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id="toc-Other_examples-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Reverse_position" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reverse_position"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Reverse position</span> </div> </a> <ul id="toc-Reverse_position-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Retrospective_gambler's_fallacy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Retrospective_gambler's_fallacy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Retrospective gambler's fallacy</span> </div> </a> <ul id="toc-Retrospective_gambler's_fallacy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Childbirth" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Childbirth"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Childbirth</span> </div> </a> <ul id="toc-Childbirth-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Monte_Carlo_Casino" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Monte_Carlo_Casino"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Monte Carlo Casino</span> </div> </a> <ul id="toc-Monte_Carlo_Casino-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Non-examples" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Non-examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Non-examples</span> </div> </a> <button aria-controls="toc-Non-examples-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 Non-examples subsection</span> </button> <ul id="toc-Non-examples-sublist" class="vector-toc-list"> <li id="toc-Non-independent_events" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Non-independent_events"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Non-independent events</span> </div> </a> <ul id="toc-Non-independent_events-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bias" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bias"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Bias</span> </div> </a> <ul id="toc-Bias-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Changing_probabilities" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Changing_probabilities"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Changing probabilities</span> </div> </a> <ul id="toc-Changing_probabilities-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Psychology" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Psychology"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Psychology</span> </div> </a> <button aria-controls="toc-Psychology-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 Psychology subsection</span> </button> <ul id="toc-Psychology-sublist" class="vector-toc-list"> <li id="toc-Origins" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Origins"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Origins</span> </div> </a> <ul id="toc-Origins-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Variations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Variations"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Variations</span> </div> </a> <ul id="toc-Variations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relationship_to_hot-hand_fallacy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Relationship_to_hot-hand_fallacy"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3</span> <span>Relationship to hot-hand fallacy</span> </div> </a> <ul id="toc-Relationship_to_hot-hand_fallacy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Neurophysiology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Neurophysiology"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.4</span> <span>Neurophysiology</span> </div> </a> <ul id="toc-Neurophysiology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Possible_solutions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Possible_solutions"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.5</span> <span>Possible solutions</span> </div> </a> <ul id="toc-Possible_solutions-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Users" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Users"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Users</span> </div> </a> <button aria-controls="toc-Users-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 Users subsection</span> </button> <ul id="toc-Users-sublist" class="vector-toc-list"> <li id="toc-Types_of_users" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Types_of_users"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Types of users</span> </div> </a> <ul id="toc-Types_of_users-sublist" class="vector-toc-list"> <li id="toc-Asylum_judges" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Asylum_judges"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1.1</span> <span>Asylum judges</span> </div> </a> <ul id="toc-Asylum_judges-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Baseball_umpires" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Baseball_umpires"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1.2</span> <span>Baseball umpires</span> </div> </a> <ul id="toc-Baseball_umpires-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Loan_officers" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Loan_officers"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1.3</span> <span>Loan officers</span> </div> </a> <ul id="toc-Loan_officers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lottery_players" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Lottery_players"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1.4</span> <span>Lottery players</span> </div> </a> <ul id="toc-Lottery_players-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Video_game_players" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Video_game_players"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1.5</span> <span>Video game players</span> </div> </a> <ul id="toc-Video_game_players-sublist" class="vector-toc-list"> </ul> </li> </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">9</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">10</span> <span>References</span> </div> </a> <ul id="toc-References-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">Gambler's fallacy</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 31 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-31" 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">31 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Dobbelaar_se_dwaling" title="Dobbelaar se dwaling – Afrikaans" lang="af" hreflang="af" data-title="Dobbelaar se dwaling" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%BA%D8%A7%D9%84%D8%B7%D8%A9_%D8%A7%D9%84%D9%85%D9%82%D8%A7%D9%85%D8%B1" title="مغالطة المقامر – Arabic" lang="ar" hreflang="ar" data-title="مغالطة المقامر" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Fal%C2%B7l%C3%A0cia_del_jugador" title="Fal·làcia del jugador – Catalan" lang="ca" hreflang="ca" data-title="Fal·làcia del jugador" 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/Omyl_hazardn%C3%ADho_hr%C3%A1%C4%8De" title="Omyl hazardního hráče – Czech" lang="cs" hreflang="cs" data-title="Omyl hazardního hráče" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Spielerfehlschluss" title="Spielerfehlschluss – German" lang="de" hreflang="de" data-title="Spielerfehlschluss" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CE%BB%CE%AC%CE%BD%CE%B7_%CF%84%CE%BF%CF%85_%CF%84%CE%B6%CE%BF%CE%B3%CE%B1%CE%B4%CF%8C%CF%81%CE%BF%CF%85" title="Πλάνη του τζογαδόρου – Greek" lang="el" hreflang="el" data-title="Πλάνη του τζογαδόρου" 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/Falacia_del_apostador" title="Falacia del apostador – Spanish" lang="es" hreflang="es" data-title="Falacia del apostador" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%BA%D8%A7%D9%84%D8%B7%D9%87_%D9%82%D9%85%D8%A7%D8%B1%D8%A8%D8%A7%D8%B2" title="مغالطه قمارباز – Persian" lang="fa" hreflang="fa" data-title="مغالطه قمارباز" 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/Erreur_du_parieur" title="Erreur du parieur – French" lang="fr" hreflang="fr" data-title="Erreur du parieur" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%8F%84%EB%B0%95%EC%82%AC%EC%9D%98_%EC%98%A4%EB%A5%98" title="도박사의 오류 – Korean" lang="ko" hreflang="ko" data-title="도박사의 오류" 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%BD%D5%A1%D5%B2%D5%A1%D5%B4%D5%B8%D5%AC%D5%AB_%D5%B4%D5%B8%D5%AC%D5%B8%D6%80%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Խաղամոլի մոլորություն – Armenian" lang="hy" hreflang="hy" data-title="Խաղամոլի մոլորություն" 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%9C%E0%A5%81%E0%A4%86%E0%A4%B0%E0%A5%80_%E0%A4%95%E0%A4%BE_%E0%A4%95%E0%A5%81%E0%A4%A4%E0%A4%B0%E0%A5%8D%E0%A4%95" title="जुआरी का कुतर्क – Hindi" lang="hi" hreflang="hi" data-title="जुआरी का कुतर्क" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Fallacia_dello_scommettitore" title="Fallacia dello scommettitore – Italian" lang="it" hreflang="it" data-title="Fallacia dello scommettitore" 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%9B%D7%A9%D7%9C_%D7%94%D7%9E%D7%94%D7%9E%D7%A8" title="כשל המהמר – Hebrew" lang="he" hreflang="he" data-title="כשל המהמר" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Lo%C5%A1%C4%97jo_klaida" title="Lošėjo klaida – Lithuanian" lang="lt" hreflang="lt" data-title="Lošėjo klaida" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Szerencsej%C3%A1t%C3%A9kosok_t%C3%A9ved%C3%A9se" title="Szerencsejátékosok tévedése – Hungarian" lang="hu" hreflang="hu" data-title="Szerencsejátékosok tévedése" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Gokkersmisvatting" title="Gokkersmisvatting – Dutch" lang="nl" hreflang="nl" data-title="Gokkersmisvatting" 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%AE%E3%83%A3%E3%83%B3%E3%83%96%E3%83%A9%E3%83%BC%E3%81%AE%E8%AA%A4%E8%AC%AC" title="ギャンブラーの誤謬 – Japanese" lang="ja" hreflang="ja" data-title="ギャンブラーの誤謬" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Paradoks_hazardzisty" title="Paradoks hazardzisty – Polish" lang="pl" hreflang="pl" data-title="Paradoks hazardzisty" 