{"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 v27.7 - 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. 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... 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In the second article, I suggested that self-reported political alignment could\u2026","rel":"","context":"In \"data science\"","block_context":{"text":"data science","link":"https:\/\/www.allendowney.com\/blog\/tag\/data-science\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2019\/08\/image-5.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":1661,"url":"https:\/\/www.allendowney.com\/blog\/2025\/12\/04\/the-lost-chapter\/","url_meta":{"origin":70,"position":1},"title":"The Lost Chapter","author":"AllenDowney","date":"December 4, 2025","format":false,"excerpt":"I'm happy to report that Probably Overthinking It is available now in paperback. If you would like a copy, you can order from Bookshop.org and Amazon (affiliate links). To celebrate, I'm publishing The Lost Chapter -- that is, the chapter I cut from the published book. It's about The Girl\u2026","rel":"","context":"In \"paradox\"","block_context":{"text":"paradox","link":"https:\/\/www.allendowney.com\/blog\/tag\/paradox\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/12\/502b755caff85849b479f54f200cc4eeb645981da95d8f8a1c908832b6539896.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":517,"url":"https:\/\/www.allendowney.com\/blog\/2020\/11\/23\/when-will-the-haunt-begin\/","url_meta":{"origin":70,"position":2},"title":"When will the haunt begin?","author":"AllenDowney","date":"November 23, 2020","format":false,"excerpt":"One of the favorite board games at my house is\u00a0Betrayal at House on the Hill. A unique feature of the game is the dice, which yield three possible outcomes, 0, 1, or 2, with equal probability. When you add them up, you get some unusual probability distributions. 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