{"id":630,"date":"2020-12-04T10:41:49","date_gmt":"2020-12-04T10:41:49","guid":{"rendered":"https:\/\/alandix.com\/statistics\/?p=630"},"modified":"2020-12-04T10:41:49","modified_gmt":"2020-12-04T10:41:49","slug":"lottery-numbers-in-a-row-what-are-the-odds-of-that","status":"publish","type":"post","link":"https:\/\/alandix.com\/statistics\/2020\/12\/04\/lottery-numbers-in-a-row-what-are-the-odds-of-that\/","title":{"rendered":"Lottery numbers in a row \u2013 what are the odds of that!"},"content":{"rendered":"<p>The South African lottery is facing suspicion of nefarious practice after the winning numbers was six consecutive numbers: 5, 6, 7, 8, 9, 10<\/p>\n<p>Given 50 numbers to choose from this seems extremely odd &#8230; or is it?<\/p>\n<p style=\"text-align: center;\"><a rel=\"noopener noreferrer\" href=\"https:\/\/www.theguardian.com\/world\/2020\/dec\/02\/six-in-a-row-winning-numbers-in-south-african-lottery-are-5-6-7-8-9-and-10\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-631 alignnone\" src=\"https:\/\/alandix.com\/statistics\/files\/2020\/12\/guardian-article.jpg\" alt=\"\" width=\"479\" height=\"537\" \/><\/a><br \/>\n&#8220;<a rel=\"noopener noreferrer\" href=\"https:\/\/www.theguardian.com\/world\/2020\/dec\/02\/six-in-a-row-winning-numbers-in-south-african-lottery-are-5-6-7-8-9-and-10\" target=\"_blank\">Six in a row: winning numbers in South African lottery are: 5, 6, 7, 8, 9 and 10<\/a>&#8221;<br \/>\nThe Guardian, South Africa, 2nd Dec 2020<\/p>\n<p>In fact, I describe a very similar surprising situation in my book <a rel=\"noopener noreferrer\" href=\"https:\/\/alandix.com\/statistics\/book\/\" target=\"_blank\">Statistics for HCI: Making Sense of Quantitative Data<\/a>, and in the accompanying video &#8220;<a rel=\"noopener noreferrer\" href=\"https:\/\/alandix.com\/statistics\/2019\/03\/11\/doing-it-8\/\" target=\"_blank\">&#8230; or worse<\/a>&#8220;.<\/p>\n<p><iframe loading=\"lazy\" title=\"Doing it! (making sense of statistics)  \u2013 \u2026or worse\" width=\"584\" height=\"329\" src=\"https:\/\/www.youtube.com\/embed\/khfPRrN1pFc?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p>In the video I had three cards in a row whilst playing a game of patience.\u00a0 At first I&#8217;d thought I&#8217;d not shuffled the cards properly, but then realised it was not nearly as unlikely as I&#8217;d first thought.<\/p>\n<p>When we see something surprising and work out the odds of it happening it might at first seem incredibly unlikely.\u00a0 However, this is an example of <a rel=\"noopener noreferrer\" href=\"https:\/\/alandix.com\/glossary\/hcistats\/sampling%20bias\" target=\"_blank\">sampling bias<\/a>, we tend to notice more unusual outcomes, and so not surprisingly they are the more unlikely ones.<\/p>\n<p>Whenever we see an apparently unlikely event like this we have to ask two questions:<\/p>\n<ol>\n<li>how many other things would seem equally surprising<\/li>\n<li>how often does event occur that gave rise to the surprising result<\/li>\n<\/ol>\n<p>It is indeed exceedingly unlikely to get any particular set of six numbers &#8230; if it weren&#8217;t you&#8217;d always be winning the lottery.\u00a0 In fact for any particular set of six numbers the odds are about one in 22 million (50!\/(6!x44!)).<\/p>\n<p>However, looking at question 1, there are 44 different start positions, so that means the odds of getting a consecutive sequence are 22 million \/ 44, that is about one in half a million.\u00a0 Still pretty surprising!<\/p>\n<p>Turning to question 2, the South African Lotto has been <a rel=\"noopener noreferrer\" href=\"https:\/\/za.national-lottery.com\/lotto\/results-archive-2000\" target=\"_blank\">running since 2000<\/a> with draws twice weekly for most of that time.\u00a0 That is there have been around 2000 draws of the Lotto, so there is about a one in 250 chance (1\/2 million \/ 2000) that one of those would be a consecutive sequence.<\/p>\n<p>Unlikely still, but a lot less unlikely than the immediate one in 22 million.<\/p>\n<p>In addition (more on question 2) there are two other bi-weekly 6 ball lottos and two bi-weekly seven ball Lottos as well as a daily five ball lotto; and (more on question 1) there are other interesting number combinations such as consecutive even numbers.<\/p>\n<p>To be honest, if I were the lottery organiser I would still double check, if only to reassure my punters, but it is not nearly as astounding as it first appears.<\/p>\n<p>On a serious note, if you are doing your own experiments, perhaps you can start to see why there are worries about <a rel=\"noopener noreferrer\" href=\"https:\/\/alandix.com\/glossary\/hcistats\/multiple%20tests\" target=\"_blank\">multiple tests<\/a>, <a rel=\"noopener noreferrer\" href=\"https:\/\/alandix.com\/glossary\/hcistats\/publication%20bias\" target=\"_blank\">publication bias<\/a> and <a rel=\"noopener noreferrer\" href=\"https:\/\/alandix.com\/glossary\/hcistats\/hark\" target=\"_blank\">HARKing<\/a> (hypothesis after the results are known).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The winning numbers in the South African lottery were six consecutive numbers: 5,6,7,8,9,10.  At first this seems extremely odd &#8230; but is it? <a href=\"https:\/\/alandix.com\/statistics\/2020\/12\/04\/lottery-numbers-in-a-row-what-are-the-odds-of-that\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":631,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-630","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/posts\/630","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/comments?post=630"}],"version-history":[{"count":3,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/posts\/630\/revisions"}],"predecessor-version":[{"id":635,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/posts\/630\/revisions\/635"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/media\/631"}],"wp:attachment":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/media?parent=630"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/categories?post=630"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/tags?post=630"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}