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</a> <ul id="toc-Use-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Construction" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Construction"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Construction</span> </div> </a> <button aria-controls="toc-Construction-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Construction subsection</span> </button> <ul id="toc-Construction-sublist" class="vector-toc-list"> <li id="toc-Arrangement" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Arrangement"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Arrangement</span> </div> </a> <ul id="toc-Arrangement-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Manufacturing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Manufacturing"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Manufacturing</span> </div> </a> <ul id="toc-Manufacturing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Etymology_and_terms" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Etymology_and_terms"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Etymology and terms</span> </div> </a> <ul id="toc-Etymology_and_terms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Unicode_representation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Unicode_representation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Unicode representation</span> </div> </a> <ul id="toc-Unicode_representation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Loaded_dice" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Loaded_dice"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Loaded dice</span> </div> </a> <ul id="toc-Loaded_dice-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Variants" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Variants"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Variants</span> </div> </a> <button aria-controls="toc-Variants-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Variants subsection</span> </button> <ul id="toc-Variants-sublist" class="vector-toc-list"> <li id="toc-Polyhedral_dice" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Polyhedral_dice"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Polyhedral dice</span> </div> </a> <ul id="toc-Polyhedral_dice-sublist" class="vector-toc-list"> <li id="toc-Common_variations" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Common_variations"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.1</span> <span>Common variations</span> </div> </a> <ul id="toc-Common_variations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rarer_variations" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Rarer_variations"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.2</span> <span>Rarer variations</span> </div> </a> <ul id="toc-Rarer_variations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Non-numeric_dice" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Non-numeric_dice"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Non-numeric dice</span> </div> </a> <ul id="toc-Non-numeric_dice-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Alternatively-numbered_dice" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Alternatively-numbered_dice"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Alternatively-numbered dice</span> </div> </a> <ul id="toc-Alternatively-numbered_dice-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spherical_dice" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Spherical_dice"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Spherical dice</span> </div> </a> <ul id="toc-Spherical_dice-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Applications</span> </div> </a> <button aria-controls="toc-Applications-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Applications subsection</span> </button> <ul id="toc-Applications-sublist" class="vector-toc-list"> <li id="toc-Notation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Notation"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Notation</span> </div> </a> <ul id="toc-Notation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Dice</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 84 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-84" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">84 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B1%D8%AF" title="نرد – Arabic" lang="ar" hreflang="ar" data-title="نرد" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Daus" title="Daus – Aragonese" lang="an" hreflang="an" data-title="Daus" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Dadu" title="Dadu – Asturian" lang="ast" hreflang="ast" data-title="Dadu" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Z%C9%99r" title="Zər – Azerbaijani" lang="az" hreflang="az" data-title="Zər" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ban mw-list-item"><a href="https://ban.wikipedia.org/wiki/Cematu" title="Cematu – Balinese" lang="ban" hreflang="ban" data-title="Cematu" data-language-autonym="Basa Bali" data-language-local-name="Balinese" class="interlanguage-link-target"><span>Basa Bali</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%BE%E0%A6%B6%E0%A6%BE_(%E0%A6%96%E0%A7%87%E0%A6%B2%E0%A6%BE)" title="পাশা (খেলা) – Bangla" lang="bn" hreflang="bn" data-title="পাশা (খেলা)" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/T%C3%A2u-%C3%A1" title="Tâu-á – Minnan" lang="nan" hreflang="nan" data-title="Tâu-á" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%86%D0%B3%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D0%BA%D0%BE%D1%81%D1%86%D1%8C" title="Ігральная косць – Belarusian" lang="be" hreflang="be" data-title="Ігральная косць" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%97%D0%B0%D1%80" title="Зар – Bulgarian" lang="bg" hreflang="bg" data-title="Зар" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kockice" title="Kockice – Bosnian" lang="bs" hreflang="bs" data-title="Kockice" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Di%C3%B1s" title="Diñs – Breton" lang="br" hreflang="br" data-title="Diñs" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Dau" title="Dau – Catalan" lang="ca" hreflang="ca" data-title="Dau" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Hrac%C3%AD_kostka" title="Hrací kostka – Czech" lang="cs" hreflang="cs" data-title="Hrací kostka" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Dis" title="Dis – Welsh" lang="cy" hreflang="cy" data-title="Dis" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Spilleterning" title="Spilleterning – Danish" lang="da" hreflang="da" data-title="Spilleterning" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-se mw-list-item"><a href="https://se.wikipedia.org/wiki/Bircu" title="Bircu – Northern Sami" lang="se" hreflang="se" data-title="Bircu" data-language-autonym="Davvisámegiella" data-language-local-name="Northern Sami" class="interlanguage-link-target"><span>Davvisámegiella</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://de.wikipedia.org/wiki/Spielw%C3%BCrfel" title="Spielwürfel – German" lang="de" hreflang="de" data-title="Spielwürfel" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/T%C3%A4ring" title="Täring – Estonian" lang="et" hreflang="et" data-title="Täring" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%96%CE%AC%CF%81%CE%B9" title="Ζάρι – Greek" lang="el" hreflang="el" data-title="Ζάρι" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Dado" title="Dado – Spanish" lang="es" hreflang="es" data-title="Dado" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/%C4%B4etpluredro" title="Ĵetpluredro – Esperanto" lang="eo" hreflang="eo" data-title="Ĵetpluredro" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Dado" title="Dado – Basque" lang="eu" hreflang="eu" data-title="Dado" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%A7%D8%B3_(%D9%88%D8%B3%DB%8C%D9%84%D9%87_%D8%A8%D8%A7%D8%B2%DB%8C)" title="تاس (وسیله بازی) – Persian" lang="fa" hreflang="fa" data-title="تاس (وسیله بازی)" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/D%C3%A9" title="Dé – French" lang="fr" hreflang="fr" data-title="Dé" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/D%C3%ADsle" title="Dísle – Irish" lang="ga" hreflang="ga" data-title="Dísle" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Dado" title="Dado – Galician" lang="gl" hreflang="gl" data-title="Dado" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A3%BC%EC%82%AC%EC%9C%84" title="주사위 – Korean" lang="ko" hreflang="ko" data-title="주사위" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B6%D5%A1%D5%BC" title="Զառ – Armenian" lang="hy" hreflang="hy" data-title="Զառ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A4%BE%E0%A4%B8%E0%A4%BE" title="पासा – Hindi" lang="hi" hreflang="hi" data-title="पासा" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kocka_(igra)" title="Kocka (igra) – Croatian" lang="hr" hreflang="hr" data-title="Kocka (igra)" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Dadu" title="Dadu – Indonesian" lang="id" hreflang="id" data-title="Dadu" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Teningur" title="Teningur – Icelandic" lang="is" hreflang="is" data-title="Teningur" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Dado_(gioco)" title="Dado (gioco) – Italian" lang="it" hreflang="it" data-title="Dado (gioco)" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%95%D7%91%D7%99%D7%99%D7%AA_%D7%9E%D7%A9%D7%97%D7%A7" title="קוביית משחק – Hebrew" lang="he" hreflang="he" data-title="קוביית משחק" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Dhadhu" title="Dhadhu – Javanese" lang="jv" hreflang="jv" data-title="Dhadhu" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Dadu" title="Dadu – Swahili" lang="sw" hreflang="sw" data-title="Dadu" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Alea_(res_lusoria)" title="Alea (res lusoria) – Latin" lang="la" hreflang="la" data-title="Alea (res lusoria)" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Metamais_kauli%C5%86%C5%A1" title="Metamais kauliņš – Latvian" lang="lv" hreflang="lv" data-title="Metamais kauliņš" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Lo%C5%A1imo_kauliukas" title="Lošimo kauliukas – Lithuanian" lang="lt" hreflang="lt" data-title="Lošimo kauliukas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Dados" title="Dados – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Dados" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Dob%C3%B3kocka" title="Dobókocka – Hungarian" lang="hu" hreflang="hu" data-title="Dobókocka" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AB%E0%A4%BE%E0%A4%B8%E0%A5%87" title="फासे – Marathi" lang="mr" hreflang="mr" data-title="फासे" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A7%D9%84%D8%B2%D9%87%D8%B1_(%D9%84%D8%B9%D8%A8%D9%87)" title="الزهر (لعبه) – Egyptian Arabic" lang="arz" hreflang="arz" data-title="الزهر (لعبه)" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Dadu" title="Dadu – Malay" lang="ms" hreflang="ms" data-title="Dadu" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/D%C3%A0u" title="Dàu – Mindong" lang="cdo" hreflang="cdo" data-title="Dàu" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Dobbelsteen" title="Dobbelsteen – Dutch" lang="nl" hreflang="nl" data-title="Dobbelsteen" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%B5%E3%82%A4%E3%82%B3%E3%83%AD" title="サイコロ – Japanese" lang="ja" hreflang="ja" data-title="サイコロ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Sp%C3%B6li-Tiarling" title="Spöli-Tiarling – Northern Frisian" lang="frr" hreflang="frr" data-title="Spöli-Tiarling" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Spillterning" title="Spillterning – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Spillterning" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Terning" title="Terning – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Terning" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Dat" title="Dat – Occitan" lang="oc" hreflang="oc" data-title="Dat" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/W%C3%B6rpel_(Speel)" title="Wörpel (Speel) – Low German" lang="nds" hreflang="nds" data-title="Wörpel (Speel)" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ko%C5%9B%C4%87_do_gry" title="Kość do gry – Polish" lang="pl" hreflang="pl" data-title="Kość do gry" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Dado_(pe%C3%A7a)" title="Dado (peça) – Portuguese" lang="pt" hreflang="pt" data-title="Dado (peça)" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Zar" title="Zar – Romanian" lang="ro" hreflang="ro" data-title="Zar" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Wayrukuna" title="Wayrukuna – Quechua" lang="qu" hreflang="qu" data-title="Wayrukuna" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D0%B3%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D0%BA%D0%BE%D1%81%D1%82%D1%8C" title="Игральная кость – Russian" lang="ru" hreflang="ru" data-title="Игральная кость" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Dice" title="Dice – Scots" lang="sco" hreflang="sco" data-title="Dice" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-stq mw-list-item"><a href="https://stq.wikipedia.org/wiki/Doobel" title="Doobel – Saterland Frisian" lang="stq" hreflang="stq" data-title="Doobel" data-language-autonym="Seeltersk" data-language-local-name="Saterland Frisian" class="interlanguage-link-target"><span>Seeltersk</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Zari" title="Zari – Albanian" lang="sq" hreflang="sq" data-title="Zari" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Dadu_(jocu)" title="Dadu (jocu) – Sicilian" lang="scn" hreflang="scn" data-title="Dadu (jocu)" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Dice" title="Dice – Simple English" lang="en-simple" hreflang="en-simple" data-title="Dice" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Hracia_kocka" title="Hracia kocka – Slovak" lang="sk" hreflang="sk" data-title="Hracia kocka" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Igralna_kocka" title="Igralna kocka – Slovenian" lang="sl" hreflang="sl" data-title="Igralna kocka" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%DB%95%D8%B1%D8%AF%DB%95%D8%B2%D8%A7%D8%B1" title="بەردەزار – Central