{"id":4508,"date":"2020-11-27T15:36:25","date_gmt":"2020-11-27T15:36:25","guid":{"rendered":"https:\/\/robertjwallace.com\/?p=4508"},"modified":"2021-06-14T15:17:32","modified_gmt":"2021-06-14T15:17:32","slug":"perspective-on-card-shuffling","status":"publish","type":"post","link":"https:\/\/robertjwallace.com\/es\/perspective-on-card-shuffling\/","title":{"rendered":"Perspectiva sobre la mezcla de cartas"},"content":{"rendered":"<p>The largest U.S. manufacture of playing cards sells approx. 100,000,000<br>decks of playing cards per year. This can be expressed as 10<sup>8<\/sup>.<\/p>\n\n\n\n<!--more-->\n\n\n\n<p>If each deck sold was fairly shuffled once every five seconds, then each deck<br>would be shuffled 86,400 times per day, or 31,536,000 times in a year.<\/p>\n\n\n\n<p>That can be expressed as approximately 3.15 x 10<sup>7<\/sup>.<\/p>\n\n\n\n<p>So if all the manufactured decks were shuffled each day, every five seconds,<br>the number of unique orderings would be 3.15 x 10<sup>7<\/sup> x 10<sup>8<\/sup> = 3.15 x 10<sup>15<\/sup>.<\/p>\n\n\n\n<p>The number of ways a deck of cards can be ordered is 52! or approximately<br>8 x 10<sup>67<\/sup>.<\/p>\n\n\n\n<p>Assuming that each shuffle gives a new order to the cards then to get each <br>possible ordering of the playing cards would only take 2.5 * 10<sup>52<\/sup> years.  (8 x 10<sup>67<\/sup>\/3.15 x 10<sup>15<\/sup>.<\/p>\n\n\n\n<p>Unfortunately, the Earth is only going to last a couple billion years or so<br>until the Sun runs out of fuel (2 x 10<sup>9<\/sup>)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">8 x 10<sup>67<\/sup> (number of ways a deck of cards can be ordered)<\/h2>\n\n\n\n<p>80,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2.5 * 10<sup>52<\/sup> (number of years to get every possible ordering of a deck of playing cards)<\/h2>\n\n\n\n<p>250,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2 * 10<sup> <\/sup>(number of years left in the life of Earth)<\/h2>\n\n\n\n<p>2,000,000,000<\/p>","protected":false},"excerpt":{"rendered":"<p>The largest U.S. manufacture of playing cards sells approx. 100,000,000decks of playing cards per year. This can be expressed as 108.<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_eb_attr":"","footnotes":""},"categories":[7],"tags":[],"class_list":["post-4508","post","type-post","status-publish","format-standard","hentry","category-magic"],"featured_image_src":null,"featured_image_src_square":null,"author_info":{"display_name":"Bob","author_link":"https:\/\/robertjwallace.com\/es\/author\/admin\/"},"_links":{"self":[{"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/posts\/4508","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/comments?post=4508"}],"version-history":[{"count":2,"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/posts\/4508\/revisions"}],"predecessor-version":[{"id":5323,"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/posts\/4508\/revisions\/5323"}],"wp:attachment":[{"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/media?parent=4508"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/categories?post=4508"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/tags?post=4508"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}