{"id":1412,"date":"2022-08-12T09:24:38","date_gmt":"2022-08-12T09:24:38","guid":{"rendered":"https:\/\/gflima.net\/?p=1412"},"modified":"2022-08-12T09:36:49","modified_gmt":"2022-08-12T09:36:49","slug":"the-variance-of-high-production-hexes-in-catan","status":"publish","type":"post","link":"https:\/\/gflima.net\/?p=1412","title":{"rendered":"The Variance of High Production Hexes in Catan"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"1412\" class=\"elementor elementor-1412\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5814880 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5814880\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-278b709\" data-id=\"278b709\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-de1cf20 elementor-widget elementor-widget-text-editor\" data-id=\"de1cf20\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.6.8 - 27-07-2022 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#818a91;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#818a91;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p>It always bugs me when I have a set up which is just as good as someone else&#8217;s, and then one of their numbers rolls twice as many times as an equivalent one of mine,\u00a0 even though their expectation is, in theory, the same. Like when the 6&#8217;s roll twice as many times as the 8&#8217;s, and, ironically, you happen to be on a 6 and not on an 8, so you just sit there watching that stream of resources going to someone else throughout the whole game.<\/p><p>This bothered me so much that I started using the<span style=\"text-decoration: underline; color: #3366ff;\"> <a style=\"color: #3366ff; text-decoration: underline;\" href=\"https:\/\/blog.colonist.io\/designing-balanced-dice\/\">balanced dice option featured in colonist.io<\/a><\/span>, and the difference was very noticeable. Given the implementation of a ranking system in Colonist, I&#8217;ve since started playing rated games, and these only feature the usual &#8220;random&#8221; dice, much to my frustration.<\/p><p>In a (likely futile) attempt to convince others to abandon the &#8220;random&#8221; dice in favor of their balanced counterpart I wrote <span style=\"text-decoration: underline;\"><span style=\"color: #3366ff; text-decoration: underline;\"><a style=\"color: #3366ff; text-decoration: underline;\" href=\"http:\/\/gflima.net\/wp-content\/uploads\/2022\/08\/Article.pdf\">this small article<\/a><\/span><\/span> that compares the probabilities of these specific imbalances occurring. And guess what, the chances of one of the high hexes (5 pips or 4 pips) rolling at least twice as many times as it&#8217;s counterpart is roughly 37%, i.e. more than one in three&#8230;<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e8eec50 elementor-align-center elementor-widget elementor-widget-button\" data-id=\"e8eec50\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/gflima.net\/wp-content\/uploads\/2022\/08\/Article.pdf\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t<span class=\"elementor-button-icon elementor-align-icon-left\">\n\t\t\t\t<i aria-hidden=\"true\" class=\"fas fa-file-pdf\"><\/i>\t\t\t<\/span>\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Download Article<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0c494ca elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0c494ca\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e86b714\" data-id=\"e86b714\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-968335c elementor-widget elementor-widget-text-editor\" data-id=\"968335c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>It always bugs me when I have a set up which is just as good as someone else&#8217;s, and then one of their numbers rolls twice as many times as an equivalent one of mine,\u00a0 even though their expectation is, in theory, the same. Like when the 6&#8217;s roll twice as many times as the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[9,10],"tags":[],"_links":{"self":[{"href":"https:\/\/gflima.net\/index.php?rest_route=\/wp\/v2\/posts\/1412"}],"collection":[{"href":"https:\/\/gflima.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gflima.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gflima.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gflima.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1412"}],"version-history":[{"count":16,"href":"https:\/\/gflima.net\/index.php?rest_route=\/wp\/v2\/posts\/1412\/revisions"}],"predecessor-version":[{"id":1433,"href":"https:\/\/gflima.net\/index.php?rest_route=\/wp\/v2\/posts\/1412\/revisions\/1433"}],"wp:attachment":[{"href":"https:\/\/gflima.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1412"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gflima.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1412"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gflima.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1412"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}