Kurdish" lang="ckb" hreflang="ckb" data-title="بەردەزار" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%BE%D1%86%D0%BA%D0%B0_(%D0%B8%D0%B3%D1%80%D0%B0)" title="Коцка (игра) – Serbian" lang="sr" hreflang="sr" data-title="Коцка (игра)" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Kocka_(igra)" title="Kocka (igra) – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Kocka (igra)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Dadu" title="Dadu – Sundanese" lang="su" hreflang="su" data-title="Dadu" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Noppa" title="Noppa – Finnish" lang="fi" hreflang="fi" data-title="Noppa" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/T%C3%A4rning" title="Tärning – Swedish" lang="sv" hreflang="sv" data-title="Tärning" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Betu-beto" title="Betu-beto – Tagalog" lang="tl" hreflang="tl" data-title="Betu-beto" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AE%BE%E0%AE%AF%E0%AE%95%E0%AF%8D_%E0%AE%95%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AF%88" title="தாயக் கட்டை – Tamil" lang="ta" hreflang="ta" data-title="தாயக் கட்டை" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Asi%C9%A3" title="Asiɣ – Kabyle" lang="kab" hreflang="kab" data-title="Asiɣ" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A5%E0%B8%B9%E0%B8%81%E0%B9%80%E0%B8%95%E0%B9%8B%E0%B8%B2" title="ลูกเต๋า – Thai" lang="th" hreflang="th" data-title="ลูกเต๋า" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Zar" title="Zar – Turkish" lang="tr" hreflang="tr" data-title="Zar" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%96_%D0%BA%D1%96%D1%81%D1%82%D0%BE%D1%87%D0%BA%D0%B8" title="Гральні кісточки – Ukrainian" lang="uk" hreflang="uk" data-title="Гральні кісточки" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B7%D8%A7%D8%B3_(%DA%A9%DA%BE%DB%8C%D9%84)" title="طاس (کھیل) – Urdu" lang="ur" hreflang="ur" data-title="طاس (کھیل)" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-za mw-list-item"><a href="https://za.wikipedia.org/wiki/Lwgsaek" title="Lwgsaek – Zhuang" lang="za" hreflang="za" data-title="Lwgsaek" data-language-autonym="Vahcuengh" data-language-local-name="Zhuang" class="interlanguage-link-target"><span>Vahcuengh</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/X%C3%BAc_x%E1%BA%AFc" title="Xúc xắc – Vietnamese" lang="vi" hreflang="vi" data-title="Xúc xắc" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/V%C3%BCrhvli" title="Vürhvli – Võro" lang="vro" hreflang="vro" data-title="Vürhvli" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E9%AA%B0" title="骰 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="骰" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%AA%B0%E5%AD%90" title="骰子 – Wu" lang="wuu" hreflang="wuu" data-title="骰子" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%AA%B0%E4%BB%94" title="骰仔 – Cantonese" lang="yue" hreflang="yue" data-title="骰仔" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%AA%B0%E5%AD%90" title="骰子 – Chinese" lang="zh" hreflang="zh" data-title="骰子" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q45089#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div 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.hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Dice_(disambiguation)" class="mw-disambig" title="Dice (disambiguation)">Dice (disambiguation)</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:6sided_dice_(cropped).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/6sided_dice_%28cropped%29.jpg/220px-6sided_dice_%28cropped%29.jpg" decoding="async" width="220" height="191" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/6sided_dice_%28cropped%29.jpg/330px-6sided_dice_%28cropped%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/6sided_dice_%28cropped%29.jpg/440px-6sided_dice_%28cropped%29.jpg 2x" data-file-width="923" data-file-height="802" /></a><figcaption>Four traditional dice showing all six different sides.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Dice-rolling-slowmotion-2018-9.webm/220px--Dice-rolling-slowmotion-2018-9.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="154" data-durationhint="11" data-mwtitle="Dice-rolling-slowmotion-2018-9.webm" data-mwprovider="wikimediacommons" resource="/wiki/File:Dice-rolling-slowmotion-2018-9.webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/96/Dice-rolling-slowmotion-2018-9.webm/Dice-rolling-slowmotion-2018-9.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="686" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/96/Dice-rolling-slowmotion-2018-9.webm/Dice-rolling-slowmotion-2018-9.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1030" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/9/96/Dice-rolling-slowmotion-2018-9.webm" type="video/webm; codecs="vp8, vorbis"" data-width="1030" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/96/Dice-rolling-slowmotion-2018-9.webm/Dice-rolling-slowmotion-2018-9.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="206" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/96/Dice-rolling-slowmotion-2018-9.webm/Dice-rolling-slowmotion-2018-9.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="344" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/96/Dice-rolling-slowmotion-2018-9.webm/Dice-rolling-slowmotion-2018-9.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="516" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/96/Dice-rolling-slowmotion-2018-9.webm/Dice-rolling-slowmotion-2018-9.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="516" data-height="360" /></video></span><figcaption>Dice of different sizes being thrown in slow motion.</figcaption></figure> <p>A <b>die</b> (<abbr title="singular form">sg.</abbr>: die or <b>dice</b>; <abbr title="plural form">pl.</abbr>: <b>dice</b>)<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> is a small, throwable object with marked sides that can rest in multiple positions. Dice are used for generating <a href="/wiki/Statistical_randomness" title="Statistical randomness">random values</a>, commonly as part of <a href="/wiki/Tabletop_game" title="Tabletop game">tabletop games</a>, including <a href="/wiki/List_of_dice_games" title="List of dice games">dice games</a>, <a href="/wiki/Board_game" title="Board game">board games</a>, <a href="/wiki/Role-playing_game" title="Role-playing game">role-playing games</a>, and <a href="/wiki/Game_of_chance" title="Game of chance">games of chance</a>. </p><p>A traditional die is a <a href="/wiki/Cube" title="Cube">cube</a> with each of its six faces marked with a different number of dots (<a href="/wiki/Pip_(counting)" title="Pip (counting)">pips</a>) from one to six. When thrown or rolled, the die comes to rest showing a random <a href="/wiki/Integer" title="Integer">integer</a> from one to six on its upper surface, with each value being equally likely. Dice may also have <a href="/wiki/Polyhedron" title="Polyhedron">polyhedral</a> or irregular shapes, may have faces marked with numerals or symbols instead of pips and may have their <a href="/wiki/Number" title="Number">numbers</a> carved out from the <a href="/wiki/Material" title="Material">material</a> of the dice instead of marked on it. Loaded dice are specifically designed or modified to favor some results over others for <a href="/wiki/Cheating" title="Cheating">cheating</a> or entertainment. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:9BFE00_-roman_lead_die_(FindID_103936).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/9BFE00_-roman_lead_die_%28FindID_103936%29.jpg/220px-9BFE00_-roman_lead_die_%28FindID_103936%29.jpg" decoding="async" width="220" height="181" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/9BFE00_-roman_lead_die_%28FindID_103936%29.jpg/330px-9BFE00_-roman_lead_die_%28FindID_103936%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/19/9BFE00_-roman_lead_die_%28FindID_103936%29.jpg/440px-9BFE00_-roman_lead_die_%28FindID_103936%29.jpg 2x" data-file-width="1281" data-file-height="1053" /></a><figcaption>Composite image of all sides of a <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style>12 mm (<span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span> in) <a href="/wiki/Culture_of_ancient_Rome" title="Culture of ancient Rome">Roman</a> die, found in <a href="/wiki/Leicestershire" title="Leicestershire">Leicestershire</a>, England</figcaption></figure> <p>Dice have been used since before recorded history, and their origin is uncertain. It is hypothesized that dice developed from the practice of fortune-telling with the <a href="/wiki/Talus_bone" title="Talus bone">talus</a> of hoofed animals, colloquially known as <a href="/wiki/Knucklebones" title="Knucklebones">knucklebones</a>.<sup id="cite_ref-Laird_2-0" class="reference"><a href="#cite_note-Laird-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Ancient_Egypt" title="Ancient Egypt">Ancient Egyptian</a> game of <a href="/wiki/Senet" title="Senet">senet</a> (played before 3000 <a href="/wiki/Common_Era" title="Common Era">BCE</a> and up to the 2nd century CE) was played with flat two-sided throwsticks which indicated the number of squares a player could move, and thus functioned as a form of dice.<sup id="cite_ref-Aruz_3-0" class="reference"><a href="#cite_note-Aruz-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Perhaps the oldest known dice were excavated as part of a <a href="/wiki/Backgammon" title="Backgammon">backgammon</a>-like game set at the <a href="/wiki/Burnt_City" class="mw-redirect" title="Burnt City">Burnt City</a>, an archeological site in south-eastern <a href="/wiki/Iran" title="Iran">Iran</a>, estimated to be from between 2800 and 2500 BCE.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Bone dice from <a href="/wiki/Skara_Brae" title="Skara Brae">Skara Brae</a>, Scotland have been dated to 3100–2400 BCE.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Excavations from graves at <a href="/wiki/Mohenjo-daro" title="Mohenjo-daro">Mohenjo-daro</a>, an <a href="/wiki/Indus_Valley_civilization" class="mw-redirect" title="Indus Valley civilization">Indus Valley civilization</a> settlement, unearthed <a href="/wiki/Terracotta" title="Terracotta">terracotta</a> dice dating to 2500–1900 BCE,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> including at least one die whose opposite sides all add up to seven, as in modern dice.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Games involving dice are mentioned in the <a href="/wiki/Outline_of_ancient_India" title="Outline of ancient India">ancient Indian</a> <i><a href="/wiki/Rigveda" title="Rigveda">Rigveda</a></i>,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> <i><a href="/wiki/Atharvaveda" title="Atharvaveda">Atharvaveda</a>,</i> <i><a href="/wiki/Mahabharata" title="Mahabharata">Mahabharata</a></i> and <a href="/wiki/List_of_games_that_Buddha_would_not_play" title="List of games that Buddha would not play">Buddhist games list</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> There are several <a href="/wiki/Bible" title="Bible">biblical</a> references to "casting lots" (<a href="/wiki/Hebrew_language" title="Hebrew language">Hebrew</a>: <span lang="he" dir="rtl">יפילו גורל</span> <i>yappîlū ḡōrāl</i>), as in <a href="/wiki/Psalm_22" title="Psalm 22">Psalm 22</a>, indicating that dicing (or a related activity) was commonplace when the psalm was composed. Knucklebones was a <a href="/wiki/Game_of_skill" title="Game of skill">game of skill</a> played in <a href="/wiki/Ancient_Greece" title="Ancient Greece">ancient Greece</a>; a derivative form had the four sides of bones receive different values like modern dice.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Wall_painting_-_scenes_around_the_pub_-_Pompeii_(VI_14_35-36)_-_Napoli_MAN_111482_-_04.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Wall_painting_-_scenes_around_the_pub_-_Pompeii_%28VI_14_35-36%29_-_Napoli_MAN_111482_-_04.jpg/220px-Wall_painting_-_scenes_around_the_pub_-_Pompeii_%28VI_14_35-36%29_-_Napoli_MAN_111482_-_04.jpg" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Wall_painting_-_scenes_around_the_pub_-_Pompeii_%28VI_14_35-36%29_-_Napoli_MAN_111482_-_04.jpg/330px-Wall_painting_-_scenes_around_the_pub_-_Pompeii_%28VI_14_35-36%29_-_Napoli_MAN_111482_-_04.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Wall_painting_-_scenes_around_the_pub_-_Pompeii_%28VI_14_35-36%29_-_Napoli_MAN_111482_-_04.jpg/440px-Wall_painting_-_scenes_around_the_pub_-_Pompeii_%28VI_14_35-36%29_-_Napoli_MAN_111482_-_04.jpg 2x" data-file-width="5472" data-file-height="3648" /></a><figcaption>Roman wall painting showing two dice-players, <a href="/wiki/Pompeii" title="Pompeii">Pompeii</a>, 1st century</figcaption></figure> <p>Although gambling was illegal, many <a href="/wiki/Culture_of_ancient_Rome" title="Culture of ancient Rome">Romans</a> were passionate gamblers who enjoyed dicing, which was known as <i>aleam ludere</i> ("to play at dice"). There were two sizes of Roman dice. <i>Tali</i> were large dice inscribed with one, three, four, and six on four sides. <i>Tesserae</i> were smaller dice with sides numbered from one to six.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Twenty-sided dice date back to the 2nd century CE<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> and from <a href="/wiki/Ptolemaic_Kingdom" title="Ptolemaic Kingdom">Ptolemaic Egypt</a> as early as the 2nd century BCE.<sup id="cite_ref-auto_14-0" class="reference"><a href="#cite_note-auto-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Dominoes" title="Dominoes">Dominoes</a> and <a href="/wiki/Playing_card" title="Playing card">playing cards</a> originated in China as developments from dice.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> The transition from dice to playing cards occurred in China around the <a href="/wiki/Tang_dynasty" title="Tang dynasty">Tang dynasty</a> (618–907 CE), and coincides with the technological transition from rolls of manuscripts to <a href="/wiki/Woodblock_printing" title="Woodblock printing">block printed</a> books.