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/Fal%C3%A1cia_do_apostador" title="Falácia do apostador – Portuguese" lang="pt" hreflang="pt" data-title="Falácia do apostador" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D1%88%D0%B8%D0%B1%D0%BA%D0%B0_%D0%B8%D0%B3%D1%80%D0%BE%D0%BA%D0%B0" title="Ошибка игрока – Russian" lang="ru" hreflang="ru" data-title="Ошибка игрока" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Gambler%27s_fallacy" title="Gambler's fallacy – Simple English" lang="en-simple" hreflang="en-simple" data-title="Gambler's fallacy" 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-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%BE%D1%86%D0%BA%D0%B0%D1%80%D1%81%D0%BA%D0%B0_%D0%B7%D0%B0%D0%B1%D0%BB%D1%83%D0%B4%D0%B0" title="Коцкарска заблуда – Serbian" lang="sr" hreflang="sr" data-title="Коцкарска заблуда" 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-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Pelurin_virhep%C3%A4%C3%A4telm%C3%A4" title="Pelurin virhepäätelmä – Finnish" lang="fi" hreflang="fi" data-title="Pelurin virhepäätelmä" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%AB%E0%B8%95%E0%B8%B8%E0%B8%9C%E0%B8%A5%E0%B8%A7%E0%B8%B4%E0%B8%9A%E0%B8%B1%E0%B8%95%E0%B8%B4%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%99%E0%B8%B1%E0%B8%81%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%9E%E0%B8%99%E0%B8%B1%E0%B8%99" title="เหตุผลวิบัติของนักการพนัน – Thai" lang="th" hreflang="th" data-title="เหตุผลวิบัติของนักการพนัน" 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/Monte_Carlo_yan%C4%B1lg%C4%B1s%C4%B1" title="Monte Carlo yanılgısı – Turkish" lang="tr" hreflang="tr" data-title="Monte Carlo yanılgısı" 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 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searchaux" style="display:none">Mistaken belief that more frequent chance events will lead to less frequent chance events</div> <p>The <b>gambler's fallacy</b>, also known as the <b>Monte Carlo fallacy</b> or the <b>fallacy of the maturity of chances</b>, is the belief that, if an event (whose occurrences are <a href="/wiki/Independent_and_identically_distributed_random_variables" title="Independent and identically distributed random variables">independent and identically distributed</a>) has occurred less frequently than expected, it is more likely to happen again in the future (or vice versa). The <a href="/wiki/Fallacy" title="Fallacy">fallacy</a> is commonly associated with <a href="/wiki/Gambling" title="Gambling">gambling</a>, where it may be believed, for example, that the next dice roll is more than usually likely to be six because there have recently been fewer than the <a href="/wiki/Expected_value" title="Expected value">expected</a> number of sixes. </p><p>The term "Monte Carlo fallacy" originates from an example of the phenomenon, in which the <a href="/wiki/Roulette" title="Roulette">roulette</a> wheel spun black 26 times in succession at the <a href="/wiki/Monte_Carlo_Casino" title="Monte Carlo Casino">Monte Carlo Casino</a> in 1913.<sup id="cite_ref-monte_carlo_1-0" class="reference"><a href="#cite_note-monte_carlo-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=1" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Coin_toss">Coin toss</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=2" title="Edit section: Coin toss"><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:Lawoflargenumbersanimation.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/9/93/Lawoflargenumbersanimation.gif" decoding="async" width="100" height="169" class="mw-file-element" data-file-width="100" data-file-height="169" /></a><figcaption>Over time, the <a href="/wiki/Ratio" title="Ratio">proportion</a> of red/blue coin tosses approaches 50-50, but the <a href="/wiki/Subtraction" title="Subtraction">difference</a> decreases to zero non-systematically.</figcaption></figure> <p>The gambler's fallacy can be illustrated by considering the repeated toss of a <a href="/wiki/Fair_coin" title="Fair coin">fair coin</a>. The outcomes in different tosses are <a href="/wiki/Statistically_independent" class="mw-redirect" title="Statistically independent">statistically independent</a> and the probability of getting heads on a single toss is <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.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><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> (one in two). The probability of getting two heads in two tosses is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">4</span></span>⁠</span> (one in four) and the probability of getting three heads in three tosses is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">8</span></span>⁠</span> (one in eight). In general, if <i>A<sub>i</sub></i> is the event where toss <i>i</i> of a <a href="/wiki/Fair_coin" title="Fair coin">fair coin</a> comes up heads, then: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Pr \left(\bigcap _{i=1}^{n}A_{i}\right)=\prod _{i=1}^{n}\Pr(A_{i})={1 \over 2^{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">Pr</mo> <mrow> <mo>(</mo> <mrow> <munderover> <mo>⋂</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>∏</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mo movablelimits="true" form="prefix">Pr</mo> <mo stretchy="false">(</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Pr \left(\bigcap _{i=1}^{n}A_{i}\right)=\prod _{i=1}^{n}\Pr(A_{i})={1 \over 2^{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7494c539f575a16ec484600c4422e1d0e37bb64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:31.778ex; height:7.509ex;" alt="{\displaystyle \Pr \left(\bigcap _{i=1}^{n}A_{i}\right)=\prod _{i=1}^{n}\Pr(A_{i})={1 \over 2^{n}}}"></span>.</dd></dl> <p>If after tossing four heads in a row, the next coin toss also came up heads, it would complete a run of five successive heads. Since the probability of a run of five successive heads is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">32</span></span>⁠</span> (one in thirty-two), a person might believe that the next flip would be more likely to come up tails rather than heads again. This is incorrect and is an example of the gambler's fallacy. The event "5 heads in a row" and the event "first 4 heads, then a tails" are equally likely, each having probability <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">32</span></span>⁠</span>. Since the first four tosses turn up heads, the probability that the next toss is a head is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Pr \left(A_{5}|A_{1}\cap A_{2}\cap A_{3}\cap A_{4}\right)=\Pr \left(A_{5}\right)={\frac {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">Pr</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>∩</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>∩</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>∩</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mo movablelimits="true" form="prefix">Pr</mo> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Pr \left(A_{5}|A_{1}\cap A_{2}\cap A_{3}\cap A_{4}\right)=\Pr \left(A_{5}\right)={\frac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c81a9913d061520b4196f58f69e3d94d9b42bac9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:42.756ex; height:5.176ex;" alt="{\displaystyle \Pr \left(A_{5}|A_{1}\cap A_{2}\cap A_{3}\cap A_{4}\right)=\Pr \left(A_{5}\right)={\frac {1}{2}}}"></span>.</dd></dl> <p>While a run of five heads has a probability of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">32</span></span>⁠</span> = 0.03125 (a little over 3%), the misunderstanding lies in not realizing that this is the case <i>only before the first coin is tossed</i>. After the first four tosses in this example, the results are no longer unknown, so their probabilities are at that point equal to 1 (100%). The probability of a run of coin tosses of any length continuing for one more toss is always 0.5. The reasoning that a fifth toss is more likely to be tails because the previous four tosses were heads, with a run of luck in the past influencing the odds in the future, forms the basis of the fallacy. </p> <div class="mw-heading mw-heading3"><h3 id="Why_the_probability_is_1/2_for_a_fair_coin"><span id="Why_the_probability_is_1.2F2_for_a_fair_coin"></span>Why the probability is 1/2 for a fair coin</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=3" title="Edit section: Why the probability is 1/2 for a fair coin"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If a fair coin is flipped 21 times, the probability of 21 heads is 1 in 2,097,152. The probability of flipping a head after having already flipped 20 heads in a row is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span>. Assuming a fair coin: </p> <ul><li>The probability of 20 heads, then 1 tail is 0.5<sup>20</sup> × 0.5 = 0.5<sup>21</sup></li> <li>The probability of 20 heads, then 1 head is 0.5<sup>20</sup> × 0.5 = 0.5<sup>21</sup></li></ul> <p>The probability of getting 20 heads then 1 tail, and the probability of getting 20 heads then another head are both 1 in 2,097,152. When flipping a fair coin 21 times, the outcome is equally likely to be 21 heads as 20 heads and then 1 tail. These two outcomes are equally as likely as any of the other combinations that can be obtained from 21 flips of a coin. All of the 21-flip combinations will have probabilities equal to 0.5<sup>21</sup>, or 1 in 2,097,152. Assuming that a change in the probability will occur as a result of the outcome of prior flips is incorrect because every outcome of a 21-flip sequence is as likely as the other outcomes. In accordance with <a href="/wiki/Bayes%27_theorem" title="Bayes' theorem">Bayes' theorem</a>, the likely outcome of each flip is the probability of the fair coin, which is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span>. </p> <div class="mw-heading mw-heading3"><h3 id="Other_examples">Other examples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=4" title="Edit section: Other examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The fallacy leads to the incorrect notion