{"id":178,"date":"2020-10-15T05:00:34","date_gmt":"2020-10-15T05:00:34","guid":{"rendered":"http:\/\/alchy.my\/blog\/?p=178"},"modified":"2020-10-15T05:00:34","modified_gmt":"2020-10-15T05:00:34","slug":"roll-3","status":"publish","type":"post","link":"https:\/\/alchy.my\/blog\/archives\/178","title":{"rendered":"Roll 3"},"content":{"rendered":"\n<p>As a follow up to a long ago post about Dice probabilities, we derive 6<sup><em>n<\/em><\/sup> as a formula to use to calculate the possible outcomes.<\/p>\n\n\n\n<p>Two dice 6<sup>2<\/sup>\u00a0= 36 outcomes.<br>Three dice 6<sup>3<\/sup>\u00a0= 216 outcomes.<\/p>\n\n\n\n<p>If we take 3 Dice, the results would range from 3 &#8211; 18,  <em>or between (n<\/em> &#8211; 6<sup><em>n<\/em><\/sup>).<\/p>\n\n\n\n<p>The tricky part comes from trying to calculate the chances of each result without doing the mathematically inept person I am did, which was to list out all the possibilities. <\/p>\n\n\n\n<ul class=\"wp-block-list\" id=\"mntl-sc-block_1-0-18\"><li>3 = 1 + 1 + 1<\/li><li>4 = 1 + 1 + 2<\/li><li>5 = 1 + 1 + 3 = 2 + 2 + 1<\/li><li>6 = 1 + 1 + 4 = 1 + 2 + 3 = 2 + 2 + 2<\/li><li>7 = 1 + 1 + 5 = 2 + 2 + 3 = 3 + 3 + 1 = 1 + 2 + 4<\/li><li>8 = 1 + 1 + 6 = 2 + 3 + 3 = 4 + 3 + 1 = 1 + 2 + 5 = 2 + 2 + 4<\/li><li>9 = 6 + 2 + 1 = 4 + 3 + 2 = 3 + 3 + 3 = 2 + 2 + 5 = 1 + 3 + 5 = 1 + 4 + 4<\/li><li>10 = 6 + 3 + 1 = 6 + 2 + 2 = 5 + 3 + 2 = 4 + 4 + 2 = 4 + 3 + 3 = 1 + 4 + 5<\/li><li>11 = 6 + 4 + 1 = 1 + 5 + 5 = 5 + 4 + 2 = 3 + 3 + 5 = 4 + 3 + 4 = 6 + 3 + 2<\/li><li>12 = 6 + 5 + 1 = 4 + 3 + 5 = 4 + 4 + 4 = 5 + 2 + 5 = 6 + 4 + 2 = 6 + 3 + 3<\/li><li>13 = 6 + 6 + 1 = 5 + 4 + 4 = 3 + 4 + 6 = 6 + 5 + 2 = 5 + 5 + 3<\/li><li>14 = 6 + 6 + 2 = 5 + 5 + 4 = 4 + 4 + 6 = 6 + 5 + 3<\/li><li>15 = 6 + 6 + 3 = 6 + 5 + 4 = 5 + 5 + 5<\/li><li>16 = 6 + 6 + 4 = 5 + 5 + 6<\/li><li>17 = 6 + 6 + 5<\/li><li>18 = 6 + 6 + 6<\/li><\/ul>\n\n\n\n<p>So the grand result would be;<\/p>\n\n\n\n<ul class=\"wp-block-list\" id=\"mntl-sc-block_1-0-25\"><li>Probability of a sum of 3: 1\/216 = 0.5%<\/li><li>Probability of a sum of 4: 3\/216 = 1.4%<\/li><li>Probability of a sum of 5: 6\/216 = 2.8%<\/li><li>Probability of a sum of 6: 10\/216 = 4.6%<\/li><li>Probability of a sum of 7: 15\/216 = 7.0%<\/li><li>Probability of a sum of 8: 21\/216 = 9.7%<\/li><li>Probability of a sum of 9: 25\/216 = 11.6%<\/li><li>Probability of a sum of 10: 27\/216 = 12.5%<\/li><li>Probability of a sum of 11: 27\/216 = 12.5%<\/li><li>Probability of a sum of 12: 25\/216 = 11.6%<\/li><li>Probability of a sum of 13: 21\/216 = 9.7%<\/li><li>Probability of a sum of 14: 15\/216 = 7.0%<\/li><li>Probability of a sum of 15: 10\/216 = 4.6%<\/li><li>Probability of a sum of 16: 6\/216 = 2.8%<\/li><li>Probability of a sum of 17: 3\/216 = 1.4%<\/li><li>Probability of a sum of 18: 1\/216 = 0.5%<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>As a follow up to a long ago post about Dice probabilities, we derive 6n as a formula to use to calculate the possible outcomes. Two dice 62\u00a0= 36 outcomes.Three [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-178","post","type-post","status-publish","format-standard","hentry","category-analog-game-development"],"_links":{"self":[{"href":"https:\/\/alchy.my\/blog\/wp-json\/wp\/v2\/posts\/178","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/alchy.my\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/alchy.my\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/alchy.my\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/alchy.my\/blog\/wp-json\/wp\/v2\/comments?post=178"}],"version-history":[{"count":1,"href":"https:\/\/alchy.my\/blog\/wp-json\/wp\/v2\/posts\/178\/revisions"}],"predecessor-version":[{"id":179,"href":"https:\/\/alchy.my\/blog\/wp-json\/wp\/v2\/posts\/178\/revisions\/179"}],"wp:attachment":[{"href":"https:\/\/alchy.my\/blog\/wp-json\/wp\/v2\/media?parent=178"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/alchy.my\/blog\/wp-json\/wp\/v2\/categories?post=178"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/alchy.my\/blog\/wp-json\/wp\/v2\/tags?post=178"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}