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> In Japan, dice were used to play a popular game called <a href="/wiki/Sugoroku" title="Sugoroku">sugoroku</a>. There are two types of sugoroku. <i>Ban-sugoroku</i> is similar to <a href="/wiki/Backgammon" title="Backgammon">backgammon</a> and dates to the <a href="/wiki/Heian_period" title="Heian period">Heian period</a> (794–1185 CE), while <i>e-sugoroku</i> is a <a href="/wiki/Race_game" title="Race game">racing game</a>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <ul class="gallery mw-gallery-packed"> <li class="gallerybox" style="width: 160px"> <div class="thumb" style="width: 158px;"><span typeof="mw:File"><a href="/wiki/File:Knuck_dice_Steatite_37x27x21_mm.JPG" class="mw-file-description" title="Knucklebones die, made of soapstone"><img alt="Knucklebones die, made of soapstone" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Knuck_dice_Steatite_37x27x21_mm.JPG/237px-Knuck_dice_Steatite_37x27x21_mm.JPG" decoding="async" width="158" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Knuck_dice_Steatite_37x27x21_mm.JPG/356px-Knuck_dice_Steatite_37x27x21_mm.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/4/4a/Knuck_dice_Steatite_37x27x21_mm.JPG 2x" data-file-width="386" data-file-height="293" /></a></span></div> <div class="gallerytext"><a href="/wiki/Knucklebones" title="Knucklebones">Knucklebones</a> die, made of <a href="/wiki/Soapstone" title="Soapstone">soapstone</a></div> </li> <li class="gallerybox" style="width: 114px"> <div class="thumb" style="width: 112px;"><span typeof="mw:File"><a href="/wiki/File:Twenty-sided_die_(icosahedron)_with_faces_inscribed_with_Greek_letters_MET_10.130.1158_001.jpg" class="mw-file-description" title="Twenty-sided serpentinite die from Ptolemaic Egypt[14]"><img alt="Twenty-sided serpentinite die from Ptolemaic Egypt[14]" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Twenty-sided_die_%28icosahedron%29_with_faces_inscribed_with_Greek_letters_MET_10.130.1158_001.jpg/168px-Twenty-sided_die_%28icosahedron%29_with_faces_inscribed_with_Greek_letters_MET_10.130.1158_001.jpg" decoding="async" width="112" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Twenty-sided_die_%28icosahedron%29_with_faces_inscribed_with_Greek_letters_MET_10.130.1158_001.jpg/252px-Twenty-sided_die_%28icosahedron%29_with_faces_inscribed_with_Greek_letters_MET_10.130.1158_001.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Twenty-sided_die_%28icosahedron%29_with_faces_inscribed_with_Greek_letters_MET_10.130.1158_001.jpg/336px-Twenty-sided_die_%28icosahedron%29_with_faces_inscribed_with_Greek_letters_MET_10.130.1158_001.jpg 2x" data-file-width="1488" data-file-height="1596" /></a></span></div> <div class="gallerytext">Twenty-sided <a href="/wiki/Serpentinite" title="Serpentinite">serpentinite</a> die from <a href="/wiki/Ptolemaic_Kingdom" title="Ptolemaic Kingdom">Ptolemaic Egypt</a><sup id="cite_ref-auto_14-1" class="reference"><a href="#cite_note-auto-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></div> </li> <li class="gallerybox" style="width: 122px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:Roman_dice_IMG_4367.JPG" class="mw-file-description" title="Roman die"><img alt="Roman die" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Roman_dice_IMG_4367.JPG/180px-Roman_dice_IMG_4367.JPG" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Roman_dice_IMG_4367.JPG/270px-Roman_dice_IMG_4367.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/26/Roman_dice_IMG_4367.JPG/360px-Roman_dice_IMG_4367.JPG 2x" data-file-width="1647" data-file-height="1647" /></a></span></div> <div class="gallerytext">Roman die</div> </li> <li class="gallerybox" style="width: 94.666666666667px"> <div class="thumb" style="width: 92.666666666667px;"><span typeof="mw:File"><a href="/wiki/File:Historical_dice.jpg" class="mw-file-description" title="A collection of historical dice from various regions of Asia"><img alt="A collection of historical dice from various regions of Asia" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Historical_dice.jpg/139px-Historical_dice.jpg" decoding="async" width="93" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Historical_dice.jpg/208px-Historical_dice.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Historical_dice.jpg/278px-Historical_dice.jpg 2x" data-file-width="1556" data-file-height="2016" /></a></span></div> <div class="gallerytext">A collection of historical dice from various regions of Asia</div> </li> <li class="gallerybox" style="width: 92px"> <div class="thumb" style="width: 90px;"><span typeof="mw:File"><a href="/wiki/File:Chinese_dice_from_Late_Yuan_Dynasty_to_early_Qing_Dynasty.jpg" class="mw-file-description" title="Chinese dice from Late Yuan Dynasty to early Qing Dynasty in Jiangyin Museum, China."><img alt="Chinese dice from Late Yuan Dynasty to early Qing Dynasty in Jiangyin Museum, China." src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Chinese_dice_from_Late_Yuan_Dynasty_to_early_Qing_Dynasty.jpg/135px-Chinese_dice_from_Late_Yuan_Dynasty_to_early_Qing_Dynasty.jpg" decoding="async" width="90" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Chinese_dice_from_Late_Yuan_Dynasty_to_early_Qing_Dynasty.jpg/202px-Chinese_dice_from_Late_Yuan_Dynasty_to_early_Qing_Dynasty.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/Chinese_dice_from_Late_Yuan_Dynasty_to_early_Qing_Dynasty.jpg/270px-Chinese_dice_from_Late_Yuan_Dynasty_to_early_Qing_Dynasty.jpg 2x" data-file-width="3060" data-file-height="4080" /></a></span></div> <div class="gallerytext">Chinese dice from Late Yuan Dynasty to early Qing Dynasty in <a href="/wiki/Jiangyin" title="Jiangyin">Jiangyin</a> Museum, China.</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Use">Use</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=2" title="Edit section: Use"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dice are thrown onto a surface either from the hand or from a container designed for this (such as a cup, tray, or <a href="/wiki/Dice_tower" title="Dice tower">tower</a>). The face (or corner, in cases such as tetrahedral dice, or edge, for odd-numbered <a href="/wiki/Long_dice" title="Long dice">long dice</a>) of the die that is uppermost when it comes to rest provides the value of the throw. </p><p>The result of a die roll is determined by the way it is thrown, according to the laws of <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical mechanics</a> (although <a href="/wiki/Luck" title="Luck">luck</a> is often credited for the results of a roll). A die roll is made <a href="/wiki/Randomness" title="Randomness">random</a> by uncertainty in minor factors such as tiny movements in the thrower's hand; they are thus a crude form of <a href="/wiki/Hardware_random_number_generator" title="Hardware random number generator">hardware random number generator</a>. </p><p>One typical contemporary <a href="/wiki/List_of_dice_games" title="List of dice games">dice game</a> is <a href="/wiki/Craps" title="Craps">craps</a>, where two dice are thrown simultaneously and wagers are made on the total value of the two dice. Dice are frequently used to introduce randomness into <a href="/wiki/Board_game" title="Board game">board games</a>, where they are often used to decide the distance through which a piece will move along the board (as in <a href="/wiki/Backgammon" title="Backgammon">backgammon</a> and <i><a href="/wiki/Monopoly_(game)" title="Monopoly (game)">Monopoly</a></i>). </p><p>Thrown or simulated dice are sometimes used to generate specific probability distributions, which are fundamental to <a href="/wiki/Probability_theory" title="Probability theory">probability theory</a>. For example, rolling a single six-sided die yields a uniform distribution, where each number from 1 to 6 has an equal chance of appearing. However, when rolling two dice and summing the results, the probability distribution shifts, as some sums (like 7) become more likely than others (like 2 or 12). These distributions can model real-world scenarios or mathematical constructs, making dice a practical tool for teaching and exploring concepts in probability theory. </p> <div class="mw-heading mw-heading2"><h2 id="Construction">Construction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=3" title="Edit section: Construction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Arrangement">Arrangement</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=4" title="Edit section: Arrangement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Chiralit%C3%A4t_von_W%C3%BCrfeln_V.2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Chiralit%C3%A4t_von_W%C3%BCrfeln_V.2.svg/220px-Chiralit%C3%A4t_von_W%C3%BCrfeln_V.2.svg.png" decoding="async" width="220" height="226" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Chiralit%C3%A4t_von_W%C3%BCrfeln_V.2.svg/330px-Chiralit%C3%A4t_von_W%C3%BCrfeln_V.2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Chiralit%C3%A4t_von_W%C3%BCrfeln_V.2.svg/440px-Chiralit%C3%A4t_von_W%C3%BCrfeln_V.2.svg.png 2x" data-file-width="848" data-file-height="870" /></a><figcaption><a href="/wiki/Chirality" title="Chirality">Chirality</a> of dice. Faces may be placed <a href="/wiki/Clockwise_and_counterclockwise" class="mw-redirect" title="Clockwise and counterclockwise">counterclockwise (top) <i>or</i> clockwise</a>.</figcaption></figure> <p>Common dice are small <a href="/wiki/Cube" title="Cube">cubes</a>, most often 1.6 cm (0.63 in) across, whose faces are numbered from one to six, usually by patterns of round dots called <a href="/wiki/Pip_(counting)" title="Pip (counting)">pips</a>. (While the use of <a href="/wiki/Arabic_numerals" title="Arabic numerals">Arabic numerals</a> is occasionally seen, such dice are less common.) </p><p>Opposite sides of a modern die traditionally add up to seven, requiring the 1, 2, and 3 faces to share a <a href="/wiki/Vertex_(geometry)" title="Vertex (geometry)">vertex</a>.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> The faces of a die may be placed <a href="/wiki/Clockwise" title="Clockwise">clockwise or counterclockwise</a> about this vertex. If the 1, 2, and 3 faces run counterclockwise, the die is called "right-handed". If those faces run clockwise, the die is called "left-handed". Western dice are normally right-handed, and Chinese dice are normally left-handed.<sup id="cite_ref-diceplay_19-0" class="reference"><a href="#cite_note-diceplay-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>The pips on standard six-sided dice are arranged in specific patterns as shown. Asian style dice bear similar patterns to Western ones, but the pips are closer to the center of the face; in addition, the pips are differently sized on Asian style dice, and the pips are colored red on the 1 and 4 sides. Red fours may be of Indian origin.<sup id="cite_ref-diceplay_19-1" class="reference"><a href="#cite_note-diceplay-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <ul class="gallery mw-gallery-packed"> <li class="gallerybox" style="width: 360px"> <div class="thumb" style="width: 358px;"><span typeof="mw:File"><a href="/wiki/File:Die_Faces.svg" class="mw-file-description" title="Typical facets showing the more compact pip arrangement of an Asian-style die (top) vs. a Western-style die (bottom)"><img alt="Typical facets showing the more compact pip arrangement of an Asian-style die (top) vs. a Western-style die (bottom)" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Die_Faces.svg/537px-Die_Faces.svg.png" decoding="async" width="358" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Die_Faces.svg/806px-Die_Faces.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Die_Faces.svg/1074px-Die_Faces.svg.png 2x" data-file-width="707" data-file-height="237" /></a></span></div> <div class="gallerytext">Typical facets showing the more compact pip arrangement of an Asian-style die (top) vs. a Western-style die (bottom)</div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Manufacturing">Manufacturing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=5" title="Edit section: Manufacturing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Dice01.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/62/Dice01.jpg" decoding="async" width="155" height="219" class="mw-file-element" data-file-width="155" data-file-height="219" /></a><figcaption>Western, Asian, and <a href="/wiki/Casino" title="Casino">casino</a> dice</figcaption></figure> <p>Non-precision dice are manufactured via the plastic <a href="/wiki/Injection_molding" class="mw-redirect" title="Injection molding">injection molding</a> process, often made of <a href="/wiki/Poly(methyl_methacrylate)" title="Poly(methyl methacrylate)">polymethyl methacrylate (PMMA)</a>. The pips or numbers on the die are a part of the mold. Different pigments can be added to the dice to make them opaque or transparent, or multiple pigments may be added to make the dice speckled or marbled.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>The coloring for numbering is achieved by submerging the die entirely in paint, which is allowed to dry. The die is then polished via a <a href="/wiki/Tumble_finishing" title="Tumble finishing">tumble finishing</a> process similar to <a href="/wiki/Rock_polishing" class="mw-redirect" title="Rock polishing">rock polishing</a>. The <a href="/wiki/Abrasion_(mechanical)" title="Abrasion (mechanical)">abrasive agent</a> scrapes off all of the paint except for the indents of the numbering. A finer abrasive is then used to polish the die. This process also produces the smoother, rounded edges on the dice. </p><p>Precision casino dice may have a polished or sand finish, making them transparent or translucent respectively. Casino dice have their pips drilled, then filled flush with a paint of the same <a href="/wiki/Density" title="Density">density</a> as the material used for the dice, such that the center of gravity of the dice is as close to the geometric center as possible. This mitigates concerns that the pips will cause a small bias.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> All such dice are stamped with a <a href="/wiki/Serial_number" title="Serial number">serial number</a> to prevent potential cheaters from substituting a die. Precision backgammon dice are made the same way; they tend to be slightly smaller and have rounded corners and edges, to allow better movement inside the dice cup and stop forceful rolls from damaging the playing surface. </p> <div class="mw-heading mw-heading3"><h3 id="Etymology_and_terms">Etymology and terms</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=6" title="Edit section: Etymology and terms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The word die comes from <a href="/wiki/Old_French" title="Old French">Old French</a> <i><a href="https://en.wiktionary.org/wiki/d%C3%A9#Old_French" class="extiw" title="wikt:dé">dé</a></i>; from <a href="/wiki/Latin" title="Latin">Latin</a> <i><a href="https://en.wiktionary.org/wiki/datum#Latin" class="extiw" title="wikt:datum">datum</a></i> "something which is given or played".