that previous failures will create an increased probability of success on subsequent attempts. For a fair 16-sided die, the probability of each outcome occurring is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">16</span></span>⁠</span> (6.25%). If a win is defined as rolling a 1, the probability of a 1 occurring at least once in 16 rolls is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1-\left[{\frac {15}{16}}\right]^{16}\,=\,64.39\%}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>−</mo> <msup> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>15</mn> <mn>16</mn> </mfrac> </mrow> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>16</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mn>64.39</mn> <mi mathvariant="normal">%</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1-\left[{\frac {15}{16}}\right]^{16}\,=\,64.39\%}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d791f63cddc590830c6ef468bbf823c14c1953f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:22.6ex; height:6.509ex;" alt="{\displaystyle 1-\left[{\frac {15}{16}}\right]^{16}\,=\,64.39\%}"></span></dd></dl> <p>The probability of a loss on the first roll is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">15</span><span class="sr-only">/</span><span class="den">16</span></span>⁠</span> (93.75%). According to the fallacy, the player should have a higher chance of winning after one loss has occurred. The probability of at least one win is now: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1-\left[{\frac {15}{16}}\right]^{15}\,=\,62.02\%}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>−</mo> <msup> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>15</mn> <mn>16</mn> </mfrac> </mrow> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>15</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mn>62.02</mn> <mi mathvariant="normal">%</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1-\left[{\frac {15}{16}}\right]^{15}\,=\,62.02\%}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b0b7ce6d128c5742499914574afc8e625b73af1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:22.6ex; height:6.509ex;" alt="{\displaystyle 1-\left[{\frac {15}{16}}\right]^{15}\,=\,62.02\%}"></span></dd></dl> <p>By losing one toss, the player's probability of winning drops by two percentage points. With 5 losses and 11 rolls remaining, the probability of winning drops to around 0.5 (50%). The probability of at least one win does not increase after a series of losses; indeed, the probability of success <i>actually decreases</i>, because there are fewer trials left in which to win. The probability of winning will eventually be equal to the probability of winning a single toss, which is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">16</span></span>⁠</span> (6.25%) and occurs when only one toss is left. </p> <div class="mw-heading mw-heading2"><h2 id="Reverse_position">Reverse position</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=5" title="Edit section: Reverse position"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Gambler%27s_fallacy" title="Special:EditPage/Gambler's fallacy">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">January 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>After a consistent tendency towards tails, a gambler may also decide that tails has become a more likely outcome. This is a rational and <a href="/wiki/Bayesian_statistics" title="Bayesian statistics">Bayesian</a> conclusion, bearing in mind the possibility that the coin may not be fair; it is not a fallacy. Believing the odds to favor tails, the gambler sees no reason to change to heads. However it is a fallacy that a sequence of trials carries a memory of past results which tend to favor or disfavor future outcomes. </p><p>The <a href="/wiki/Inverse_gambler%27s_fallacy" title="Inverse gambler's fallacy">inverse gambler's fallacy</a> described by <a href="/wiki/Ian_Hacking" title="Ian Hacking">Ian Hacking</a> is a situation where a gambler entering a room and seeing a person rolling a double six on a pair of dice may erroneously conclude that the person must have been rolling the dice for quite a while, as they would be unlikely to get a double six on their first attempt.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Retrospective_gambler's_fallacy"><span id="Retrospective_gambler.27s_fallacy"></span>Retrospective gambler's fallacy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=6" title="Edit section: Retrospective gambler's fallacy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Researchers have examined whether a similar <a href="/wiki/Bias" title="Bias">bias</a> exists for inferences about unknown past events based upon known subsequent events, calling this the "retrospective gambler's fallacy".<sup id="cite_ref-retrospective_3-0" class="reference"><a href="#cite_note-retrospective-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>An example of a retrospective gambler's fallacy would be to observe multiple successive "heads" on a coin toss and conclude from this that the previously unknown flip was "tails".<sup id="cite_ref-retrospective_3-1" class="reference"><a href="#cite_note-retrospective-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Real world examples of retrospective gambler's fallacy have been argued to exist in events such as the origin of the <a href="/wiki/Universe" title="Universe">Universe</a>. In his book <i>Universes</i>, <a href="/wiki/John_A._Leslie" title="John A. Leslie">John Leslie</a> argues that "the presence of vastly <a href="/wiki/Many-worlds_interpretation" title="Many-worlds interpretation">many universes</a> very different in their characters might be our best explanation for why at least one universe has a life-permitting character".<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> <a href="/wiki/Daniel_M._Oppenheimer" title="Daniel M. Oppenheimer">Daniel M. Oppenheimer</a> and Benoît Monin argue that "In other words, the 'best explanation' for a low-probability event is that it is only one in a multiple of trials, which is the core intuition of the reverse gambler's fallacy."<sup id="cite_ref-retrospective_3-2" class="reference"><a href="#cite_note-retrospective-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Philosophical arguments are ongoing about whether such arguments are or are not a fallacy, arguing that the occurrence of our universe says nothing about the existence of other universes or trials of universes.<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><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> Three studies involving Stanford University students tested the existence of a retrospective gamblers' fallacy. All three studies concluded that people have a gamblers' fallacy retrospectively as well as to future events.<sup id="cite_ref-retrospective_3-3" class="reference"><a href="#cite_note-retrospective-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The authors of all three studies concluded their findings have significant "<a href="/wiki/Methodology" title="Methodology">methodological</a> implications" but may also have "important theoretical implications" that need investigation and research, saying "[a] thorough understanding of such reasoning processes requires that we not only examine how they influence our predictions of the future, but also our perceptions of the past."<sup id="cite_ref-retrospective_3-4" class="reference"><a href="#cite_note-retrospective-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Childbirth">Childbirth</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=7" title="Edit section: Childbirth"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1796, <a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Pierre-Simon Laplace</a> described in <i><a href="/wiki/A_Philosophical_Essay_on_Probabilities" title="A Philosophical Essay on Probabilities">A Philosophical Essay on Probabilities</a></i> the ways in which men calculated their probability of having sons: "I have seen men, ardently desirous of having a son, who could learn only with anxiety of the births of boys in the month when they expected to become fathers. Imagining that the ratio of these births to those of girls ought to be the same at the end of each month, they judged that the boys already born would render more probable the births next of girls." The expectant fathers feared that if more sons were born in the surrounding community, then they themselves would be more likely to have a daughter. This essay by Laplace is regarded as one of the earliest descriptions of the fallacy.<sup id="cite_ref-BarronLeider2010_7-0" class="reference"><a href="#cite_note-BarronLeider2010-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Likewise, after having multiple children of the same sex, some parents may erroneously believe that they are due to have a child of the opposite sex. </p> <div class="mw-heading mw-heading2"><h2 id="Monte_Carlo_Casino">Monte Carlo Casino</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=8" title="Edit section: Monte Carlo Casino"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An example of the gambler's fallacy occurred in a game of <a href="/wiki/Roulette" title="Roulette">roulette</a> at the <a href="/wiki/Monte_Carlo_Casino" title="Monte Carlo Casino">Monte Carlo Casino</a> on August 18, 1913, when the ball fell in black 26 times in a row. This was an extremely unlikely occurrence: the probability of a sequence of either red or black occurring 26 times in a row is <span class="texhtml">(<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">18</span><span class="sr-only">/</span><span class="den">37</span></span>⁠</span>)<sup>26-1</sup></span> or around 1 in 66.6 million, assuming the mechanism is unbiased. Gamblers lost millions of francs betting against black, reasoning incorrectly that the streak was causing an imbalance in the randomness of the wheel, and that it had to be followed by a long streak of red.