{"id":87,"date":"2016-06-06T18:13:05","date_gmt":"2016-06-06T22:43:05","guid":{"rendered":"http:\/\/www.blogs.euni.org\/?p=87"},"modified":"2016-06-06T18:13:05","modified_gmt":"2016-06-06T22:43:05","slug":"elevens-and-twelves","status":"publish","type":"post","link":"https:\/\/www.blogs.euni.org\/?p=87","title":{"rendered":"Elevens and Twelves"},"content":{"rendered":"<p>Casino manager Mango is worried about the new dice game &#8220;Elevens and Twelves&#8221; he invented, as the casino is losing money on it at a rate of about 1%. He fears that casino owner Don Corleone will certainly not be very happy about this.<\/p>\n<p>The game is based on throwing three dice and getting 11 or 12 as a result. The casino pays even money to the player on throws of 11 and the player loses on throws of 12.<\/p>\n<p>Players throw the three dice until they get an 11 or a 12. Then they can make another bet and repeat the process.<\/p>\n<p>Mango had studied probability theory, made some calculations and concluded that the casino would make a profit of about\u00a01% on this game, but, alas, it has not been working out that way.<\/p>\n<p>How did Mango mess this up?<\/p>\n<div class=\"sharedaddy sd-sharing-enabled\"><div class=\"robots-nocontent sd-block sd-social sd-social-icon sd-sharing\"><h3 class=\"sd-title\">Share this:<\/h3><div class=\"sd-content\"><ul><li class=\"share-twitter\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-twitter-87\" class=\"share-twitter sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=87&amp;share=twitter\" target=\"_blank\" title=\"Click to share on Twitter\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on Twitter (Opens in new window)<\/span><\/a><\/li><li class=\"share-facebook\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-facebook-87\" class=\"share-facebook sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=87&amp;share=facebook\" target=\"_blank\" title=\"Click to share on Facebook\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on Facebook (Opens in new window)<\/span><\/a><\/li><li class=\"share-linkedin\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-linkedin-87\" class=\"share-linkedin sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=87&amp;share=linkedin\" target=\"_blank\" title=\"Click to share on LinkedIn\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on LinkedIn (Opens in new window)<\/span><\/a><\/li><li class=\"share-jetpack-whatsapp\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"\" class=\"share-jetpack-whatsapp sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=87&amp;share=jetpack-whatsapp\" target=\"_blank\" title=\"Click to share on WhatsApp\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on WhatsApp (Opens in new window)<\/span><\/a><\/li><li class=\"share-end\"><\/li><\/ul><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Casino manager Mango is worried about the new dice game &#8220;Elevens and Twelves&#8221; he invented, as the casino is losing money on it at a rate of about 1%. He fears that casino owner Don Corleone will certainly not be very happy about this. The game is based on throwing three dice and getting 11 [&hellip;]<\/p>\n<div class=\"sharedaddy sd-sharing-enabled\"><div class=\"robots-nocontent sd-block sd-social sd-social-icon sd-sharing\"><h3 class=\"sd-title\">Share this:<\/h3><div class=\"sd-content\"><ul><li class=\"share-twitter\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-twitter-87\" class=\"share-twitter sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=87&amp;share=twitter\" target=\"_blank\" title=\"Click to share on Twitter\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on Twitter (Opens in new window)<\/span><\/a><\/li><li class=\"share-facebook\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-facebook-87\" class=\"share-facebook sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=87&amp;share=facebook\" target=\"_blank\" title=\"Click to share on Facebook\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on Facebook (Opens in new window)<\/span><\/a><\/li><li class=\"share-linkedin\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-linkedin-87\" class=\"share-linkedin sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=87&amp;share=linkedin\" target=\"_blank\" title=\"Click to share on LinkedIn\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on LinkedIn (Opens in new window)<\/span><\/a><\/li><li class=\"share-jetpack-whatsapp\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"\" class=\"share-jetpack-whatsapp sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=87&amp;share=jetpack-whatsapp\" target=\"_blank\" title=\"Click to share on WhatsApp\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on WhatsApp (Opens in new window)<\/span><\/a><\/li><li class=\"share-end\"><\/li><\/ul><\/div><\/div><\/div>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false},"categories":[10],"tags":[27,28],"jetpack_featured_media_url":"","jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7zDaf-1p","jetpack-related-posts":[{"id":259,"url":"https:\/\/www.blogs.euni.org\/?p=259","url_meta":{"origin":87,"position":0},"title":"Three Dice Cups","date":"November 6, 2016","format":false,"excerpt":"Jackson was concentrating on the three cups filled with dice placed in front of him on the table covered with green felt, wondering which to choose. \u201cSome say that the result of any of the cups will be the same, just a fifty percent chance,\u201d said Snipes the slick gambler.\u2026","rel":"","context":"In &quot;Probability&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":693,"url":"https:\/\/www.blogs.euni.org\/?p=693","url_meta":{"origin":87,"position":1},"title":"The Dice Club Project","date":"September 30, 2018","format":false,"excerpt":"One Saturday afternoon, as Jack, a new member, entered the Snake Eyes Dice Club he saw many people busy throwing dice at various felt-covered tables. \u201cWhy are you repeatedly throwing that die, Vince, won\u2019t you get a sore arm,\u201d asked Jack. \u201cHope not. I\u2019m checking how many throws are needed\u2026","rel":"","context":"In &quot;Combinations&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":900,"url":"https:\/\/www.blogs.euni.org\/?p=900","url_meta":{"origin":87,"position":2},"title":"The Dice Club Game","date":"April 27, 2019","format":false,"excerpt":"One Saturday afternoon, as Jack, now a full-fledged member, entered the Snake Eyes Dice Club in River City, he saw four persons throwing dice at a felt-covered table with Vince, the dealer. \u201cWhat\u2019s up today, Vince?\u201d asked Jack. \u201cLet me introduce you to Simon, Mary, Seamus and Henry here,\u201d said\u2026","rel":"","context":"In &quot;Algebra&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":375,"url":"https:\/\/www.blogs.euni.org\/?p=375","url_meta":{"origin":87,"position":3},"title":"The Four Aces","date":"April 30, 2017","format":false,"excerpt":"Fred was playing poker with his three friends Henry, John and Mack and had just dealt a hand for each. Fred saw that he had an Ace and wondered what the probability was that each of the other players also had an Ace. Later in the evening after the game,\u2026","rel":"","context":"In &quot;Combinations&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":688,"url":"https:\/\/www.blogs.euni.org\/?p=688","url_meta":{"origin":87,"position":4},"title":"Bags with Gold and Silver Coins","date":"September 29, 2018","format":false,"excerpt":"\u201cJack and Jill, which bag do you choose for a chance of winning ten thousand dollars,\u201d hailed the cheerful game show host Dusty Farlone, \u201cthe blue bag with three gold and seven silver coins, or the red bag with four gold and three silver coins. What do you say?\u201d \u201cDusty,\u2026","rel":"","context":"In &quot;Probability&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":168,"url":"https:\/\/www.blogs.euni.org\/?p=168","url_meta":{"origin":87,"position":5},"title":"Coin Flipping","date":"August 13, 2016","format":false,"excerpt":"Jack and Jill were sitting in the shade of a large tree, relaxing after attending some university lectures. \u201cWhat about flipping some coins, Jack,\u201d suggested Jill. \u201cGood idea, I have a silver dollar,\u201d offered Jack. \u201cProfessor Wiseman suggested a coin flipping game,\u201d said Jill. \u201cWe alternately flip a coin and\u2026","rel":"","context":"In &quot;Probability&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts\/87"}],"collection":[{"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=87"}],"version-history":[{"count":4,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts\/87\/revisions"}],"predecessor-version":[{"id":91,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts\/87\/revisions\/91"}],"wp:attachment":[{"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=87"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=87"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=87"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}