<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>While the terms <i><a href="/wiki/Ace" title="Ace">ace</a></i>, <i>deuce</i>, <i>trey</i>, <i>cater</i>, <i>cinque</i> and <i>sice</i> are generally obsolete, with the names of the numbers preferred, they are still used by some professional gamblers to designate different sides of the dice. <i>Ace</i> is from the Latin <i>as</i>, meaning "a unit";<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> the others are 2 to 6 in <a href="/wiki/Old_French" title="Old French">Old French</a>.<sup id="cite_ref-Conant_25-0" class="reference"><a href="#cite_note-Conant-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>When rolling two dice, certain combinations have slang names. The term <i>snake eyes</i> is a roll of one <a href="/wiki/Pip_(counting)" title="Pip (counting)">pip</a> on each die. The <i><a href="/wiki/Online_Etymology_Dictionary" title="Online Etymology Dictionary">Online Etymology Dictionary</a></i> traces use of the term as far back as 1919.<sup id="cite_ref-ref1_26-0" class="reference"><a href="#cite_note-ref1-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> The US term <i>boxcars</i>, also known as <i>midnight</i>, is a roll of six pips on each die. The pair of six pips resembles a pair of <a href="/wiki/Boxcar" title="Boxcar">boxcars</a> on a freight train. Many rolls have <a href="/wiki/Craps#Names_of_rolls" title="Craps">names in the game of craps</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Unicode_representation">Unicode representation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=7" title="Edit section: Unicode representation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th>Symbol </th> <td style="font-size:250%">⚀ </td> <td style="font-size:250%">⚁ </td> <td style="font-size:250%">⚂ </td> <td style="font-size:250%">⚃ </td> <td style="font-size:250%">⚄ </td> <td style="font-size:250%">⚅ </td> <td style="font-size:250%">🎲 </td></tr> <tr> <th>Unicode </th> <td>U+2680 </td> <td>U+2681 </td> <td>U+2682 </td> <td>U+2683 </td> <td>U+2684 </td> <td>U+2685 </td> <td>U+1F3B2 </td></tr> <tr> <th>Decimal </th> <td>&#9856; </td> <td>&#9857; </td> <td>&#9858; </td> <td>&#9859; </td> <td>&#9860; </td> <td>&#9861; </td> <td>&#127922; </td></tr></tbody></table> <p>Using <a href="/wiki/Unicode" title="Unicode">Unicode</a> characters, the faces can be shown in text using the range U+2680 to U+2685 or using decimal <code>&#9856;</code> to <code>&#9861;</code>,<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> and the emoji using U+1F3B2 or <code>&#127922;</code> from the <a href="/wiki/Miscellaneous_Symbols_and_Pictographs" title="Miscellaneous Symbols and Pictographs">Miscellaneous Symbols and Pictographs</a> block. </p> <div class="mw-heading mw-heading2"><h2 id="Loaded_dice">Loaded dice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=8" title="Edit section: Loaded dice"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A loaded, weighted, cheat, or crooked die is one that has been tampered with so that it will land with a specific side facing upwards more often or less often than a fair die would. There are several methods for making loaded dice, including rounded faces, off-square faces, and weights. Casinos and gambling halls frequently use transparent <a href="/wiki/Cellulose_acetate" title="Cellulose acetate">cellulose acetate</a> dice, as tampering is easier to detect than with opaque dice.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Variants">Variants</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=9" title="Edit section: Variants"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Polyhedral_dice">Polyhedral dice</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=10" title="Edit section: Polyhedral dice"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:6dice(cropped).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/6dice%28cropped%29.jpg/220px-6dice%28cropped%29.jpg" decoding="async" width="220" height="188" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/6dice%28cropped%29.jpg/330px-6dice%28cropped%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/6dice%28cropped%29.jpg/440px-6dice%28cropped%29.jpg 2x" data-file-width="2312" data-file-height="1979" /></a><figcaption>A typical set of polyhedral dice in various colors. They consist of the five Platonic solids, along with a ten-sided die that is also used for generating percentages.</figcaption></figure> <p>Various shapes such as two-sided or four-sided dice are documented in archaeological findings; for example, from Ancient Egypt and the Middle East. While the cubical six-sided die became the most common type in many parts of the world, other shapes were always known, like 20-sided dice in Ptolemaic and Roman times. </p><p>The modern tradition of using <i>sets</i> of polyhedral dice started around the end of the 1960s when non-cubical dice became popular among players of <a href="/wiki/Wargame" title="Wargame">wargames</a>,<sup id="cite_ref-Peterson2012_29-0" class="reference"><a href="#cite_note-Peterson2012-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> and since have been employed extensively in <a href="/wiki/Role-playing_game" title="Role-playing game">role-playing games</a> and <a href="/wiki/Collectible_card_game" title="Collectible card game">trading card games</a>. Dice using both the numerals 6 and 9, which are reciprocally symmetric through rotation, typically distinguish them with a dot or underline. </p> <div class="mw-heading mw-heading4"><h4 id="Common_variations">Common variations</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=11" title="Edit section: Common variations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Isohedral_figure" title="Isohedral figure">Isohedron</a></div> <p>Dice are often sold in sets, matching in color, of six different shapes. Five of the dice are shaped like the <a href="/wiki/Platonic_solid" title="Platonic solid">Platonic solids</a>, whose faces are <a href="/wiki/Regular_polygon" title="Regular polygon">regular polygons</a>. Aside from the cube, the other four Platonic solids have 4, 8, 12, and 20 faces, allowing for those number ranges to be generated. The only other common non-cubical die is the 10-sided die, a <a href="/wiki/Pentagonal_trapezohedron" title="Pentagonal trapezohedron">pentagonal trapezohedron</a> die, whose faces are ten <a href="/wiki/Kite_(geometry)" title="Kite (geometry)">kites</a>, each with two different edge lengths, three different angles, and two different kinds of vertices. Such sets frequently include a second 10-sided die either of contrasting color or numbered by tens, allowing the pair of 10-sided dice to be combined to generate numbers between 1 and 100. </p><p>Using these dice in various ways, games can closely approximate a variety of <a href="/wiki/Probability_distribution" title="Probability distribution">probability distributions</a>. For instance, 10-sided dice can be rolled in pairs to produce a <a href="/wiki/Discrete_uniform_distribution" title="Discrete uniform distribution">uniform distribution</a> of random percentages, and summing the values of multiple dice will produce approximations to <a href="/wiki/Normal_distribution" title="Normal distribution">normal distributions</a>.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p><p>Unlike other common dice, a <a href="/wiki/Four-sided_die" title="Four-sided die">four-sided (tetrahedral) die</a> does not have a side that faces upward when it is at rest on a surface, so it must be read in a different way. On some four-sided dice, each face features multiple numbers, with the same number printed near each vertex on all sides. In this case, the number around the vertex pointing up is used. Alternatively, the numbers on a tetrahedral die can be placed at the middle of the edges, in which case the numbers around the base are used. </p><p>Normally, the faces on a die will be placed so opposite faces will add up to one more than the number of faces. (This is not possible with 4-sided dice and dice with an odd number of faces.) Some dice, such as those with 10 sides, are usually numbered sequentially beginning with 0, in which case the opposite faces will add to one less than the number of faces. </p><p>Some twenty-sided dice have a different arrangement used for the purpose of keeping track of an integer that counts down, such as health points. These <i>spindown dice</i> are arranged such that adjacent integers appear on adjacent faces, allowing the user to easily find the next lower number. They are commonly used with <a href="/wiki/Collectible_card_game" title="Collectible card game">collectible card games</a>.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable"> <tbody><tr> <th>Faces/sides </th> <th colspan="2">Shape </th> <th>Notes </th></tr> <tr> <td><a href="/wiki/Four-sided_dice" class="mw-redirect" title="Four-sided dice">4</a></td> <td><a href="/wiki/Tetrahedron" title="Tetrahedron">Tetrahedron</a></td> <td><span typeof="mw:File"><a href="/wiki/File:Tetrahedron.png" class="mw-file-description" title="Tetrahedron"><img alt="Tetrahedron" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Tetrahedron.png/48px-Tetrahedron.png" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Tetrahedron.png/72px-Tetrahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/25/Tetrahedron.png/96px-Tetrahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td>Each face has three numbers, arranged such that the upright number, placed either near the vertex or near the opposite edge, is the same on all three visible faces. The upright numbers represent the value of the roll. This die does not roll well and thus it is usually thrown into the air instead. </td></tr> <tr> <td>6</td> <td><a href="/wiki/Cube" title="Cube">Cube</a></td> <td><span typeof="mw:File"><a href="/wiki/File:Hexahedron.png" class="mw-file-description" title="Cube"><img alt="Cube" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Hexahedron.png/48px-Hexahedron.png" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Hexahedron.png/72px-Hexahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Hexahedron.png/96px-Hexahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td>A common die. The sum of the numbers on opposite faces is 7. </td></tr> <tr> <td>8</td> <td><a href="/wiki/Octahedron" title="Octahedron">Octahedron</a></td> <td><span typeof="mw:File"><a href="/wiki/File:Octahedron.png" class="mw-file-description" title="Octahedron"><img alt="Octahedron" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Octahedron.png/48px-Octahedron.png" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Octahedron.png/72px-Octahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Octahedron.png/96px-Octahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td>Each face is triangular and the die resembles two <a href="/wiki/Square_pyramid" title="Square pyramid">square pyramids</a> attached base-to-base. Usually, the sum of the opposite faces is 9. </td></tr> <tr> <td><a href="/wiki/Ten-sided_die" class="mw-redirect" title="Ten-sided die">10</a></td> <td><a href="/wiki/Pentagonal_trapezohedron" title="Pentagonal trapezohedron">Pentagonal trapezohedron</a></td> <td><span typeof="mw:File"><a href="/wiki/File:Trapezohedron5.jpg" class="mw-file-description" title="Pentagonal trapezohedron"><img alt="Pentagonal trapezohedron" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Trapezohedron5.jpg/40px-Trapezohedron5.jpg" decoding="async" width="40" height="68" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Trapezohedron5.jpg/60px-Trapezohedron5.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Trapezohedron5.jpg/80px-Trapezohedron5.jpg 2x" data-file-width="452" data-file-height="773" /></a></span> </td> <td>Each face is a <a href="/wiki/Kite_(geometry)" title="Kite (geometry)">kite</a>. The die has two sharp corners, where five kites meet, and ten blunter corners, where three kites meet. The ten faces usually bear numbers from zero to nine rather than one to ten (zero being read as "ten" in many applications). Often, all <a href="/wiki/Parity_(mathematics)" title="Parity (mathematics)">odd numbered</a> faces converge at one sharp corner, and the <a href="/wiki/Parity_(mathematics)" title="Parity (mathematics)">even</a> ones at the other. The sum of the numbers on opposite faces is usually 9 (if numbered 0–9) or 11 (if numbered 1–10). </td></tr> <tr> <td>12</td> <td><a href="/wiki/Regular_dodecahedron" title="Regular dodecahedron">Dodecahedron</a></td> <td><span typeof="mw:File"><a href="/wiki/File:Dodecahedron.png" class="mw-file-description" title="Dodecahedron"><img alt="Dodecahedron" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Dodecahedron.png/48px-Dodecahedron.png" decoding="async" width="48" height="46" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Dodecahedron.png/72px-Dodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Dodecahedron.png/96px-Dodecahedron.png 2x" data-file-width="984" data-file-height="951" /></a></span> </td> <td>Each face is a regular pentagon. The sum of the numbers on opposite faces is usually 13. </td></tr> <tr> <td>20</td> <td><a href="/wiki/Regular_icosahedron" title="Regular icosahedron">Icosahedron</a></td> <td><span typeof="mw:File"><a href="/wiki/File:Icosahedron.png" class="mw-file-description" title="Icosahedron"><img alt="Icosahedron" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Icosahedron.png/48px-Icosahedron.png" decoding="async" width="48" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Icosahedron.png/72px-Icosahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Icosahedron.png/96px-Icosahedron.png 2x" data-file-width="911" data-file-height="952" /></a></span> </td> <td>Faces are <a href="/wiki/Equilateral_triangle" title="Equilateral triangle">equilateral triangles</a>. Icosahedra have been found dating to Roman/Ptolemaic times, but it is not known if they were used as gaming dice. Modern dice with 20 sides are sometimes numbered 0–9 twice as an alternative to 10-sided dice. The sum of the numbers on opposite faces is 21 if numbered 1–20. </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="Rarer_variations">Rarer variations</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=12" title="Edit section: Rarer variations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Dices_collection.