<sup id="cite_ref-monte_carlo_1-1" class="reference"><a href="#cite_note-monte_carlo-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Non-examples">Non-examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=9" title="Edit section: Non-examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Non-independent_events">Non-independent events</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=10" title="Edit section: Non-independent events"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The gambler's fallacy does not apply when the probability of different events is not <a href="/wiki/Statistical_independence" class="mw-redirect" title="Statistical independence">independent</a>. In such cases, the probability of future events can change based on the outcome of past events, such as the statistical <a href="/wiki/Permutation" title="Permutation">permutation</a> of events. An example is when cards are drawn from a deck without replacement. If an <a href="/wiki/Ace" title="Ace">ace</a> is drawn from a deck and not reinserted, the next card drawn is less likely to be an ace and more likely to be of another rank. The probability of drawing another ace, assuming that it was the first card drawn and that there are no <a href="/wiki/Joker_(playing_card)" title="Joker (playing card)">jokers</a>, has decreased from <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">4</span><span class="sr-only">/</span><span class="den">52</span></span>⁠</span> (7.69%) to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">3</span><span class="sr-only">/</span><span class="den">51</span></span>⁠</span> (5.88%), while the probability for each other rank has increased from <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">4</span><span class="sr-only">/</span><span class="den">52</span></span>⁠</span> (7.69%) to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">4</span><span class="sr-only">/</span><span class="den">51</span></span>⁠</span> (7.84%). This effect allows <a href="/wiki/Card_counting" title="Card counting">card counting</a> systems to work in games such as <a href="/wiki/Blackjack" title="Blackjack">blackjack</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Bias">Bias</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=11" title="Edit section: Bias"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In most illustrations of the gambler's fallacy and the reverse gambler's fallacy, the trial (e.g. flipping a coin) is assumed to be fair. In practice, this assumption may not hold. For example, if a coin is flipped 21 times, the probability of 21 heads with a fair coin is 1 in 2,097,152. Since this probability is so small, if it happens, it may well be that the coin is somehow <a href="/wiki/Bias_(statistics)" title="Bias (statistics)">biased</a> towards landing on heads, or that it is being controlled by hidden magnets, or similar.<sup id="cite_ref-Gardner1986_8-0" class="reference"><a href="#cite_note-Gardner1986-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> In this case, the smart bet is "heads" because <a href="/wiki/Bayesian_inference" title="Bayesian inference">Bayesian inference</a> from the <a href="/wiki/Empirical_evidence" title="Empirical evidence">empirical evidence</a> — 21 heads in a row — suggests that the coin is likely to be biased toward heads. Bayesian inference can be used to show that when the long-run proportion of different outcomes is unknown but <a href="/wiki/Exchangeable_random_variables" title="Exchangeable random variables">exchangeable</a> (meaning that the random process from which the outcomes are generated may be biased but is equally likely to be biased in any direction) and that previous observations demonstrate the likely direction of the bias, the outcome which has occurred the most in the observed data is the most likely to occur again.<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> </p><p>For example, if the <i><a href="/wiki/A_priori_and_a_posteriori" title="A priori and a posteriori">a priori</a></i> probability of a biased coin is say 1%, and assuming that such a biased coin would come down heads say 60% of the time, then after 21 heads the probability of a biased coin has increased to about 32%. </p><p>The opening scene of the play <i><a href="/wiki/Rosencrantz_and_Guildenstern_Are_Dead" title="Rosencrantz and Guildenstern Are Dead">Rosencrantz and Guildenstern Are Dead</a></i> by <a href="/wiki/Tom_Stoppard" title="Tom Stoppard">Tom Stoppard</a> discusses these issues as one man continually flips heads and the other considers various possible explanations. </p> <div class="mw-heading mw-heading3"><h3 id="Changing_probabilities">Changing probabilities</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=12" title="Edit section: Changing probabilities"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If external factors are allowed to change the probability of the events, the gambler's fallacy may not hold. For example, a change in the game rules might favour one player over the other, improving his or her win percentage. Similarly, an inexperienced player's success may decrease after opposing teams learn about and play against their weaknesses. This is another example of bias. </p> <div class="mw-heading mw-heading2"><h2 id="Psychology">Psychology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=13" title="Edit section: Psychology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Origins">Origins</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=14" title="Edit section: Origins"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The gambler's fallacy arises out of a belief in a <a href="/wiki/Hasty_generalization" class="mw-redirect" title="Hasty generalization">law of small numbers</a>, leading to the erroneous belief that small samples must be representative of the larger population. According to the fallacy, streaks must eventually even out in order to be representative.<sup id="cite_ref-TverskyKahneman1971_10-0" class="reference"><a href="#cite_note-TverskyKahneman1971-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Amos_Tversky" title="Amos Tversky">Amos Tversky</a> and <a href="/wiki/Daniel_Kahneman" title="Daniel Kahneman">Daniel Kahneman</a> first proposed that the gambler's fallacy is a <a href="/wiki/Cognitive_bias" title="Cognitive bias">cognitive bias</a> produced by a <a href="/wiki/Heuristics_in_judgement_and_decision_making" class="mw-redirect" title="Heuristics in judgement and decision making">psychological heuristic</a> called the <a href="/wiki/Representativeness_heuristic" title="Representativeness heuristic">representativeness heuristic</a>, which states that people evaluate the probability of a certain event by assessing how similar it is to events they have experienced before, and how similar the events surrounding those two processes are.<sup id="cite_ref-TverskyKahneman1974_11-0" class="reference"><a href="#cite_note-TverskyKahneman1974-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-TverskyKahneman1971_10-1" class="reference"><a href="#cite_note-TverskyKahneman1971-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> According to this view, "after observing a long run of red on the roulette wheel, for example, most people erroneously believe that black will result in a more representative sequence than the occurrence of an additional red",<sup id="cite_ref-TverskyKahneman1974_11-1" class="reference"><a href="#cite_note-TverskyKahneman1974-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> so people expect that a short run of random outcomes should share properties of a longer run, specifically in that deviations from average should balance out. When people are asked to make up a random-looking sequence of coin tosses, they tend to make sequences where the proportion of heads to tails stays closer to 0.5 in any short segment than would be predicted by chance, a phenomenon known as <a href="/wiki/Insensitivity_to_sample_size" title="Insensitivity to sample size">insensitivity to sample size</a>.<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> Kahneman and Tversky interpret this to mean that people believe short sequences of random events should be representative of longer ones.<sup id="cite_ref-TverskyKahneman1971_10-2" class="reference"><a href="#cite_note-TverskyKahneman1971-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The representativeness heuristic is also cited behind the related phenomenon of the <a href="/wiki/Clustering_illusion" title="Clustering illusion">clustering illusion</a>, according to which people see streaks of random events as being non-random when such streaks are actually much more likely to occur in small samples than people expect.<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> </p><p>The gambler's fallacy can also be attributed to the mistaken belief that gambling, or even chance itself, is a fair process that can correct itself in the event of streaks, known as the <a href="/wiki/Just-world_hypothesis" class="mw-redirect" title="Just-world hypothesis">just-world hypothesis</a>.<sup id="cite_ref-Rogers1998_14-0" class="reference"><a href="#cite_note-Rogers1998-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Other researchers believe that belief in the fallacy may be the result of a mistaken belief in an <a href="/wiki/Internal_locus_of_control" class="mw-redirect" title="Internal locus of control">internal locus of control</a>. When a person believes that gambling outcomes are the result of their own skill, they may be more susceptible to the gambler's fallacy because they reject the idea that chance could overcome skill or talent.