+...+16+18+19+20)/19 ~ 10.16</p><p>d) (1+2+...+17+19+20)/19 ~ 10.11</p><p>e,f) (1+2+...+18+20)/19 ~ 10.05</p><p></p><p>Since the average is a function of the number eliminated the higher the number you can eliminate the better of you are. Now let's look at the d30 distribution and average to see if what you propose is better then what can easily be done with dice we already have.</p><p></p><p>(1+2+3+4+5+6+7+7+8+8+9+9+10+10+10+11+11+11+12+12+13+13+14+14+15+16+17+18+19+20)/30 = 315/30 = 10.5 comes out the same as 1d20. Though I if you talk probability you have a 3 1/3 chance to roll any given side so you have a </p><p>3 1/3% chance of rolling 1,2,3,4,5,6,15,16,17,18,19,20</p><p>6 2/3% chance of rolling 7,8,9,12,13,14</p><p>10% chance of rolling 10,11</p><p></p><p>I don't feel like doing anymore math but I bet the the best bell curve is going to come from 5d4.</p></blockquote><p></p>
[QUOTE="Drawmack, post: 547461, member: 4981"] For easy bell cuvre just roll 2d20 and divide the result by 2, rounding down. Of use 2d10 and loose a number, as mentioned earlier you can loose 1 or one that I saw a while ago rolled 2d10-1 unless you rolled a natural 20 which effectively got rid of the 19. The logic was that 1 is a critical fumble and 20 is a critical pass so 19 was a much less important number then either of those two. It also did something wierd to the average roll (1+2+3+...+18+20)/19 ~ 10.05. You can vary the dice find any combination of dice that totals 20 when rolled to max. a) 5d4 b) 3d4 + 1d8 c) 2d4 + 2d6 b) 2d4 + 1d12 e) 2d6 + 1d8 f) 1d8 + 1d12 g) 2d10 Then subtract N-1 where N = the number of dice rolled, in all cases except when all dice maxe out. a) - 4 b) - 3 c) - 3 d) - 2 e) - 2 f) -1 g) - 1 The number that you eliminate is 20-(N-1). a) 20 - 4 = 16 b,c) 20 - 3 = 17 d) 20 - 2 = 18 e,f) 20 - 1 = 19 so you averages become a) (1+2+...+15+17+18+19+20)/19 ~ 10.21 b,c) (1+2+...+16+18+19+20)/19 ~ 10.16 d) (1+2+...+17+19+20)/19 ~ 10.11 e,f) (1+2+...+18+20)/19 ~ 10.05 Since the average is a function of the number eliminated the higher the number you can eliminate the better of you are. Now let's look at the d30 distribution and average to see if what you propose is better then what can easily be done with dice we already have. (1+2+3+4+5+6+7+7+8+8+9+9+10+10+10+11+11+11+12+12+13+13+14+14+15+16+17+18+19+20)/30 = 315/30 = 10.5 comes out the same as 1d20. Though I if you talk probability you have a 3 1/3 chance to roll any given side so you have a 3 1/3% chance of rolling 1,2,3,4,5,6,15,16,17,18,19,20 6 2/3% chance of rolling 7,8,9,12,13,14 10% chance of rolling 10,11 I don't feel like doing anymore math but I bet the the best bell curve is going to come from 5d4. [/QUOTE]
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