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Dices_collection.png/420px-Dices_collection.png" decoding="async" width="420" height="84" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Dices_collection.png/630px-Dices_collection.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Dices_collection.png/840px-Dices_collection.png 2x" data-file-width="4000" data-file-height="800" /></a><figcaption>Dice collection: D2–D22, D24, D26, D28, D30, D36, D48, D50, D60 and D100.</figcaption></figure> <p>"Uniform fair dice" are dice where all faces have an equal probability of outcome due to the symmetry of the die as it is <a href="/wiki/Isohedral_figure" title="Isohedral figure">face-transitive</a>. In addition to the Platonic solids, these theoretically include: </p> <ul><li><a href="/wiki/Catalan_solid" title="Catalan solid">Catalan solids</a>, the <a href="/wiki/Dual_polyhedron" title="Dual polyhedron">duals</a> of the 13 <a href="/wiki/Archimedean_solid" title="Archimedean solid">Archimedean solids</a>: 12, 24, 30, 48, 60, 120 sides</li> <li><a href="/wiki/Trapezohedron" title="Trapezohedron">Trapezohedra</a>, the duals of the infinite set of <a href="/wiki/Antiprism" title="Antiprism">antiprisms</a>, with kite faces: any even number not divisible by 4 (so that a face will face up), starting from 6</li> <li><a href="/wiki/Bipyramid" title="Bipyramid">Bipyramids</a>, the duals of the infinite set of <a href="/wiki/Prism_(geometry)" title="Prism (geometry)">prisms</a>, with triangle faces: any multiple of 4 (so that a face will face up), starting from 8</li> <li><a href="/wiki/Disphenoid" title="Disphenoid">Disphenoids</a>, an infinite set of tetrahedra made from congruent non-regular triangles: 4 sides. This is a less symmetric tetrahedron than the Platonic tetrahedron but still sufficiently symmetrical to be face-transitive. Similarly, <a href="/wiki/Pyritohedron" class="mw-redirect" title="Pyritohedron">pyritohedra</a> and <a href="/wiki/Tetartoid" class="mw-redirect" title="Tetartoid">tetartoids</a> are less symmetrical but still face-transitive dodecahedra: 12 sides.</li></ul> <p>Two other types of polyhedra are technically not face-transitive but are still fair dice due to symmetry: </p> <ul><li><a href="/wiki/Antiprism" title="Antiprism">antiprisms</a>: the basis of <a href="/wiki/Barrel_dice" class="mw-redirect" title="Barrel dice">barrel dice</a></li> <li><a href="/wiki/Prism_(geometry)" title="Prism (geometry)">prisms</a>: the basis of long dice and teetotums</li></ul> <p><a href="/wiki/Long_dice" title="Long dice">Long dice</a> and <a href="/wiki/Teetotum" title="Teetotum">teetotums</a> can, in principle, be made with any number of faces, including odd numbers.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> Long dice are based on the infinite set of <a href="/wiki/Prism_(geometry)" title="Prism (geometry)">prisms</a>. All the rectangular faces are mutually face-transitive, so they are equally probable. The two ends of the prism may be rounded or capped with a pyramid, designed so that the die cannot rest on those faces. 4-sided long dice are easier to roll than tetrahedra and are used in the traditional board games <a href="/wiki/Dayakattai" title="Dayakattai">dayakattai</a> and <a href="/wiki/Dald%C3%B8s" title="Daldøs">daldøs</a>. </p> <table class="wikitable"> <tbody><tr> <th>Faces/sides </th> <th>Shape </th> <th>Image </th> <th>Notes </th></tr> <tr> <td>1 </td> <td><a href="/wiki/M%C3%B6bius_strip" title="Möbius strip">Möbius strip</a> or <a href="/wiki/Sphere" title="Sphere">sphere</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D1_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/D1_dice.JPG/48px-D1_dice.JPG" decoding="async" width="48" height="64" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/D1_dice.JPG/72px-D1_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/D1_dice.JPG/96px-D1_dice.JPG 2x" data-file-width="1152" data-file-height="1527" /></a></span> </td> <td>Most commonly a <a href="/wiki/Practical_joke" title="Practical joke">joke</a> die, this is either a sphere with a 1 marked on it or shaped like a <a href="/wiki/M%C3%B6bius_strip" title="Möbius strip">Möbius strip</a>. It entirely defies the aforementioned use of a die. </td></tr> <tr> <td>2 </td> <td>Flat <a href="/wiki/Cylinder_(geometry)" class="mw-redirect" title="Cylinder (geometry)">Cylinder</a> or Flat <a href="/wiki/Prism_(geometry)" title="Prism (geometry)">Prism</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D02.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/D02.JPG/48px-D02.JPG" decoding="async" width="48" height="42" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/D02.JPG/72px-D02.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/D02.JPG/96px-D02.JPG 2x" data-file-width="212" data-file-height="186" /></a></span> </td> <td>A <a href="/wiki/Coin_flip" class="mw-redirect" title="Coin flip">coin flip</a>. Some coins with 1 marked on one side and 2 on the other are available, but most simply use a common coin. </td></tr> <tr> <td>3 </td> <td>Rounded-off <a href="/wiki/Triangular_prism" title="Triangular prism">triangular prism</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D03_wood.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/D03_wood.jpg/48px-D03_wood.jpg" decoding="async" width="48" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/D03_wood.jpg/72px-D03_wood.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2b/D03_wood.jpg/96px-D03_wood.jpg 2x" data-file-width="236" data-file-height="118" /></a></span> </td> <td>A long die intended to be rolled lengthwise. When the die is rolled, one edge (rather than a side) appears facing upwards. On either side of each edge the same number is printed (from 1 to 3). The numbers on either side of the up-facing edge are read as the result of the die roll. </td></tr> <tr> <td>4 </td> <td>Capped 4-sided <a href="/wiki/Long_die" class="mw-redirect" title="Long die">long die</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dald%C3%B8s_die.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Dald%C3%B8s_die.jpg/48px-Dald%C3%B8s_die.jpg" decoding="async" width="48" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Dald%C3%B8s_die.jpg/72px-Dald%C3%B8s_die.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Dald%C3%B8s_die.jpg/96px-Dald%C3%B8s_die.jpg 2x" data-file-width="1780" data-file-height="1120" /></a></span> </td> <td>A long die intended to be rolled lengthwise. It cannot stand on end as the ends are capped. </td></tr> <tr> <td rowspan="3">5 </td></tr> <tr> <td><a href="/wiki/Triangular_prism" title="Triangular prism">Triangular prism</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D05.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/D05.jpg/48px-D05.jpg" decoding="async" width="48" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/D05.jpg/72px-D05.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/D05.jpg/96px-D05.jpg 2x" data-file-width="822" data-file-height="756" /></a></span> </td> <td>A prism thin enough to land either on its "edge" or "face". When landing on an edge, the result is displayed by digits (2–4) close to the prism's top edge. The triangular faces are labeled with the digits 1 and 5. </td></tr> <tr> <td>Capped 5-sided <a href="/wiki/Long_die" class="mw-redirect" title="Long die">long die</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Game_of_Dignitaries_long_die_Culin_1898_fig_136.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Game_of_Dignitaries_long_die_Culin_1898_fig_136.png/48px-Game_of_Dignitaries_long_die_Culin_1898_fig_136.png" decoding="async" width="48" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Game_of_Dignitaries_long_die_Culin_1898_fig_136.png/72px-Game_of_Dignitaries_long_die_Culin_1898_fig_136.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Game_of_Dignitaries_long_die_Culin_1898_fig_136.png/96px-Game_of_Dignitaries_long_die_Culin_1898_fig_136.png 2x" data-file-width="1283" data-file-height="433" /></a></span> </td> <td>Five-faced long die for the Korean Game of Dignitaries; notches indicating values are cut into the edges, since in an odd-faced long die these land uppermost. </td></tr> <tr> <td>6 </td> <td>Capped 6-sided <a href="/wiki/Long_die" class="mw-redirect" title="Long die">long die</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Owzthat_Dice_Game.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Owzthat_Dice_Game.jpg/48px-Owzthat_Dice_Game.jpg" decoding="async" width="48" height="35" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Owzthat_Dice_Game.jpg/72px-Owzthat_Dice_Game.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Owzthat_Dice_Game.jpg/96px-Owzthat_Dice_Game.jpg 2x" data-file-width="682" data-file-height="491" /></a></span> </td> <td>Two six-faced long dice are used to simulate the activity of scoring runs and taking wickets in the game of <a href="/wiki/Cricket" title="Cricket">cricket</a>. Originally played with labeled six-sided pencils, and often referred to as <a href="/wiki/Pencil_cricket" class="mw-redirect" title="Pencil cricket">pencil cricket</a>. </td></tr> <tr> <td rowspan="2">7 </td> <td><a href="/wiki/Pentagonal_prism" title="Pentagonal prism">Pentagonal prism</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D07.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/D07.jpg/48px-D07.jpg" decoding="async" width="48" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/D07.jpg/72px-D07.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/D07.jpg/96px-D07.jpg 2x" data-file-width="813" data-file-height="758" /></a></span> </td> <td>Similar in constitution to the 5-sided die. Seven-sided dice are used in a <a href="/wiki/Seven-sided_backgammon" class="mw-redirect" title="Seven-sided backgammon">seven-player variant</a> of <a href="/wiki/Backgammon" title="Backgammon">backgammon</a>. Seven-sided dice are described in the 13th century <span title="Spanish-language text"><i lang="es"><a href="/wiki/Libro_de_los_juegos" title="Libro de los juegos">Libro de los juegos</a></i></span> as having been invented by <a href="/wiki/Alfonso_X_of_Castile" title="Alfonso X of Castile">Alfonso X</a> in order to speed up play in <a href="/wiki/Chess_variants" class="mw-redirect" title="Chess variants">chess variants</a>.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/Spherical_cap" title="Spherical cap">Truncated sphere</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D7_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/D7_dice.JPG/48px-D7_dice.JPG" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/D7_dice.JPG/72px-D7_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6e/D7_dice.JPG/96px-D7_dice.JPG 2x" data-file-width="879" data-file-height="876" /></a></span> </td> <td>A truncated sphere with seven landing positions. </td></tr> <tr> <td>9 </td> <td>Truncated sphere </td> <td><span typeof="mw:File"><a href="/wiki/File:D9-dice-impact.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/D9-dice-impact.png/48px-D9-dice-impact.png" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/D9-dice-impact.png/72px-D9-dice-impact.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/39/D9-dice-impact.png/96px-D9-dice-impact.png 2x" data-file-width="1283" data-file-height="1283" /></a></span> </td> <td>A truncated sphere with nine landing positions. </td></tr> <tr> <td>10 </td> <td>Decahedron </td> <td><span typeof="mw:File"><a href="/wiki/File:D10_truncated.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/D10_truncated.jpg/48px-D10_truncated.jpg" decoding="async" width="48" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/D10_truncated.jpg/72px-D10_truncated.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/D10_truncated.jpg/96px-D10_truncated.jpg 2x" data-file-width="157" data-file-height="155" /></a></span> </td> <td>A ten-sided die made by truncating two opposite vertices of an octahedron. </td></tr> <tr> <td>11 </td> <td>Truncated sphere </td> <td><span typeof="mw:File"><a href="/wiki/File:D11_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/D11_dice.JPG/48px-D11_dice.JPG" decoding="async" width="48" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/D11_dice.JPG/72px-D11_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/D11_dice.JPG/96px-D11_dice.JPG 2x" data-file-width="831" data-file-height="810" /></a></span> </td> <td>A truncated sphere with eleven landing positions. </td></tr> <tr> <td>12 </td> <td><a href="/wiki/Rhombic_dodecahedron" title="Rhombic dodecahedron">Rhombic dodecahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D12_rhombic_dodecahedron.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/D12_rhombic_dodecahedron.JPG/48px-D12_rhombic_dodecahedron.JPG" decoding="async" width="48" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/D12_rhombic_dodecahedron.JPG/72px-D12_rhombic_dodecahedron.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/D12_rhombic_dodecahedron.JPG/96px-D12_rhombic_dodecahedron.JPG 2x" data-file-width="886" data-file-height="832" /></a></span> </td> <td>Each face is a <a href="/wiki/Rhombus" title="Rhombus">rhombus</a>. </td></tr> <tr> <td>13 </td> <td>Truncated sphere </td> <td><span typeof="mw:File"><a href="/wiki/File:D13_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/D13_dice.JPG/48px-D13_dice.JPG" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/D13_dice.JPG/72px-D13_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/D13_dice.JPG/96px-D13_dice.JPG 2x" data-file-width="813" data-file-height="807" /></a></span> </td> <td>A truncated sphere with thirteen landing positions. </td></tr> <tr> <td rowspan="3">14 </td> <td><a href="/wiki/Heptagonal_trapezohedron" class="mw-redirect" title="Heptagonal trapezohedron">Heptagonal trapezohedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:14%E9%9D%A2%E4%BD%93%E3%83%80%E3%82%A4%E3%82%B9.