<sup id="cite_ref-SundaliCroson2006_15-0" class="reference"><a href="#cite_note-SundaliCroson2006-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Variations">Variations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=15" title="Edit section: Variations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some researchers believe that it is possible to define two types of gambler's fallacy: type one and type two. Type one is the classic gambler's fallacy, where individuals believe that a particular outcome is due after a long streak of another outcome. Type two gambler's fallacy, as defined by Gideon Keren and Charles Lewis, occurs when a gambler underestimates how many observations are needed to detect a favorable outcome, such as watching a roulette wheel for a length of time and then betting on the numbers that appear most often. For events with a high degree of randomness, detecting a bias that will lead to a favorable outcome takes an impractically large amount of time and is very difficult, if not impossible, to do.<sup id="cite_ref-KerenLewis1994_16-0" class="reference"><a href="#cite_note-KerenLewis1994-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> The two types differ in that type one wrongly assumes that gambling conditions are fair and perfect, while type two assumes that the conditions are biased, and that this bias can be detected after a certain amount of time. </p><p>Another variety, known as the retrospective gambler's fallacy, occurs when individuals judge that a seemingly rare event must come from a longer sequence than a more common event does. The belief that an imaginary sequence of die rolls is more than three times as long when a set of three sixes is observed as opposed to when there are only two sixes. This effect can be observed in isolated instances, or even sequentially. Another example would involve hearing that a teenager has <a href="/wiki/Unprotected_sex" class="mw-redirect" title="Unprotected sex">unprotected sex</a> and becomes pregnant on a given night, and concluding that she has been engaging in unprotected sex for longer than if we hear she had unprotected sex but did not become pregnant, when the probability of becoming pregnant as a result of each intercourse is independent of the amount of prior intercourse.<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> <div class="mw-heading mw-heading3"><h3 id="Relationship_to_hot-hand_fallacy">Relationship to hot-hand fallacy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=16" title="Edit section: Relationship to hot-hand fallacy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Another psychological perspective states that gambler's fallacy can be seen as the counterpart to basketball's <a href="/wiki/Hot-hand_fallacy" class="mw-redirect" title="Hot-hand fallacy">hot-hand fallacy</a>, in which people tend to predict the same outcome as the previous event - known as positive recency - resulting in a belief that a high scorer will continue to score. In the gambler's fallacy, people predict the opposite outcome of the previous event - negative recency - believing that since the roulette wheel has landed on black on the previous six occasions, it is due to land on red the next. Ayton and Fischer have theorized that people display positive recency for the hot-hand fallacy because the fallacy deals with human performance, and that people do not believe that an inanimate object can become "hot."<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> Human performance is not perceived as random, and people are more likely to continue streaks when they believe that the process generating the results is nonrandom.<sup id="cite_ref-Burns2004_19-0" class="reference"><a href="#cite_note-Burns2004-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> When a person exhibits the gambler's fallacy, they are more likely to exhibit the hot-hand fallacy as well, suggesting that one construct is responsible for the two fallacies.<sup id="cite_ref-SundaliCroson2006_15-1" class="reference"><a href="#cite_note-SundaliCroson2006-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>The difference between the two fallacies is also found in economic decision-making. A study by Huber, Kirchler, and Stockl in 2010 examined how the hot hand and the gambler's fallacy are exhibited in the financial market. The researchers gave their participants a choice: they could either bet on the outcome of a series of coin tosses, use an expert opinion to sway their decision, or choose a risk-free alternative instead for a smaller financial reward. Participants turned to the expert opinion to make their decision 24% of the time based on their past experience of success, which exemplifies the hot-hand. If the expert was correct, 78% of the participants chose the expert's opinion again, as opposed to 57% doing so when the expert was wrong. The participants also exhibited the gambler's fallacy, with their selection of either heads or tails decreasing after noticing a streak of either outcome. This experiment helped bolster Ayton and Fischer's theory that people put more faith in human performance than they do in seemingly random processes.<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> <div class="mw-heading mw-heading3"><h3 id="Neurophysiology">Neurophysiology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=17" title="Edit section: Neurophysiology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>While the <a href="/wiki/Representativeness_heuristic" title="Representativeness heuristic">representativeness heuristic</a> and other cognitive biases are the most commonly cited cause of the gambler's fallacy, research suggests that there may also be a <a href="/wiki/Neurology" title="Neurology">neurological</a> component. <a href="/wiki/Functional_magnetic_resonance_imaging" title="Functional magnetic resonance imaging">Functional magnetic resonance imaging</a> has shown that after losing a bet or gamble, known as riskloss, the <a href="/wiki/Frontoparietal_network" title="Frontoparietal network">frontoparietal network</a> of the brain is activated, resulting in more risk-taking behavior. In contrast, there is decreased activity in the <a href="/wiki/Amygdala" title="Amygdala">amygdala</a>, <a href="/wiki/Caudate_nucleus" title="Caudate nucleus">caudate</a>, and <a href="/wiki/Ventral_striatum" class="mw-redirect" title="Ventral striatum">ventral striatum</a> after a riskloss. Activation in the amygdala is <a href="/wiki/Negative_correlation" class="mw-redirect" title="Negative correlation">negatively correlated</a> with gambler's fallacy, so that the more activity exhibited in the amygdala, the less likely an individual is to fall prey to the gambler's fallacy. These results suggest that gambler's fallacy relies more on the <a href="/wiki/Prefrontal_cortex" title="Prefrontal cortex">prefrontal cortex</a>, which is responsible for <a href="/wiki/Executive_functions" title="Executive functions">executive</a>, goal-directed processes, and less on the brain areas that control <a href="/wiki/Affect_(psychology)" title="Affect (psychology)">affective</a> decision-making. </p><p>The desire to continue gambling or betting is controlled by the <a href="/wiki/Striatum" title="Striatum">striatum</a>, which supports a choice-outcome contingency learning method. The striatum processes the errors in prediction and the behavior changes accordingly. After a win, the positive behavior is <a href="/wiki/Reinforcement" title="Reinforcement">reinforced</a> and after a loss, the behavior is <a href="/wiki/Operant_conditioning" title="Operant conditioning">conditioned</a> to be avoided. In individuals exhibiting the gambler's fallacy, this choice-outcome contingency method is impaired, and they continue to make risks after a series of losses.<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> <div class="mw-heading mw-heading3"><h3 id="Possible_solutions">Possible solutions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=18" title="Edit section: Possible solutions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The gambler's fallacy is a deep-seated cognitive bias and can be very hard to overcome. Educating individuals about the nature of randomness has not always proven effective in reducing or eliminating any manifestation of the fallacy. Participants in a study by Beach and Swensson in 1967 were shown a shuffled deck of index cards with shapes on them, and were instructed to guess which shape would come next in a sequence. The <a href="/wiki/Treatment_and_control_groups" title="Treatment and control groups">experimental group</a> of participants was informed about the nature and existence of the gambler's fallacy, and were explicitly instructed not to rely on run dependency to make their guesses. The <a href="/wiki/Control_group" class="mw-redirect" title="Control group">control group</a> was not given this information. The response styles of the two groups were similar, indicating that the experimental group still based their choices on the length of the run sequence. This led to the conclusion that instructing individuals about randomness is not sufficient in lessening the gambler's fallacy.<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> </p><p>An individual's susceptibility to the gambler's fallacy may decrease with age. A study by Fischbein and Schnarch in 1997 administered a questionnaire to five groups: students in grades 5, 7, 9, 11, and college students specializing in teaching mathematics. None of the participants had received any prior education regarding probability. The question asked was: "Ronni flipped a coin three times and in all cases heads came up. Ronni intends to flip the coin again. What is the chance of getting heads the fourth time?" The results indicated that as the students got older, the less likely they were to answer with "smaller than the chance of getting tails", which would indicate a negative recency effect. 35% of the 5th graders, 35% of the 7th graders, and 20% of the 9th graders exhibited the negative recency effect. Only 10% of the 11th graders answered this way, and none of the college students did. Fischbein and Schnarch theorized that an individual's tendency to rely on the <a href="/wiki/Representativeness_heuristic" title="Representativeness heuristic">representativeness heuristic</a> and other cognitive biases can be overcome with age.