{"id":1794,"date":"2005-12-22T22:39:57","date_gmt":"2005-12-23T06:39:57","guid":{"rendered":"http:\/\/www.ogre.nu\/wp\/?p=1794"},"modified":"2005-12-23T15:41:52","modified_gmt":"2005-12-23T23:41:52","slug":"fifty-two-choose-five","status":"publish","type":"post","link":"https:\/\/bendwavy.org\/wp\/?p=1794","title":{"rendered":"fifty-two choose five"},"content":{"rendered":"<p>So I was writing a little allegorical paragraph which invited the reader to imagine a poker game in which a dispute arises over whether a flush beats a straight or not.  &#8220;(The one holding the straight,&#8221; I explained, &#8220;is a math nerd who assumes that the rank reflects the probability.)&#8221;<\/p>\n<p>But it&#8217;s a lucky thing I stopped to make sure.  There are 10&times;4<sup>5<\/sup> = 10240 possible straights, and only 4&times;13!\/5!8! = 5148 possible flushes.  Yet somehow I&#8217;ve believed for most of my life that a straight is more unlikely than a flush, and the ranking of flushes over straights a mere arbitrary anomaly.  I wonder how the heck I got that idea.<\/p>\n<p><small>(I&#8217;ve temporarily removed <i>poker<\/i> from the spam list so that you can respond to this without excessive awkwardness.  If after clicking the button you find yourself looking at the FBI&#8217;s homepage, you&#8217;ve found another word on the list.)<\/small><\/p>\n","protected":false},"excerpt":{"rendered":"<p>So I was writing a little allegorical paragraph which invited the reader to imagine a poker game in which a dispute arises over whether a flush beats a straight or not. &#8220;(The one holding the straight,&#8221; I explained, &#8220;is a &hellip; <a href=\"https:\/\/bendwavy.org\/wp\/?p=1794\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-1794","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"_links":{"self":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/1794","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1794"}],"version-history":[{"count":0,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/1794\/revisions"}],"wp:attachment":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1794"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1794"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1794"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}