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/14%E9%9D%A2%E4%BD%93%E3%83%80%E3%82%A4%E3%82%B9.jpg/48px-14%E9%9D%A2%E4%BD%93%E3%83%80%E3%82%A4%E3%82%B9.jpg" decoding="async" width="48" height="49" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/14%E9%9D%A2%E4%BD%93%E3%83%80%E3%82%A4%E3%82%B9.jpg/72px-14%E9%9D%A2%E4%BD%93%E3%83%80%E3%82%A4%E3%82%B9.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/14%E9%9D%A2%E4%BD%93%E3%83%80%E3%82%A4%E3%82%B9.jpg/96px-14%E9%9D%A2%E4%BD%93%E3%83%80%E3%82%A4%E3%82%B9.jpg 2x" data-file-width="649" data-file-height="658" /></a></span> </td> <td>Each face is a <a href="/wiki/Kite_(geometry)" title="Kite (geometry)">kite</a>. </td></tr> <tr> <td><a href="/wiki/Truncated_octahedron" title="Truncated octahedron">Truncated octahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Korean14dice2.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Korean14dice2.JPG/48px-Korean14dice2.JPG" decoding="async" width="48" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Korean14dice2.JPG/72px-Korean14dice2.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Korean14dice2.JPG/96px-Korean14dice2.JPG 2x" data-file-width="172" data-file-height="160" /></a></span> </td> <td>A truncated octahedron. Each face is either a square or a hexagon. </td></tr> <tr> <td>Truncated sphere </td> <td><span typeof="mw:File"><a href="/wiki/File:D14_truncated_octahedron.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/D14_truncated_octahedron.jpg/48px-D14_truncated_octahedron.jpg" decoding="async" width="48" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/D14_truncated_octahedron.jpg/72px-D14_truncated_octahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/18/D14_truncated_octahedron.jpg/96px-D14_truncated_octahedron.jpg 2x" data-file-width="882" data-file-height="864" /></a></span> </td> <td>A truncated sphere with fourteen landing positions. The design is based on the <a href="/wiki/Cuboctahedron" title="Cuboctahedron">cuboctahedron</a>. </td></tr> <tr> <td>15 </td> <td>Truncated sphere </td> <td><span typeof="mw:File"><a href="/wiki/File:D15_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/D15_dice.JPG/48px-D15_dice.JPG" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/D15_dice.JPG/72px-D15_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/D15_dice.JPG/96px-D15_dice.JPG 2x" data-file-width="783" data-file-height="786" /></a></span> </td> <td>A truncated sphere with fifteen landing positions. </td></tr> <tr> <td>16 </td> <td><a href="/wiki/Octagonal_bipyramid" class="mw-redirect" title="Octagonal bipyramid">Octagonal bipyramid</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D16_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/D16_dice.JPG/48px-D16_dice.JPG" decoding="async" width="48" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/D16_dice.JPG/72px-D16_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/D16_dice.JPG/96px-D16_dice.JPG 2x" data-file-width="1017" data-file-height="831" /></a></span> </td> <td>Each face is an isosceles triangle. </td></tr> <tr> <td>17 </td> <td>Truncated sphere </td> <td><span typeof="mw:File"><a href="/wiki/File:D17_dice_2.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/D17_dice_2.JPG/48px-D17_dice_2.JPG" decoding="async" width="48" height="46" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/D17_dice_2.JPG/72px-D17_dice_2.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/D17_dice_2.JPG/96px-D17_dice_2.JPG 2x" data-file-width="906" data-file-height="867" /></a></span> </td> <td>A truncated sphere with seventeen landing positions. </td></tr> <tr> <td>18 </td> <td>Rounded <a href="/wiki/Rhombicuboctahedron" title="Rhombicuboctahedron">rhombicuboctahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D18_rhombicuboctahedron.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/D18_rhombicuboctahedron.JPG/48px-D18_rhombicuboctahedron.JPG" decoding="async" width="48" height="49" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/D18_rhombicuboctahedron.JPG/72px-D18_rhombicuboctahedron.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/D18_rhombicuboctahedron.JPG/96px-D18_rhombicuboctahedron.JPG 2x" data-file-width="795" data-file-height="804" /></a></span> </td> <td>Eighteen faces are squares. The eight triangular faces are rounded and cannot be landed on. </td></tr> <tr> <td>19 </td> <td>Truncated sphere </td> <td><span typeof="mw:File"><a href="/wiki/File:D19_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/D19_dice.JPG/48px-D19_dice.JPG" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/D19_dice.JPG/72px-D19_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2a/D19_dice.JPG/96px-D19_dice.JPG 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td>A truncated sphere with nineteen landing positions. </td></tr> <tr> <td>21 </td> <td>Truncated sphere </td> <td><span typeof="mw:File"><a href="/wiki/File:D21_dice.webp" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/D21_dice.webp/48px-D21_dice.webp.png" decoding="async" width="48" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/D21_dice.webp/72px-D21_dice.webp.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e6/D21_dice.webp/96px-D21_dice.webp.png 2x" data-file-width="659" data-file-height="681" /></a></span> </td> <td>A truncated sphere with twenty-one landing positions. </td></tr> <tr> <td>22 </td> <td>Truncated sphere </td> <td><span typeof="mw:File"><a href="/wiki/File:D22_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/D22_dice.JPG/48px-D22_dice.JPG" decoding="async" width="48" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/D22_dice.JPG/72px-D22_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/D22_dice.JPG/96px-D22_dice.JPG 2x" data-file-width="909" data-file-height="894" /></a></span> </td> <td>A truncated sphere with twenty-two landing positions. </td></tr> <tr> <td rowspan="5">24 </td> <td><a href="/wiki/Triakis_octahedron" title="Triakis octahedron">Triakis octahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D24_triakis_octahedron_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/D24_triakis_octahedron_dice.JPG/48px-D24_triakis_octahedron_dice.JPG" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/D24_triakis_octahedron_dice.JPG/72px-D24_triakis_octahedron_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/27/D24_triakis_octahedron_dice.JPG/96px-D24_triakis_octahedron_dice.JPG 2x" data-file-width="720" data-file-height="720" /></a></span> </td> <td>Each face is an isosceles triangle. </td></tr> <tr> <td><a href="/wiki/Tetrakis_hexahedron" title="Tetrakis hexahedron">Tetrakis hexahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D24_tetrakis_hexahedron.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/D24_tetrakis_hexahedron.JPG/48px-D24_tetrakis_hexahedron.JPG" decoding="async" width="48" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/D24_tetrakis_hexahedron.JPG/72px-D24_tetrakis_hexahedron.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/D24_tetrakis_hexahedron.JPG/96px-D24_tetrakis_hexahedron.JPG 2x" data-file-width="1011" data-file-height="957" /></a></span> </td> <td>Each face is an isosceles triangle. </td></tr> <tr> <td><a href="/wiki/Deltoidal_icositetrahedron" title="Deltoidal icositetrahedron">Deltoidal icositetrahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D24_deltoidal_icositetrahedron.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/D24_deltoidal_icositetrahedron.JPG/48px-D24_deltoidal_icositetrahedron.JPG" decoding="async" width="48" height="49" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/D24_deltoidal_icositetrahedron.JPG/72px-D24_deltoidal_icositetrahedron.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/D24_deltoidal_icositetrahedron.JPG/96px-D24_deltoidal_icositetrahedron.JPG 2x" data-file-width="954" data-file-height="969" /></a></span> </td> <td>Each face is a kite. </td></tr> <tr> <td>Pseudo-deltoidal icositetrahedron </td> <td><span typeof="mw:File"><a href="/wiki/File:D24_pseudo_uniform_polyhedrondice.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/D24_pseudo_uniform_polyhedrondice.jpg/48px-D24_pseudo_uniform_polyhedrondice.jpg" decoding="async" width="48" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/D24_pseudo_uniform_polyhedrondice.jpg/72px-D24_pseudo_uniform_polyhedrondice.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/D24_pseudo_uniform_polyhedrondice.jpg/96px-D24_pseudo_uniform_polyhedrondice.jpg 2x" data-file-width="1251" data-file-height="1224" /></a></span> </td> <td>Each face is a kite. </td></tr> <tr> <td><a href="/wiki/Pentagonal_icositetrahedron" title="Pentagonal icositetrahedron">Pentagonal icositetrahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D24_pentagonal_icositetrahedron_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/D24_pentagonal_icositetrahedron_dice.JPG/48px-D24_pentagonal_icositetrahedron_dice.JPG" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/D24_pentagonal_icositetrahedron_dice.JPG/72px-D24_pentagonal_icositetrahedron_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/D24_pentagonal_icositetrahedron_dice.JPG/96px-D24_pentagonal_icositetrahedron_dice.JPG 2x" data-file-width="800" data-file-height="800" /></a></span> </td> <td>Each face is an irregular pentagon. </td></tr> <tr> <td>26 </td> <td>Truncated sphere </td> <td><span typeof="mw:File"><a href="/wiki/File:D26_dice.webp" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/D26_dice.webp/48px-D26_dice.webp.png" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/D26_dice.webp/72px-D26_dice.webp.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/D26_dice.webp/96px-D26_dice.webp.png 2x" data-file-width="470" data-file-height="470" /></a></span> </td> <td>A truncated sphere with twenty-six landing positions. </td></tr> <tr> <td>28 </td> <td>Truncated sphere </td> <td><span typeof="mw:File"><a href="/wiki/File:D28_dice.webp" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/D28_dice.webp/48px-D28_dice.webp.png" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/D28_dice.webp/72px-D28_dice.webp.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/D28_dice.webp/96px-D28_dice.webp.png 2x" data-file-width="715" data-file-height="715" /></a></span> </td> <td>A truncated sphere with twenty-eight landing positions. </td></tr> <tr> <td>30 </td> <td><a href="/wiki/Rhombic_triacontahedron" title="Rhombic triacontahedron">Rhombic triacontahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D30.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/D30.jpg/48px-D30.jpg" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/D30.jpg/72px-D30.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/71/D30.jpg/96px-D30.jpg 2x" data-file-width="1022" data-file-height="1029" /></a></span> </td> <td>Each face is a rhombus. </td></tr> <tr> <td>32 </td> <td>Truncated sphere </td> <td><span typeof="mw:File"><a href="/wiki/File:D32_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/D32_dice.JPG/48px-D32_dice.JPG" decoding="async" width="48" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/D32_dice.JPG/72px-D32_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/D32_dice.JPG/96px-D32_dice.JPG 2x" data-file-width="1236" data-file-height="1206" /></a></span> </td> <td>A truncated sphere with thirty-two landing positions. The design is similar to that of a <a href="/wiki/Truncated_icosahedron" title="Truncated icosahedron">truncated icosahedron</a>. </td></tr> <tr> <td>34 </td> <td><a href="/wiki/Heptadecagon" title="Heptadecagon">Heptadecagonal</a> trapezohedron </td> <td><span typeof="mw:File"><a href="/wiki/File:D34.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/D34.jpg/48px-D34.jpg" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/D34.jpg/72px-D34.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d8/D34.jpg/96px-D34.jpg 2x" data-file-width="1325" data-file-height="1325" /></a></span> </td> <td>Each face is a kite. </td></tr> <tr> <td>36 </td> <td>Truncated sphere </td> <td><span typeof="mw:File"><a href="/wiki/File:D36_dice.webp" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/D36_dice.webp/48px-D36_dice.webp.png" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/D36_dice.webp/72px-D36_dice.webp.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/D36_dice.webp/96px-D36_dice.webp.png 2x" data-file-width="720" data-file-height="720" /></a></span> </td> <td>A truncated sphere with thirty-six landing positions. Rows of spots are present above and below each number 1 through 36 so that this die can be used to roll two six-sided dice simultaneously. </td></tr> <tr> <td>48 </td> <td><a href="/wiki/Disdyakis_dodecahedron" title="Disdyakis dodecahedron">Disdyakis dodecahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D48_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/D48_dice.JPG/48px-D48_dice.JPG" decoding="async" width="48" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/D48_dice.JPG/72px-D48_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/D48_dice.JPG/96px-D48_dice.JPG 2x" data-file-width="1275" data-file-height="1248" /></a></span> </td> <td>Each face is a <a href="/wiki/Scalene_triangle" class="mw-redirect" title="Scalene triangle">scalene triangle</a>. </td></tr> <tr> <td>50 </td> <td>Icosipentagonal trapezohedron </td> <td><span typeof="mw:File"><a href="/wiki/File:D50_trapezohedron_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/D50_trapezohedron_dice.JPG/48px-D50_trapezohedron_dice.JPG" decoding="async" width="48" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/D50_trapezohedron_dice.JPG/72px-D50_trapezohedron_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/D50_trapezohedron_dice.JPG/96px-D50_trapezohedron_dice.JPG 2x" data-file-width="1236" data-file-height="1215" /></a></span> </td> <td>Each face is a kite. </td></tr> <tr> <td rowspan="4">60 </td> <td><a href="/wiki/Deltoidal_hexecontahedron" title="Deltoidal hexecontahedron">Deltoidal hexecontahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D60_60men-saikoro.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/D60_60men-saikoro.JPG/48px-D60_60men-saikoro.JPG" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/D60_60men-saikoro.JPG/72px-D60_60men-saikoro.