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General Tabletop Discussion
*TTRPGs General
Dice Math - what are the chances for these rolls?
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<blockquote data-quote="Agback" data-source="post: 1422742" data-attributes="member: 5328"><p>As you can readily confirm, the number of combinations where the faces total to each sum is as follows:</p><p></p><p>0 1</p><p>1 4</p><p>2 10</p><p>3 20</p><p>4 35</p><p>5 56</p><p>6 80</p><p>7 104</p><p>8 125</p><p>9 140</p><p>10 146</p><p>11 140</p><p>12 125</p><p>13 104</p><p>14 80</p><p>15 56</p><p>16 35</p><p>17 20</p><p>18 10</p><p>19 4</p><p>20 1</p><p></p><p>So the number of combinations summing to each total or less is</p><p></p><p>0 1</p><p>1 5</p><p>2 15</p><p>3 35</p><p>4 70</p><p>5 126</p><p>6 206</p><p>7 310</p><p>8 435</p><p>9 575</p><p>10 721</p><p>11 861</p><p>12 986</p><p>13 1090</p><p>14 1170</p><p>15 1226</p><p>16 1261</p><p>17 1281</p><p>18 1291</p><p>19 1295</p><p>20 1296</p><p></p><p>For the associated probabilities, divide by the total number of combinations (6^4). The results are approximately:</p><p></p><p>0 0.077%</p><p>1 0.386%</p><p>2 1.157%</p><p>3 2.701%</p><p>4 5.401%</p><p>5 9.722%</p><p>6 15.895%</p><p>7 23.920%</p><p>8 33.565%</p><p>9 44.367%</p><p>10 55.633%</p><p>11 66.435%</p><p>12 76.080%</p><p>13 84.105%</p><p>14 90.278%</p><p>15 94.599%</p><p>16 97.299%</p><p>17 98.843%</p><p>18 99.614%</p><p>19 99.923%</p><p>20 100.000%</p><p></p><p></p><p></p><p>Six different combinations count as matches. P = 6/1296 = 1/216 which is approximately 0.46296%.</p><p></p><p></p><p></p><p>Each specific match is one combination out of 1296, so P = 1/1296, which is approximately 0.07716%.</p><p></p><p>Regards,</p><p></p><p></p><p>Agback</p></blockquote><p></p>
[QUOTE="Agback, post: 1422742, member: 5328"] As you can readily confirm, the number of combinations where the faces total to each sum is as follows: 0 1 1 4 2 10 3 20 4 35 5 56 6 80 7 104 8 125 9 140 10 146 11 140 12 125 13 104 14 80 15 56 16 35 17 20 18 10 19 4 20 1 So the number of combinations summing to each total or less is 0 1 1 5 2 15 3 35 4 70 5 126 6 206 7 310 8 435 9 575 10 721 11 861 12 986 13 1090 14 1170 15 1226 16 1261 17 1281 18 1291 19 1295 20 1296 For the associated probabilities, divide by the total number of combinations (6^4). The results are approximately: 0 0.077% 1 0.386% 2 1.157% 3 2.701% 4 5.401% 5 9.722% 6 15.895% 7 23.920% 8 33.565% 9 44.367% 10 55.633% 11 66.435% 12 76.080% 13 84.105% 14 90.278% 15 94.599% 16 97.299% 17 98.843% 18 99.614% 19 99.923% 20 100.000% Six different combinations count as matches. P = 6/1296 = 1/216 which is approximately 0.46296%. Each specific match is one combination out of 1296, so P = 1/1296, which is approximately 0.07716%. Regards, Agback [/QUOTE]
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