<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>Another possible solution comes from Roney and Trick, <a href="/wiki/Gestalt_psychology" title="Gestalt psychology">Gestalt</a> psychologists who suggest that the fallacy may be eliminated as a result of grouping. When a future event such as a coin toss is described as part of a sequence, no matter how arbitrarily, a person will automatically consider the event as it relates to the past events, resulting in the gambler's fallacy. When a person considers every event as independent, the fallacy can be greatly reduced.<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> </p><p>Roney and Trick told participants in their experiment that they were betting on either two blocks of six coin tosses, or on two blocks of seven coin tosses. The fourth, fifth, and sixth tosses all had the same outcome, either three heads or three tails. The seventh toss was grouped with either the end of one block, or the beginning of the next block. Participants exhibited the strongest gambler's fallacy when the seventh trial was part of the first block, directly after the sequence of three heads or tails. The researchers pointed out that the participants that did not show the gambler's fallacy showed less confidence in their bets and bet fewer times than the participants who picked with the gambler's fallacy. When the seventh trial was grouped with the second block, and was perceived as not being part of a streak, the gambler's fallacy did not occur. </p><p>Roney and Trick argued that instead of teaching individuals about the nature of randomness, the fallacy could be avoided by training people to treat each event as if it is a beginning and not a continuation of previous events. They suggested that this would prevent people from gambling when they are losing, in the mistaken hope that their chances of winning are due to increase based on an interaction with previous events. </p> <div class="mw-heading mw-heading2"><h2 id="Users">Users</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=19" title="Edit section: Users"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Types_of_users">Types of users</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=20" title="Edit section: Types of users"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Within a real-world setting, numerous studies have uncovered that for various decision makers placed in high stakes scenarios, it is likely they will reflect some degree of strong negative autocorrelation in their judgement. </p> <div class="mw-heading mw-heading4"><h4 id="Asylum_judges">Asylum judges</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=21" title="Edit section: Asylum judges"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In a study aimed at discovering if the negative autocorrelation that exists with the gambler's fallacy existed in the decision made by U.S. asylum judges, results showed that after two successive asylum grants, a judge would be 5.5% less likely to approve a third grant.<sup id="cite_ref-:0_25-0" class="reference"><a href="#cite_note-:0-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Baseball_umpires">Baseball umpires</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=22" title="Edit section: Baseball umpires"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the game of <a href="/wiki/Baseball" title="Baseball">baseball</a>, decisions are made every minute. One particular decision made by <a href="/wiki/Umpire" title="Umpire">umpires</a> which is often subject to scrutiny is the 'strike zone' decision. Whenever a batter does not swing, the umpire must decide if the ball was within a fair region for the batter, known as the <a href="/wiki/Strike_zone" title="Strike zone">strike zone</a>. If outside of this zone, the ball does not count towards outing the batter. In a study of over 12,000 games, results showed that umpires are 1.3% less likely to call a strike if the previous two balls were also strikes.<sup id="cite_ref-:0_25-1" class="reference"><a href="#cite_note-:0-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Loan_officers">Loan officers</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=23" title="Edit section: Loan officers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the decision making of <a href="/wiki/Loan_officer" title="Loan officer">loan officers</a>, it can be argued that monetary incentives are a key factor in biased decision making, rendering it harder to examine the gambler's fallacy effect. However, research shows that loan officers who are not incentivised by monetary gain are 8% less likely to approve a loan if they approved one for the previous client.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Lottery_players">Lottery players</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=24" title="Edit section: Lottery players"><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:Gamblers_Fallacy_Effect_on_Lottery.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Gamblers_Fallacy_Effect_on_Lottery.jpg/220px-Gamblers_Fallacy_Effect_on_Lottery.jpg" decoding="async" width="220" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Gamblers_Fallacy_Effect_on_Lottery.jpg/330px-Gamblers_Fallacy_Effect_on_Lottery.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Gamblers_Fallacy_Effect_on_Lottery.jpg/440px-Gamblers_Fallacy_Effect_on_Lottery.jpg 2x" data-file-width="657" data-file-height="671" /></a><figcaption>The effect of gambler's fallacy on lottery selections, based on studies by Dek Terrell. After winning numbers are drawn, lottery players respond by reducing the number of times they select those numbers in following draws. This effect slowly corrects over time, as players become less affected by the fallacy.<sup id="cite_ref-:2_27-0" class="reference"><a href="#cite_note-:2-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup></figcaption></figure><p>Lottery play and jackpots entice gamblers around the globe, with the biggest decision for hopeful winners being what numbers to pick. While most people will have their own strategy, evidence shows that after a number is selected as a winner in the current draw, the same number will experience a significant drop in selections in the following lottery. A popular study by <a href="/wiki/Charles_T._Clotfelter" title="Charles T. Clotfelter">Charles Clotfelter</a> and <a href="/wiki/Philip_J._Cook" title="Philip J. Cook">Philip Cook</a> investigated this effect in 1991, where they concluded bettors would cease to select numbers immediately after they were selected, ultimately recovering selection popularity within three months.<sup id="cite_ref-:1_28-0" class="reference"><a href="#cite_note-:1-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> Soon after, a 1994 study was constructed by Dek Terrell to test the findings of Clotfelter and Cook. The key change in Terrell's study was the examination of a <a href="/wiki/Parimutuel_betting" title="Parimutuel betting">pari-mutuel</a> lottery in which, a number selected with lower total wagers placed on it will result in a higher pay-out. While this examination did conclude that players in both types of lotteries exhibited behaviour in-line with the gambler's fallacy theory, those who took part in pari-mutuel betting seemed to be less influenced.<sup id="cite_ref-:2_27-1" class="reference"><a href="#cite_note-:2-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p><table class="wikitable" style="text-align:right;"> <caption>Table 1. Percentage change in numbers selected by lottery players based on Clotfelter, Cook (1991)<sup id="cite_ref-:1_28-1" class="reference"><a href="#cite_note-:1-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </caption> <tbody><tr> <td colspan="2"> </td> <th colspan="5">Amount bet by lottery players </th></tr> <tr> <th colspan="2">Numbers drawn 14 April 1988 </th> <th>Draw day </th> <th colspan="4">Days after draw </th></tr> <tr> <th>April </th> <th>Winner Numbers </th> <td>0 </td> <td>1 </td> <td>3 </td> <td>7 </td> <td>56 </td></tr> <tr> <td>11 </td> <td>244 </td> <td>41 </td> <td>34 </td> <td>24 </td> <td>27 </td> <td>30 </td></tr> <tr> <td>12 </td> <td>504 </td> <td>29 </td> <td>20 </td> <td>12 </td> <td>18 </td> <td>15 </td></tr> <tr> <td>13 </td> <td>718 </td> <td>28 </td> <td>20 </td> <td>17 </td> <td>19 </td> <td>25 </td></tr> <tr> <td>14 </td> <td>323 </td> <td>134 </td> <td>95 </td> <td>79 </td> <td>81 </td> <td>76 </td></tr> <tr> <td>15 </td> <td>640 </td> <td>10 </td> <td>20 </td> <td>18 </td> <td>16 </td> <td>20 </td></tr> <tr> <td>16 </td> <td>957 </td> <td>30 </td> <td>22 </td> <td>20 </td> <td>24 </td> <td>32 </td></tr> <tr> <th colspan="3">Average percentage of players selecting previously <p>winning numbers compared to day of draw </p> </th> <td>78% </td> <td>63% </td> <td>68% </td> <td>73% </td></tr></tbody></table> <p>The effect the of gambler's fallacy can be observed as numbers are chosen far less frequently soon after they are selected as winners, recovering slowly over a two-month period. For example, on the 11th of April 1988, 41 players selected 244 as the winning combination. Three days later only 24 individuals selected 244, a 41.5% decrease. This is the gambler's fallacy in motion, as lottery players believe that the occurrence of a winning combination in previous days will decrease its likelihood of occurring today. </p> <div class="mw-heading mw-heading4"><h4 id="Video_game_players">Video game players</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gambler%27s_fallacy&action=edit&section=25" title="Edit section: Video game players"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Several <a href="/wiki/Video_game" title="Video game">video games</a> feature the use of <a href="/wiki/Loot_box" title="Loot box">loot boxes</a>, a collection of in-game items awarded on opening with random contents set by rarity metrics, as a <a href="/wiki/Video_game_monetization" title="Video game monetization">monetization</a> scheme. Since around 2018, loot boxes have come under scrutiny from governments and advocates on the basis they are akin to gambling, particularly for games aimed at youth. Some games use a special "pity-timer" mechanism, that if the player has opened several loot boxes in a row without obtaining a high-rarity item, subsequent loot boxes will improve the odds of a higher-rate item drop. This is considered to feed into the gambler's fallacy since it reinforces the idea that a player will eventually obtain a high-rarity item (a win) after only receiving common items from a string of previous loot boxes.