{"id":70,"date":"2018-10-02T12:50:11","date_gmt":"2018-10-02T12:50:11","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=70"},"modified":"2018-10-02T12:50:11","modified_gmt":"2018-10-02T12:50:11","slug":"the-dungeons-and-dragons-problem","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2018\/10\/02\/the-dungeons-and-dragons-problem\/","title":{"rendered":"The Dungeons and Dragons problem"},"content":{"rendered":"<p>Last week I posed this problem in my Bayesian Statistics class:<\/p>\n<blockquote><p><em>Suppose there are 10 people in my Dungeons and Dragons club; on any game day, each of them has a 70% chance of showing up.<\/em><\/p>\n<p><em>Each player has one character and each character has 6 attributes, each of which is generated by rolling and adding up 3 6-sided dice.<\/em><\/p>\n<p><em>At the beginning of the game, I ask whose character has the lowest attribute. The wizard says, &#8220;My constitution is 5; does anyone have a lower attribute?&#8221;, and no one does.<\/em><\/p>\n<p><em>The warrior says &#8220;My strength is 16; does anyone have a higher attribute?&#8221;, and no one does.<\/em><\/p>\n<p><em>How many characters are in the party?<\/em><\/p><\/blockquote>\n<p>My solution is in this Jupyter notebook:<\/p>\n<div class=\"oembed-gist\"><script src=\"https:\/\/gist.github.com\/AllenDowney\/8ad4ec6a88d2902801de19b3fce187b9.js\"><\/script><noscript>View the code on <a href=\"https:\/\/gist.github.com\/AllenDowney\/8ad4ec6a88d2902801de19b3fce187b9\">Gist<\/a>.<\/noscript><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Last week I posed this problem in my Bayesian Statistics class: Suppose there are 10 people in my Dungeons and Dragons club; on any game day, each of them has a 70% chance of showing up. Each player has one character and each character has 6 attributes, each of which is generated by rolling and adding up 3 6-sided dice. At the beginning of the game, I ask whose character has the lowest attribute. The wizard says, &#8220;My constitution is&#8230;<\/p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https:\/\/www.allendowney.com\/blog\/2018\/10\/02\/the-dungeons-and-dragons-problem\/\"> Read More<span class=\"screen-reader-text\">  Read More<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[1],"tags":[],"class_list":["post-70","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>The Dungeons and Dragons problem - Probably Overthinking It<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.allendowney.com\/blog\/2018\/10\/02\/the-dungeons-and-dragons-problem\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Dungeons and Dragons problem - Probably Overthinking It\" \/>\n<meta property=\"og:description\" content=\"Last week I posed this problem in my Bayesian Statistics class: Suppose there are 10 people in my Dungeons and Dragons club; on any game day, each of them has a 70% chance of showing up. 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