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/D60_60men-saikoro.JPG/96px-D60_60men-saikoro.JPG 2x" data-file-width="983" data-file-height="984" /></a></span> </td> <td>Each face is a kite. </td></tr> <tr> <td><a href="/wiki/Pentakis_dodecahedron" title="Pentakis dodecahedron">Pentakis dodecahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D60_pentakis_dodecahedron_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/D60_pentakis_dodecahedron_dice.JPG/48px-D60_pentakis_dodecahedron_dice.JPG" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/D60_pentakis_dodecahedron_dice.JPG/72px-D60_pentakis_dodecahedron_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1f/D60_pentakis_dodecahedron_dice.JPG/96px-D60_pentakis_dodecahedron_dice.JPG 2x" data-file-width="800" data-file-height="800" /></a></span> </td> <td>Each face is an isosceles triangle. </td></tr> <tr> <td><a href="/wiki/Pentagonal_hexecontahedron" title="Pentagonal hexecontahedron">Pentagonal hexecontahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D60_pentagonal_hexecontahedron_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/D60_pentagonal_hexecontahedron_dice.JPG/48px-D60_pentagonal_hexecontahedron_dice.JPG" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/D60_pentagonal_hexecontahedron_dice.JPG/72px-D60_pentagonal_hexecontahedron_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1f/D60_pentagonal_hexecontahedron_dice.JPG/96px-D60_pentagonal_hexecontahedron_dice.JPG 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td>Each face is an irregular pentagon. </td></tr> <tr> <td><a href="/wiki/Triakis_icosahedron" title="Triakis icosahedron">Triakis icosahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D60_triakis_icosahedron_dice.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/D60_triakis_icosahedron_dice.JPG/48px-D60_triakis_icosahedron_dice.JPG" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/D60_triakis_icosahedron_dice.JPG/72px-D60_triakis_icosahedron_dice.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ef/D60_triakis_icosahedron_dice.JPG/96px-D60_triakis_icosahedron_dice.JPG 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td>Each face is an isosceles triangle. </td></tr> <tr> <td>100 </td> <td><a href="/wiki/Zocchihedron" title="Zocchihedron">Zocchihedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Zocchihedron2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Zocchihedron2.jpg/48px-Zocchihedron2.jpg" decoding="async" width="48" height="52" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Zocchihedron2.jpg/72px-Zocchihedron2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/Zocchihedron2.jpg/96px-Zocchihedron2.jpg 2x" data-file-width="552" data-file-height="600" /></a></span> </td> <td>A sphere containing another sphere with 100 facets flattened into it. Note that this design is not isohedral; it does not function as a uniform fair die as some results are more likely than others. </td></tr> <tr> <td>120 </td> <td><a href="/wiki/Disdyakis_triacontahedron" title="Disdyakis triacontahedron">Disdyakis triacontahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:D120.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/D120.jpg/48px-D120.jpg" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/D120.jpg/72px-D120.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/D120.jpg/96px-D120.jpg 2x" data-file-width="1806" data-file-height="1806" /></a></span> </td> <td>Each face is a scalene triangle. </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Non-numeric_dice">Non-numeric dice</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=13" title="Edit section: Non-numeric dice"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:White_Fudge_Dice.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/White_Fudge_Dice.jpg/220px-White_Fudge_Dice.jpg" decoding="async" width="220" height="128" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/White_Fudge_Dice.jpg/330px-White_Fudge_Dice.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/34/White_Fudge_Dice.jpg/440px-White_Fudge_Dice.jpg 2x" data-file-width="1707" data-file-height="996" /></a><figcaption>A set of <a href="/wiki/Fudge_(role-playing_game_system)" title="Fudge (role-playing game system)">Fudge dice</a></figcaption></figure> <p>The faces of most dice are labelled using sequences of whole numbers, usually starting at one, expressed with either pips or digits. However, there are some applications that require results other than numbers. Examples include letters for <a href="/wiki/Boggle" title="Boggle">Boggle</a>, directions for <i><a href="/wiki/Warhammer_Fantasy_Battle" class="mw-redirect" title="Warhammer Fantasy Battle">Warhammer Fantasy Battle</a></i>, <a href="/wiki/Fudge_(role-playing_game_system)#Fudge_dice" title="Fudge (role-playing game system)">Fudge dice</a>, playing card symbols for <a href="/wiki/Poker_dice" title="Poker dice">poker dice</a>, and instructions for sexual acts using <a href="/wiki/Sex_dice" title="Sex dice">sex dice</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Alternatively-numbered_dice">Alternatively-numbered dice</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=14" title="Edit section: Alternatively-numbered dice"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dice may have numbers that do not form a counting sequence starting at one. One variation on the standard die is known as the "average" die.<sup id="cite_ref-em4_35-0" class="reference"><a href="#cite_note-em4-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-tmp_36-0" class="reference"><a href="#cite_note-tmp-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> These are six-sided dice with sides numbered <code>2, 3, 3, 4, 4, 5</code>, which have the same <a href="/wiki/Arithmetic_mean" title="Arithmetic mean">arithmetic mean</a> as a standard die (3.5 for a single die, 7 for a pair of dice), but have a narrower range of possible values (2 through 5 for one, 4 through 10 for a pair). They are used in some table-top <a href="/wiki/Wargame" title="Wargame">wargames</a>, where a narrower range of numbers is required.<sup id="cite_ref-tmp_36-1" class="reference"><a href="#cite_note-tmp-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> Other numbered variations include <a href="/wiki/Sicherman_dice" title="Sicherman dice">Sicherman dice</a> and <a href="/wiki/Intransitive_dice" title="Intransitive dice">intransitive dice</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Spherical_dice">Spherical dice</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=15" title="Edit section: Spherical dice"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Black_and_red_round_6-sided_die_(cropped).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Black_and_red_round_6-sided_die_%28cropped%29.jpg/110px-Black_and_red_round_6-sided_die_%28cropped%29.jpg" decoding="async" width="110" height="115" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Black_and_red_round_6-sided_die_%28cropped%29.jpg/165px-Black_and_red_round_6-sided_die_%28cropped%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Black_and_red_round_6-sided_die_%28cropped%29.jpg/220px-Black_and_red_round_6-sided_die_%28cropped%29.jpg 2x" data-file-width="1965" data-file-height="2050" /></a><figcaption>A spherical die</figcaption></figure> <p>A die can be constructed in the shape of a sphere, with the addition of an internal cavity in the shape of the <a href="/wiki/Dual_polyhedron" title="Dual polyhedron">dual polyhedron</a> of the desired die shape and an internal weight. The weight will settle in one of the points of the internal cavity, causing it to settle with one of the numbers uppermost. For instance, a sphere with an octahedral cavity and a small internal weight will settle with one of the 6 points of the cavity held downwards by the weight. </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=16" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Master_Jean_de_Maul%C3%A9on_-_Playing_Dice_-_Walters_W4492V_(cropped).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Master_Jean_de_Maul%C3%A9on_-_Playing_Dice_-_Walters_W4492V_%28cropped%29.jpg/220px-Master_Jean_de_Maul%C3%A9on_-_Playing_Dice_-_Walters_W4492V_%28cropped%29.jpg" decoding="async" width="220" height="199" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Master_Jean_de_Maul%C3%A9on_-_Playing_Dice_-_Walters_W4492V_%28cropped%29.jpg/330px-Master_Jean_de_Maul%C3%A9on_-_Playing_Dice_-_Walters_W4492V_%28cropped%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/4/49/Master_Jean_de_Maul%C3%A9on_-_Playing_Dice_-_Walters_W4492V_%28cropped%29.jpg 2x" data-file-width="406" data-file-height="367" /></a><figcaption><i>Playing Dice</i> by Master Jean de Mauléon (c. 1520)</figcaption></figure> <p>Many board games use dice to randomize how far pieces move or to settle conflicts. Typically, this has meant that rolling higher numbers is better. Some games, such as <i><a href="/wiki/Axis_%26_Allies" title="Axis & Allies">Axis & Allies</a></i>, have inverted this system by making the lower values more potent. In the modern age,<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers#Chronological_items" title="Wikipedia:Manual of Style/Dates and numbers"><span title="The time period mentioned near this tag is ambiguous. (August 2021)">when?</span></a></i>]</sup> a few games and game designers have approached dice in a different way by making each side of the die similarly valuable. In <i><a href="/wiki/Castles_of_Burgundy" class="mw-redirect" title="Castles of Burgundy">Castles of Burgundy</a></i>, players spend their dice to take actions based on the die's value. In this game, a six is not better than a one, or vice versa. In <i><a href="/wiki/Quarriors" class="mw-redirect" title="Quarriors">Quarriors</a></i> (and its descendant, <i><a href="/wiki/Dice_Masters" class="mw-redirect" title="Dice Masters">Dice Masters</a></i>), different sides of the dice can offer completely different abilities. Several sides often give resources while others grant the player useful actions.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p><p>Dice can be used for <a href="/wiki/Divination" title="Divination">divination</a> and using dice for such a purpose is called <a href="/wiki/Cleromancy" title="Cleromancy">cleromancy</a>. A pair of common dice is usual, though other forms of polyhedra can be used. Tibetan Buddhists sometimes use this <a href="/wiki/Mo_(divination)" title="Mo (divination)">method of divination</a>. It is highly likely that the <a href="/wiki/Pythagoreans" class="mw-redirect" title="Pythagoreans">Pythagoreans</a> used the <a href="/wiki/Platonic_solids" class="mw-redirect" title="Platonic solids">Platonic solids</a> as dice. They referred to such dice as "the dice of the gods" and they sought to understand the universe through an understanding of geometry in polyhedra.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Wuerfel5.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Wuerfel5.jpg/220px-Wuerfel5.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Wuerfel5.jpg/330px-Wuerfel5.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Wuerfel5.jpg/440px-Wuerfel5.jpg 2x" data-file-width="640" data-file-height="480" /></a><figcaption>Typical role-playing dice, showing a variety of colors and styles. Note the older hand-inked green 12-sided die (showing an 11), manufactured before pre-inked dice were common. Many players collect or acquire a large number of mixed and unmatching dice.</figcaption></figure> <p>Polyhedral dice are commonly used in role-playing games. The fantasy role-playing game <i><a href="/wiki/Dungeons_%26_Dragons" title="Dungeons & Dragons">Dungeons & Dragons</a></i> (D&D) is largely credited with popularizing dice in such games. Some games use only one type, like <i><a href="/wiki/Exalted" title="Exalted">Exalted</a></i> which uses only ten-sided dice. Others use numerous types for different game purposes, such as D&D, which makes use of all common polyhedral dice. Dice are usually used to determine the outcome of events. Games typically determine results either as a total on one or more dice above or below a fixed number, or a certain number of rolls above a certain number on one or more dice. Due to circumstances or character skill, the initial roll may have a number added to or subtracted from the final result, or have the player roll extra or fewer dice. To keep track of rolls easily, <a href="/wiki/Dice_notation" title="Dice notation">dice notation</a> is frequently used. </p><p>Astrological dice are a specialized set of three 12-sided dice for divination; the first die represents the planets, the Sun, the Moon, and the <a href="/wiki/Orbital_node" title="Orbital node">nodes</a> of the Moon, the second die represents the 12 <a href="/wiki/Astrological_sign" title="Astrological sign">zodiac signs</a>, and the third represents the <a href="/wiki/House_(astrology)" title="House (astrology)">12 houses</a>. A specialized icosahedron die provides the answers of the <a href="/wiki/Magic_8_Ball" title="Magic 8 Ball">Magic 8 Ball</a>, conventionally used to provide answers to yes-or-no questions. </p><p>Dice can be used to generate random numbers for use in <a href="/wiki/Password" title="Password">passwords</a> and <a href="/wiki/Cryptography" title="Cryptography">cryptography</a> applications. The <a href="/wiki/Electronic_Frontier_Foundation" title="Electronic Frontier Foundation">Electronic Frontier Foundation</a> describes a method by which dice can be used to generate <a href="/wiki/Passphrase" title="Passphrase">passphrases</a>.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Diceware" title="Diceware">Diceware</a> is a method recommended for generating secure but memorable passphrases, by repeatedly rolling five dice and picking the corresponding word from a pre-generated list.