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<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=Gambler%27s_fallacy&action=edit&section=26" 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" style="column-width: 25em;"> <ul><li><a href="/wiki/Availability_heuristic" title="Availability heuristic">Availability heuristic</a></li> <li><a href="/wiki/Gambler%27s_conceit" title="Gambler's conceit">Gambler's conceit</a></li> <li><a href="/wiki/Gambler%27s_ruin" title="Gambler's ruin">Gambler's ruin</a></li> <li><a href="/wiki/Inverse_gambler%27s_fallacy" title="Inverse gambler's fallacy">Inverse gambler's fallacy</a></li> <li><a href="/wiki/Hot_hand_fallacy" class="mw-redirect" title="Hot hand fallacy">Hot hand fallacy</a></li> <li><a href="/wiki/Law_of_averages" title="Law of averages">Law of averages</a></li> <li><a href="/wiki/Martingale_(betting_system)" title="Martingale (betting system)">Martingale (betting system)</a></li> <li><a href="/wiki/Mean_reversion_(finance)" title="Mean reversion (finance)">Mean reversion (finance)</a></li> <li><a href="/wiki/Memorylessness" title="Memorylessness">Memorylessness</a></li> <li><a href="/wiki/Oscar%27s_grind" title="Oscar's grind">Oscar's grind</a></li> <li><a href="/wiki/Regression_toward_the_mean" title="Regression toward the mean">Regression toward the mean</a></li> <li><a href="/wiki/Statistical_regularity" title="Statistical regularity">Statistical regularity</a></li> <li><a href="/wiki/Problem_gambling" title="Problem gambling">Problem gambling</a></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=Gambler%27s_fallacy&action=edit&section=27" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 33em;"> <ol class="references"> <li id="cite_note-monte_carlo-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-monte_carlo_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-monte_carlo_1-1"><sup><i><b>b</b></i></sup></a></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 a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.bbc.com/future/story/20150127-why-we-gamble-like-monkeys">"Why we gamble like monkeys"</a>. <i>BBC.com</i>. 2015-01-02.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=BBC.com&rft.atitle=Why+we+gamble+like+monkeys&rft.date=2015-01-02&rft_id=http%3A%2F%2Fwww.bbc.com%2Ffuture%2Fstory%2F20150127-why-we-gamble-like-monkeys&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGambler%27s+fallacy" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</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://spinsavvy.co.uk/monte-carlo-fallacy-understanding-probability-in-gambling/">"Monte Carlo Fallacy: Understanding Probability in Gambling - SpinSavvy"</a>. 2024-03-08<span class="reference-accessdate">. Retrieved <span class="nowrap">2024-11-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Monte+Carlo+Fallacy%3A+Understanding+Probability+in+Gambling+-+SpinSavvy&rft.date=2024-03-08&rft_id=https%3A%2F%2Fspinsavvy.co.uk%2Fmonte-carlo-fallacy-understanding-probability-in-gambling%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGambler%27s+fallacy" class="Z3988"></span></span> </li> <li id="cite_note-retrospective-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-retrospective_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-retrospective_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-retrospective_3-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-retrospective_3-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-retrospective_3-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text">Oppenheimer, D.M., & Monin, B. (2009). The retrospective gambler’s fallacy: Unlikely events, constructing the past, and multiple universes. <i>Judgment and Decision Making, vol. 4, no. 5,</i> pp. 326-334</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Leslie, J. (1989). <i>Universes</i>. London: Routledge.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHacking1987" class="citation journal cs1">Hacking, I (1987). "The inverse gambler's fallacy: The argument from design. 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href="/wiki/Template:Fallacies" title="Template:Fallacies"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Fallacies" title="Template talk:Fallacies"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Fallacies" title="Special:EditPage/Template:Fallacies"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Common_fallacies_(list)" style="font-size:114%;margin:0 4em">Common <a href="/wiki/Fallacy" title="Fallacy">fallacies</a> (<a href="/wiki/List_of_fallacies" title="List of fallacies">list</a>)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Formal_fallacy" title="Formal fallacy">Formal</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">In <a href="/wiki/Propositional_calculus" title="Propositional calculus">propositional logic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Affirming_a_disjunct" title="Affirming a disjunct">Affirming a disjunct</a></li> <li><a href="/wiki/Affirming_the_consequent" title="Affirming the consequent">Affirming the consequent</a></li> <li><a href="/wiki/Denying_the_antecedent" title="Denying the antecedent">Denying the antecedent</a></li> <li><a href="/wiki/Argument_from_fallacy" title="Argument from fallacy">Argument from fallacy</a></li> <li><a href="/wiki/Masked-man_fallacy" title="Masked-man fallacy">Masked man</a></li> <li><a href="/wiki/Mathematical_fallacy" title="Mathematical fallacy">Mathematical fallacy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">In <a href="/wiki/Quantifier_(logic)" title="Quantifier (logic)">quantificational logic</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Existential_fallacy" title="Existential fallacy">Existential</a></li> <li><a href="/wiki/Affirming_the_consequent" title="Affirming the consequent">Illicit conversion</a></li> <li><a href="/wiki/Proof_by_example" title="Proof by example">Proof by example</a></li> <li><a href="/wiki/Quantifier_shift" title="Quantifier shift">Quantifier shift</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Syllogistic_fallacy" class="mw-redirect" title="Syllogistic fallacy">Syllogistic fallacy</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Affirmative_conclusion_from_a_negative_premise" title="Affirmative conclusion from a negative premise">Affirmative conclusion from a negative premise</a></li> <li><a href="/wiki/Negative_conclusion_from_affirmative_premises" title="Negative conclusion from affirmative premises">Negative conclusion from affirmative premises</a></li> <li><a href="/wiki/Fallacy_of_exclusive_premises" title="Fallacy of exclusive premises">Exclusive premises</a></li> <li><a href="/wiki/Existential_fallacy" title="Existential fallacy">Existential</a></li> <li><a href="/wiki/Modal_scope_fallacy" title="Modal scope fallacy">Necessity</a></li> <li><a href="/wiki/Fallacy_of_four_terms" title="Fallacy of four terms">Four terms</a></li> <li><a href="/wiki/Illicit_major" title="Illicit major">Illicit major</a></li> <li><a href="/wiki/Illicit_minor" title="Illicit minor">Illicit minor</a></li> <li><a href="/wiki/Fallacy_of_the_undistributed_middle" title="Fallacy of the undistributed middle">Undistributed middle</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Informal_fallacy" title="Informal fallacy">Informal</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Equivocation</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Equivocation" title="Equivocation">Equivocation</a></li> <li><a href="/wiki/False_equivalence" title="False equivalence">False equivalence</a></li> <li><a href="/wiki/False_attribution" title="False attribution">False attribution</a></li> <li><a href="/wiki/Quoting_out_of_context" title="Quoting out of context">Quoting out of context</a></li> <li><a href="/wiki/Loki%27s_Wager" class="mw-redirect" title="Loki's Wager">Loki's Wager</a></li> <li><a href="/wiki/No_true_Scotsman" title="No true Scotsman">No true Scotsman</a></li> <li><a href="/wiki/Reification_(fallacy)" title="Reification (fallacy)">Reification</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Question-begging</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Circular_reasoning" title="Circular reasoning">Circular reasoning</a> / <a href="/wiki/Begging_the_question" title="Begging the question">Begging the question</a></li> <li><a href="/wiki/Loaded_language" title="Loaded language">Loaded language</a> <ul><li><a href="/wiki/Leading_question" title="Leading question">Leading question</a></li></ul></li> <li><a href="/wiki/Double-barreled_question" title="Double-barreled question">Compound question</a> / <a href="/wiki/Loaded_question" title="Loaded question">Loaded question</a> / <a href="/wiki/Complex_question" title="Complex question">Complex question</a></li> <li><a href="/wiki/No_true_Scotsman" title="No true Scotsman">No true Scotsman</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Correlative-based_fallacies" title="Correlative-based fallacies">Correlative-based</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/False_dilemma" title="False dilemma">False dilemma</a> <ul><li><a href="/wiki/Nirvana_fallacy" title="Nirvana fallacy">Perfect solution</a></li></ul></li> <li><a href="/wiki/Denying_the_correlative" title="Denying the correlative">Denying the correlative</a></li> <li><a href="/wiki/Suppressed_correlative" title="Suppressed correlative">Suppressed correlative</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Fallacies_of_illicit_transference" title="Fallacies of illicit transference">Illicit transference</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Fallacy_of_composition" title="Fallacy of composition">Composition</a></li> <li><a