The probabilities of rolling particular numbers on 3 6-sided dice: (Sample space is 6 * 6 * 6 = 216) n twin div +/- decimal pct cum ---------------------------------------------- 3 [18] - 1/216 (--) = 0.00463 = 0.5% -- 4 [17] - 3/216 (+2) = 0.01851 = 1.9% 1.9% 5 [16] - 6/216 (+3) = 0.02778 = 2.8% 4.7% 6 [15] - 10/216 (+4) = 0.04629 = 4.6% 9.3% 7 [14] - 15/216 (+5) = 0.06944 = 6.9% 16.2% 8 [13] - 21/216 (+6) = 0.09722 = 9.7% 25.9% 9 [12] - 25/216 (+4) = 0.11574 = 11.6% 37.5% 10 [11] - 27/216 (+2) = 0.125 = 12.5% 50.0% 11 [10] - 27/216 (+2) = 0.125 = 12.5% 62.5% 12 [ 9] - 25/216 (+4) = 0.11574 = 11.6% 74.1% 13 [ 8] - 21/216 (+6) = 0.09722 = 9.7% 83.8% 14 [ 7] - 15/216 (+5) = 0.06944 = 6.9% 90.7% 15 [ 6] - 10/216 (+4) = 0.04629 = 4.6% 95.3% 16 [ 5] - 6/216 (+3) = 0.02778 = 2.8% 98.1% 17 [ 4] - 3/216 (+2) = 0.01851 = 1.9% 100.0% 18 [ 3] - 1/216 (--) = 0.00463 = 0.5% -- Notes: "Middle Chunk" percentage: The way you read this is: "You will roll 9 through 12 (inclusive) 48.2% of the time." - 10-11 = 25.0% - 9-12 = 48.2% - 8-13 = 67.6% - 7-14 = 81.4% - 6-15 = 90.6% - 5-16 = 96.2% - 4-17 = 100.0% - 3-18 = 101.0% (the extremes are essentially rounding errors) "Twins" percentage: The way you read this is: "You will roll 9 or his twin 12 23.2% of the time." (this is handy information if you are making up a random effects / encounters / rumors table. - 10-11 = 25.0% - 9-12 = 23.2% - 8-13 = 19.4% - 7-14 = 13.8% - 6-15 = 9.2% - 5-16 = 5.6% - 4-17 = 3.8% - 3-18 = 1.0% Emulating other dice: One of the neat things about 3d6 is that they subsume a lot of other divisional / fractional scales. Examples follow. Left-hand side shows the integer scale, right hand side shows the equivalent rolls on 3d6: 1d2: 1 = 3-10 2 = 11-18 1d3: 1 = 3-9 2 = 10-11 3 = 12-18 1d4: 1 = 3-8 2 = 9-10 3 = 11-12 4 = 13-18 1d6: 1 = 3-7 2 = 8-9 3 = 10 4 = 11 5 = 12-13 6 = 14-18 Show your work! 3 [18] ------ 1 | 1 2 | 1 3 | 1 x1 4 [17] ------ 1 | 1 2 | 1 3 | 2 x3 5 [16] ------ 1 | 1 1 2 | 1 2 3 | 3 2 x3 x3 6 [15] ------ 1 | 1 1 2 2 | 1 2 2 3 | 4 3 2 x3 x6 x1 7 [14] ------ 1 | 1 1 1 2 2 | 1 2 3 2 3 | 5 4 3 3 x3 x6 x3 x3 8 [13] ------ 1 | 1 1 1 2 2 2 | 1 2 3 2 3 3 | 6 5 4 4 3 x3 x6 x6 x3 x3 9 [12] ------ 1 | 1 1 1 2 2 3 2 | 2 3 4 2 3 3 3 | 6 5 4 5 4 3 x6 x6 x3 x3 x6 x1 10 [11] ------ 1 | 1 1 2 2 2 3 2 | 3 4 2 3 4 3 3 | 6 5 6 5 4 4 x6 x6 x3 x6 x3 x3 11 [10] ------ 1 | 1 1 2 2 3 3 2 | 4 5 3 4 3 4 3 | 6 5 6 5 5 4 x6 x3 x6 x6 x3 x3 12 [9] ------ 1 | 1 2 2 3 3 4 2 | 5 4 5 3 4 4 3 | 6 6 5 6 5 4 x6 x6 x3 x3 x6 x1 13 [8] ------ 1 | 1 2 3 3 4 2 | 6 5 4 5 4 3 | 6 6 6 5 5 x3 x6 x6 x3 x3 14 [7] ------ 1 | 2 3 4 4 2 | 6 5 4 5 3 | 6 6 6 5 x3 x6 x3 x3 15 [6] ------ 1 | 3 4 5 2 | 6 5 5 3 | 6 6 5 x3 x6 x1 16 [5] ------ 1 | 4 5 2 | 6 5 3 | 6 6 x3 x3 17 [4] ------ 1 | 5 2 | 6 3 | 6 x3 18 [3] ------ 1 | 6 2 | 6 3 | 6 x1 Test case: Rolled 100 dice, counted results: (for i in `seq 100`; do rolldice 3d6; done | sort -n | uniq -c) cnt roll 1 4 2 5 6 6 7 7 8 8 14 9 9 10 11 11 15 12 9 13 5 14 5 15 4 16 4 17 Same test, 1000 rolls: (for i in `seq 1000`; do rolldice 3d6; done | sort -n | uniq -c) cnt roll 4 3 14 4 23 5 57 6 70 7 103 8 109 9 116 10 113 11 122 12 113 13 63 14 45 15 26 16 15 17 7 18