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Notation">Notation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=17" title="Edit section: Notation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Dice_notation" title="Dice notation">Dice notation</a></div> <p>In many gaming contexts, especially tabletop role-playing games, shorthand notations representing different dice rolls are used. A very common notation, considered a <a href="/wiki/Dice_notation" title="Dice notation">standard</a>, expresses a dice roll as <i>n</i>d<i>s</i> or <i>n</i>D<i>s</i>, where <i>n</i> is the number of dice rolled and <i>s</i> is the number of sides on each die; if only one die is rolled, <i>n</i> is normally not shown. For example, <code>d4</code> denotes one four-sided die; <code>6d8</code> means the player should roll six eight-sided dice and sum the results. </p><p>The notation also allows for adding or subtracting a constant amount <i>c</i> to the roll. When an amount is added, the notation is <i>n</i>d<i>s</i>+<i>c</i> or <i>n</i>D<i>s</i>+<i>c</i>; for example, <code>3d6+4</code> instructs the player to roll three six-sided dice, calculate the total, and add four to it. When an amount is to be subtracted, the notation is <i>n</i>d<i>s</i>-<i>c</i> or <i>n</i>D<i>s</i>-<i>c;</i> so <code>3d6-4</code> instructs the player to subtract four from the result of rolling <code>3d6</code>. If the result of a modified dice roll is negative, it is often taken to be zero or one; for instance, when the dice roll determines the amount of damage to a creature.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=18" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col"> <ul><li><a href="/wiki/Astragalomancy" title="Astragalomancy">Astragalomancy</a> – Form of divination</li> <li><a href="/wiki/Crown_and_Anchor" title="Crown and Anchor">Crown and Anchor</a> – Dice game</li> <li><a href="/wiki/D20_System" title="D20 System">d20 System</a> – Role-playing game system</li> <li><a href="/wiki/Dreidel" title="Dreidel">Dreidel</a> – Four-sided spinning top used on Hanukkah</li> <li><a href="/wiki/Fuzzy_dice" title="Fuzzy dice">Fuzzy dice</a> – Automobile decoration</li> <li><a href="/wiki/Musikalisches_W%C3%BCrfelspiel" title="Musikalisches Würfelspiel"><i>Musikalisches Würfelspiel</i></a> – Musical dice games used to randomly generate music</li> <li><a href="/wiki/Die_throw_(review)" title="Die throw (review)">Die throw (review)</a> – Method of review often used in Norway</li> <li><a href="/wiki/Intransitive_dice" title="Intransitive dice">Intransitive dice</a> – Game variations and descriptions of intransitive die and their behaviour</li> <li><a href="/wiki/Quincunx" title="Quincunx">Quincunx</a> – Pattern of five points, four in a square or rectangle and a fifth at its center</li> <li><a href="/wiki/Teetotum" title="Teetotum">Teetotum</a> – Spinning lot, generating random outcomes</li> <li><a href="/wiki/Urim_and_Thummim" title="Urim and Thummim">Urim and Thummim</a> – Objects used for divination in the early Abrahamic religions</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=19" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style 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class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon 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Retrieved <span class="nowrap">18 June</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=games.rengeekcentral.com&rft.pub=games.rengeekcentral.com&rft_id=http%3A%2F%2Fgames.rengeekcentral.com%2Ftc4.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADice" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://wwmat.mat.fc.ul.pt/~jnsilva/HJT2k9/AlfonsoX.pdf">"wwmat.mat.fc.ul.pt"</a> <span class="cs1-format">(PDF)</span>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110302034551/http://wwmat.mat.fc.ul.pt/~jnsilva/HJT2k9/AlfonsoX.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2 March 2011<span class="reference-accessdate">. Retrieved <span class="nowrap">18 June</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=wwmat.mat.fc.ul.pt&rft_id=http%3A%2F%2Fwwmat.mat.fc.ul.pt%2F~jnsilva%2FHJT2k9%2FAlfonsoX.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADice" class="Z3988"></span></span> </li> <li id="cite_note-em4-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-em4_35-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.em4miniatures.com/acatalog/SPECIALIST_D6.html">"Specialist D6"</a>. <i>em4miniatures</i><span class="reference-accessdate">. Retrieved <span class="nowrap">18 August</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=em4miniatures&rft.atitle=Specialist+D6&rft_id=http%3A%2F%2Fwww.em4miniatures.com%2Facatalog%2FSPECIALIST_D6.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADice" class="Z3988"></span></span> </li> <li id="cite_note-tmp-36"><span class="mw-cite-backlink">^ <a href="#cite_ref-tmp_36-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-tmp_36-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://theminiaturespage.com/boards/msg.mv?id=184673">"[TMP] 'What are Average Dice' Topic"</a>. <i>The Miniatures Page</i>. 20 November 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">18 August</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+Miniatures+Page&rft.atitle=%5BTMP%5D+%27What+are+Average+Dice%27+Topic&rft.date=2009-11-20&rft_id=http%3A%2F%2Ftheminiaturespage.com%2Fboards%2Fmsg.mv%3Fid%3D184673&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADice" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://boingboing.net/2014/10/02/making-better-use-of-dice-in-g.html">"Making better use of dice in games"</a>. 2 October 2014.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Making+better+use+of+dice+in+games&rft.date=2014-10-02&rft_id=http%3A%2F%2Fboingboing.net%2F2014%2F10%2F02%2Fmaking-better-use-of-dice-in-g.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADice" class="Z3988"></span></span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGuthrie1988" class="citation book cs1">Guthrie, Kenneth (1988). <i>The Pythagorean sourcebook and library: an anthology of ancient writings which relate to Pythagoras and Pythagorean philosophy</i>. Grand Rapids, MI: Phanes Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-933999-50-3" title="Special:BookSources/978-0-933999-50-3"><bdi>978-0-933999-50-3</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/255212063">255212063</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Pythagorean+sourcebook+and+library%3A+an+anthology+of+ancient+writings+which+relate+to+Pythagoras+and+Pythagorean+philosophy&rft.place=Grand+Rapids%2C+MI&rft.pub=Phanes+Press&rft.date=1988&rft_id=info%3Aoclcnum%2F255212063&rft.isbn=978-0-933999-50-3&rft.aulast=Guthrie&rft.aufirst=Kenneth&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADice" class="Z3988"></span></span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://www.eff.org/dice">"EFF Dice-Generated Passphrases"</a>. <i>Electronic Frontier Foundation</i>. 12 May 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">16 November</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Electronic+Frontier+Foundation&rft.atitle=EFF+Dice-Generated+Passphrases&rft.date=2016-05-12&rft_id=https%3A%2F%2Fwww.eff.org%2Fdice&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADice" class="Z3988"></span></span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.eff.org/deeplinks/2016/07/new-wordlists-random-passphrases">"EFF's New Wordlists for Random Passphrases"</a>. <i>Electronic Frontier Foundation</i>. 19 July 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">4 December</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Electronic+Frontier+Foundation&rft.atitle=EFF%27s+New+Wordlists+for+Random+Passphrases&rft.date=2016-07-19&rft_id=https%3A%2F%2Fwww.eff.org%2Fdeeplinks%2F2016%2F07%2Fnew-wordlists-random-passphrases&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADice" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSim2007" class="citation book cs1">Sim, Chris (2007). <i>Dungeons & Dragons Rules Compendium</i>. Renton, WA USA. p. 17. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780786947256" title="Special:BookSources/9780786947256"><bdi>9780786947256</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dungeons+%26+Dragons+Rules+Compendium&rft.place=Renton%2C+WA+USA&rft.pages=17&rft.date=2007&rft.isbn=9780786947256&rft.aulast=Sim&rft.aufirst=Chris&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADice" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMearls2016" class="citation web cs1">Mearls, Mike; et al. (2016). <a rel="nofollow" class="external text" href="https://media.wizards.com/2016/downloads/DND/SRD-OGL_V5.1.pdf">"System Reference Document 5.1"</a> <span class="cs1-format">(PDF)</span>. p. 96<span class="reference-accessdate">. Retrieved <span class="nowrap">12 September</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=System+Reference+Document+5.1&rft.pages=96&rft.date=2016&rft.aulast=Mearls&rft.aufirst=Mike&rft_id=https%3A%2F%2Fmedia.wizards.com%2F2016%2Fdownloads%2FDND%2FSRD-OGL_V5.1.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADice" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Bibliography">Bibliography</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=20" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Persi_Diaconis" title="Persi Diaconis">Diaconis, Persi</a>; and Keller, Joseph B.; <a rel="nofollow" class="external text" href="http://www-stat.stanford.edu/~cgates/PERSI/papers/fairdice.pdf">"Fair Dice"</a>, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080221165308/http://www-stat.stanford.edu/~cgates/PERSI/papers/fairdice.pdf">Archived</a> 21 February 2008 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, <i>The American Mathematical Monthly</i>, 96(4):337–339, 1989 (Discussion of dice that are fair "by symmetry" and "by continuity".)</li> <li>Iverson, G. R.; Longcour, W. H.; et al.; <i>Bias and Runs in Dice Throwing and Recording: A Few Million Throws</i>, Psychometrika, vol. 36, no. 1, March 1971</li> <li><a href="/wiki/Reiner_Knizia" title="Reiner Knizia">Knizia, Reiner</a>, <i>Dice Games Properly Explained</i>, Elliot Right Way Books, 1999, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7160-2112-9" title="Special:BookSources/0-7160-2112-9">0-7160-2112-9</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dice&action=edit&section=21" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/dice" class="extiw" title="wiktionary:dice">dice</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Dice" class="extiw" title="commons:Category:Dice">Dice</a></span>.</div></div> </div> <ul><li><span class="citation mathworld" id="Reference-Mathworld-Dice"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeisstein" class="citation web cs1"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/Dice.html">"Dice"</a>. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathWorld&rft.atitle=Dice&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FDice.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADice" class="Z3988"></span></span> –  analysis of dice probabilities, also featuring Uspenski's work on rolling multiple dice</li></ul> <p><span class="noprint"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png" decoding="async" width="12" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/18px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/24px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></span></span> </span>This article incorporates text from a publication now in the <a href="/wiki/Public_domain" title="Public domain">public domain</a>: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChisholm1911" class="citation encyclopaedia cs1"><a href="/wiki/Hugh_Chisholm" title="Hugh Chisholm">Chisholm, Hugh</a>, ed. (1911). "<a href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Dice" class="extiw" title="s:1911 Encyclopædia Britannica/Dice">Dice</a>". <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i>. Vol. 8 (11th ed.). Cambridge University Press. p. 176–177.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Dice&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.pages=176-177&rft.edition=11th&rft.pub=Cambridge+University+Press&rft.date=1911&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADice" class="Z3988"></span> </p> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist 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.navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Craps" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Craps" title="Template:Craps"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Craps" title="Template talk:Craps"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Craps" title="Special:EditPage/Template:Craps"><abbr title="Edit this 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width="110" height="70" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Two_red_dice_01.svg/165px-Two_red_dice_01.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/36/Two_red_dice_01.svg/220px-Two_red_dice_01.svg.png 2x" data-file-width="671" data-file-height="430" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Advantage_gambling" title="Advantage gambling">Advantage play</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Dice_control" title="Dice control">Dice control</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mathematics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Craps_principle" title="Craps principle">Craps principle</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Frank_Scoblete" title="Frank Scoblete">Frank Scoblete</a></li> <li><a href="/wiki/Jerry_L._Patterson" title="Jerry L. Patterson">Jerry L. Patterson</a></li> <li><a href="/wiki/Stanford_Wong" title="Stanford Wong">Stanford Wong</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q45089#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q45089#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q45089#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/892791/">FAST</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/7632420-5">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85037657">United States</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Dés à jouer"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb16194934s">France</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Dés à jouer"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb16194934s">BnF data</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007552917105171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalog.archives.gov/id/10646683">NARA</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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