href="/wiki/Fallacy_of_division" title="Fallacy of division">Division</a></li> <li><a href="/wiki/Ecological_fallacy" title="Ecological fallacy">Ecological</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><i><a href="/wiki/Secundum_quid" title="Secundum quid">Secundum quid</a></i></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Accident_(fallacy)" title="Accident (fallacy)">Accident</a></li> <li><a href="/wiki/Converse_accident" title="Converse accident">Converse accident</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Faulty_generalization" title="Faulty generalization">Faulty generalization</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anecdotal_evidence" title="Anecdotal evidence">Anecdotal evidence</a></li> <li><a href="/wiki/Sampling_bias" title="Sampling bias">Sampling bias</a> <ul><li><a href="/wiki/Cherry_picking" title="Cherry picking">Cherry picking</a></li> <li><a href="/wiki/McNamara_fallacy" title="McNamara fallacy">McNamara</a></li></ul></li> <li><a href="/wiki/Base_rate_fallacy" title="Base rate fallacy">Base rate</a> / <a href="/wiki/Conjunction_fallacy" title="Conjunction fallacy">Conjunction</a></li> <li><a href="/wiki/Double_counting_(fallacy)" title="Double counting (fallacy)">Double counting</a></li> <li><a href="/wiki/Argument_from_analogy" title="Argument from analogy">False analogy</a></li> <li><a href="/wiki/Slothful_induction" title="Slothful induction">Slothful induction</a></li> <li><a href="/wiki/Overwhelming_exception" title="Overwhelming exception">Overwhelming exception</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ambiguity" title="Ambiguity">Ambiguity</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Fallacy_of_accent" title="Fallacy of accent">Accent</a></li> <li><a href="/wiki/False_precision" title="False precision">False precision</a></li> <li><a href="/wiki/Moving_the_goalposts" title="Moving the goalposts">Moving the goalposts</a></li> <li><a href="/wiki/Quoting_out_of_context" title="Quoting out of context">Quoting out of context</a></li> <li><a href="/wiki/Slippery_slope" title="Slippery slope">Slippery slope</a></li> <li><a href="/wiki/Sorites_paradox" title="Sorites paradox">Sorites paradox</a></li> <li><a href="/wiki/Syntactic_ambiguity" title="Syntactic ambiguity">Syntactic ambiguity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Questionable_cause" title="Questionable cause">Questionable cause</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Animistic_fallacy" title="Animistic fallacy">Animistic</a> <ul><li><a href="/wiki/Furtive_fallacy" title="Furtive fallacy">Furtive</a></li></ul></li> <li>Correlation implies causation <ul><li><i><a href="/wiki/Correlation_does_not_imply_causation" title="Correlation does not imply causation">Cum hoc</a></i></li> <li><i><a href="/wiki/Post_hoc_ergo_propter_hoc" title="Post hoc ergo propter hoc">Post hoc</a></i></li></ul></li> <li><a class="mw-selflink selflink">Gambler's</a> <ul><li><a href="/wiki/Inverse_gambler%27s_fallacy" title="Inverse gambler's fallacy">Inverse</a></li></ul></li> <li><a href="/wiki/Regression_fallacy" title="Regression fallacy">Regression</a></li> <li><a href="/wiki/Fallacy_of_the_single_cause" title="Fallacy of the single cause">Single cause</a></li> <li><a href="/wiki/Slippery_slope" title="Slippery slope">Slippery slope</a></li> <li><a href="/wiki/Texas_sharpshooter_fallacy" title="Texas sharpshooter fallacy">Texas sharpshooter</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Appeals</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Appeal_to_the_law" title="Appeal to the law">Law/Legality</a></li> <li><a href="/wiki/Appeal_to_the_stone" title="Appeal to the stone">Stone</a> / <a href="/wiki/Proof_by_assertion" title="Proof by assertion">Proof by assertion</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Appeal_to_consequences" title="Appeal to consequences">Consequences</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Argumentum_ad_baculum" title="Argumentum ad baculum">Argumentum ad baculum</a></i></li> <li><a href="/wiki/Wishful_thinking" title="Wishful thinking">Wishful thinking</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Appeal_to_emotion" title="Appeal to emotion">Emotion</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Think_of_the_children" title="Think of the children">Children</a></li> <li><a href="/wiki/Appeal_to_fear" title="Appeal to fear">Fear</a></li> <li><a href="/wiki/Appeal_to_flattery" title="Appeal to flattery">Flattery</a></li> <li><a href="/wiki/Appeal_to_novelty" title="Appeal to novelty">Novelty</a></li> <li><a href="/wiki/Appeal_to_pity" title="Appeal to pity">Pity</a></li> <li><a href="/wiki/Appeal_to_ridicule" title="Appeal to ridicule">Ridicule</a></li> <li><a href="/wiki/In-group_favoritism" title="In-group favoritism">In-group favoritism</a></li> <li><a href="/wiki/Invented_here" title="Invented here">Invented here</a> / <a href="/wiki/Not_invented_here" title="Not invented here">Not invented here</a></li> <li><a href="/wiki/Island_mentality" title="Island mentality">Island mentality</a></li> <li><a href="/wiki/Appeal_to_loyalty" title="Appeal to loyalty">Loyalty</a></li> <li><a href="/wiki/Parade_of_horribles" title="Parade of horribles">Parade of horribles</a></li> <li><a href="/wiki/Appeal_to_spite" class="mw-redirect" title="Appeal to spite">Spite</a></li> <li><a href="/wiki/Flag-waving" title="Flag-waving">Stirring symbols</a></li> <li><a href="/wiki/Wisdom_of_repugnance" title="Wisdom of repugnance">Wisdom of repugnance</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Genetic_fallacy" title="Genetic fallacy">Genetic fallacy</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Ad_hominem" scope="row" class="navbox-group" style="width:1%"><i><a href="/wiki/Ad_hominem" title="Ad hominem">Ad hominem</a></i></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Appeal_to_motive" title="Appeal to motive">Appeal to motive</a></li> <li><a href="/wiki/Association_fallacy" title="Association fallacy">Association</a> <ul><li><i><a href="/wiki/Reductio_ad_Hitlerum" title="Reductio ad Hitlerum">Reductio ad Hitlerum</a></i> <ul><li><a href="/wiki/Godwin%27s_law" title="Godwin's law">Godwin's law</a></li></ul></li> <li><i><a href="/wiki/Red-baiting" title="Red-baiting">Reductio ad Stalinum</a></i></li></ul></li> <li><a href="/wiki/Bulverism" title="Bulverism">Bulverism</a></li> <li><a href="/wiki/Poisoning_the_well" title="Poisoning the well">Poisoning the well</a></li> <li><a href="/wiki/Tone_policing" title="Tone policing">Tone</a></li> <li><i><a href="/wiki/Tu_quoque" title="Tu quoque">Tu quoque</a></i></li> <li><a href="/wiki/Whataboutism" title="Whataboutism">Whataboutism</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Argument_from_authority" title="Argument from authority">Authority</a> <ul><li><a href="/wiki/Appeal_to_accomplishment" title="Appeal to accomplishment">Accomplishment</a></li> <li><i><a href="/wiki/Ipse_dixit" title="Ipse dixit">Ipse dixit</a></i></li> <li><a href="/wiki/Argumentum_ad_lazarum" title="Argumentum ad lazarum">Poverty</a> / <a href="/wiki/Argumentum_ad_crumenam" title="Argumentum ad crumenam">Wealth</a></li></ul></li> <li><a href="/wiki/Etymological_fallacy" title="Etymological fallacy">Etymology</a></li> <li><a href="/wiki/Appeal_to_nature" title="Appeal to nature">Nature</a></li> <li><a href="/wiki/Appeal_to_tradition" title="Appeal to tradition">Tradition</a> / <a href="/wiki/Appeal_to_novelty" title="Appeal to novelty">Novelty</a> <ul><li><a href="/wiki/Chronological_snobbery" title="Chronological snobbery">Chronological snobbery</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other <a href="/wiki/Fallacy_of_relevance" class="mw-redirect" title="Fallacy of relevance">fallacies<br /> of relevance</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Arguments" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Argument" title="Argument">Arguments</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Ad_nauseam" title="Ad nauseam">Ad nauseam</a></i> <ul><li><a href="/wiki/Sealioning" title="Sealioning">Sealioning</a></li></ul></li> <li><a href="/wiki/Argument_from_anecdote" title="Argument from anecdote">Argument from anecdote</a></li> <li><a href="/wiki/Argument_from_silence" title="Argument from silence">Argument from silence</a></li> <li><a href="/wiki/Argument_to_moderation" title="Argument to moderation">Argument to moderation</a></li> <li><i><a href="/wiki/Argumentum_ad_populum" title="Argumentum ad populum">Argumentum ad populum</a></i></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Clich%C3%A9" title="Cliché">Cliché</a></li> <li><i><a href="/wiki/The_Four_Great_Errors" title="The Four Great Errors">The Four Great Errors</a></i></li> <li><a href="/wiki/I%27m_entitled_to_my_opinion" title="I'm entitled to my opinion">I'm entitled to my opinion</a></li> <li><i><a href="/wiki/Irrelevant_conclusion" title="Irrelevant conclusion">Ignoratio elenchi</a></i></li> <li><a href="/wiki/Invincible_ignorance_fallacy" title="Invincible ignorance fallacy">Invincible ignorance</a></li> <li><a href="/wiki/Moralistic_fallacy" title="Moralistic fallacy">Moralistic</a> / <a href="/wiki/Naturalistic_fallacy" title="Naturalistic fallacy">Naturalistic</a></li> <li><a href="/wiki/Motte-and-bailey_fallacy" title="Motte-and-bailey fallacy">Motte-and-bailey fallacy</a></li> <li><a href="/wiki/Psychologist%27s_fallacy" title="Psychologist's fallacy">Psychologist's fallacy</a></li> <li><a href="/wiki/Rationalization_(psychology)" title="Rationalization (psychology)">Rationalization</a></li> <li><a href="/wiki/Red_herring" title="Red herring">Red herring</a> <ul><li><a href="/wiki/Two_wrongs_make_a_right" class="mw-redirect" title="Two wrongs make a right">Two wrongs make a right</a></li></ul></li> <li><a href="/wiki/Special_pleading" title="Special pleading">Special pleading</a></li> <li><a href="/wiki/Straw_man" title="Straw man">Straw man</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" 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