{"id":74,"date":"2026-07-07T06:48:34","date_gmt":"2026-07-07T06:48:34","guid":{"rendered":"https:\/\/hocabul.net\/?p=74"},"modified":"2026-07-07T06:48:34","modified_gmt":"2026-07-07T06:48:34","slug":"buyuk-sayilar-yasasi-kumarbazin-yanilgisiyla-neden-surekli-karistirilir","status":"publish","type":"post","link":"https:\/\/hocabul.net\/?p=74","title":{"rendered":"B\u00fcy\u00fck Say\u0131lar Yasas\u0131: Kumarbaz\u0131n Yan\u0131lg\u0131s\u0131yla Neden S\u00fcrekli Kar\u0131\u015ft\u0131r\u0131l\u0131r?"},"content":{"rendered":"\n

Bir madeni paray\u0131 10 kez att\u0131\u011f\u0131n\u0131zda 7 kez tura gelebilir \u2014 bu, hi\u00e7 de \u015fa\u015f\u0131rt\u0131c\u0131 de\u011fil. Ama ayn\u0131 paray\u0131 10 milyon kez att\u0131\u011f\u0131n\u0131zda, tura gelme oran\u0131n\u0131n neredeyse tam olarak y\u00fczde 50’ye yakla\u015faca\u011f\u0131ndan emin olabilirsiniz. Bu basit ama derin g\u00f6zlem, istatisti\u011fin en temel prensiplerinden birinin \u00f6zeti: B\u00fcy\u00fck Say\u0131lar Yasas\u0131. Ne var ki bu yasa, kumarbaz\u0131n yan\u0131lg\u0131s\u0131 yaz\u0131m\u0131zda<\/a> anlatt\u0131\u011f\u0131m\u0131z mant\u0131k hatas\u0131yla s\u00fcrekli kar\u0131\u015ft\u0131r\u0131l\u0131yor \u2014 oysa ikisi birbirinin neredeyse tam tersini s\u00f6yl\u00fcyor.<\/p>\n\n\n\n

B\u00fcy\u00fck Say\u0131lar Yasas\u0131 Asl\u0131nda Ne Diyor?<\/h2>\n\n\n\n

Bu yasa basit\u00e7e \u015funu s\u00f6yl\u00fcyor: bir rastgele deneyi ne kadar \u00e7ok tekrarlarsan\u0131z, g\u00f6zlemledi\u011finiz ortalama sonu\u00e7, o kadar \u00e7ok teorik (beklenen) de\u011fere yakla\u015f\u0131r. Bir zar att\u0131\u011f\u0131n\u0131zda tek bir at\u0131\u015f\u0131n sonucu tamamen \u00f6ng\u00f6r\u00fclemez; ama zar\u0131 bir milyon kez att\u0131\u011f\u0131n\u0131zda, her bir say\u0131n\u0131n (1’den 6’ya) yakla\u015f\u0131k alt\u0131da bir oran\u0131nda geldi\u011fini g\u00f6receksiniz \u2014 bu, tesad\u00fcf de\u011fil, matematiksel bir kesinlik.<\/p>\n\n\n\n

Bu prensip ilk olarak 18. y\u00fczy\u0131lda \u0130svi\u00e7reli matematik\u00e7i Jakob Bernoulli taraf\u0131ndan kan\u0131tland\u0131 ve o zamandan beri olas\u0131l\u0131k teorisinin temel ta\u015flar\u0131ndan biri olarak kabul ediliyor. Sigorta \u015firketlerinden kumarhanelere, anket \u015firketlerinden bilimsel deneylere kadar say\u0131s\u0131z alan, bu yasan\u0131n \u00f6ng\u00f6r\u00fclebilirli\u011fine dayan\u0131yor.<\/p>\n\n\n\n

Kumarbaz\u0131n Yan\u0131lg\u0131s\u0131yla Kar\u0131\u015ft\u0131r\u0131lma Sebebi<\/h2>\n\n\n\n

\u0130\u015fte tam burada i\u015fler kar\u0131\u015f\u0131yor. Kumarbaz\u0131n yan\u0131lg\u0131s\u0131, bir madeni para \u00fcst \u00fcste be\u015f kez tura geldi\u011finde “art\u0131k yaz\u0131 gelmeli, \u00e7\u00fcnk\u00fc ortalama dengelenmeli” diye d\u00fc\u015f\u00fcnme hatas\u0131d\u0131r. Bu d\u00fc\u015f\u00fcnce, B\u00fcy\u00fck Say\u0131lar Yasas\u0131’n\u0131n yanl\u0131\u015f anla\u015f\u0131lm\u0131\u015f bir versiyonu: insanlar, “uzun vadede ortalamaya yakla\u015f\u0131lacaksa, bu yakla\u015f\u0131m\u0131n k\u0131sa vadede bir ‘d\u00fczeltme’ ile ger\u00e7ekle\u015fmesi gerekti\u011fini” d\u00fc\u015f\u00fcn\u00fcyor. Ama ger\u00e7ek \u015fu ki, bir sonraki at\u0131\u015f\u0131n sonucu \u00f6nceki at\u0131\u015flardan tamamen ba\u011f\u0131ms\u0131z; madeni paran\u0131n “haf\u0131zas\u0131” yok.<\/p>\n\n\n\n

B\u00fcy\u00fck Say\u0131lar Yasas\u0131’n\u0131n ger\u00e7ek anlam\u0131 \u015fu: ortalamaya yakla\u015fma, ge\u00e7mi\u015fteki sapmalar\u0131 “telafi eden” yeni sonu\u00e7larla de\u011fil, sadece yeterince \u00e7ok yeni g\u00f6zlem eklendi\u011finde ge\u00e7mi\u015fteki sapmalar\u0131n istatistiksel olarak \u00f6nemsizle\u015fmesiyle<\/em> ger\u00e7ekle\u015fiyor. Yani 5 tura’dan sonra 5 yaz\u0131 gelmesi gerekmiyor; sadece milyonlarca yeni at\u0131\u015f eklendi\u011finde, o ilk 5 turan\u0131n toplam orana etkisi istatistiksel olarak s\u0131f\u0131ra yakla\u015f\u0131yor.<\/p>\n\n\n\n

Neden Bu Ayr\u0131m Bu Kadar \u00d6nemli?<\/h2>\n\n\n\n

Bu ayr\u0131m\u0131 do\u011fru yapmak, g\u00fcnl\u00fck hayatta \u00f6nemli kararlar\u0131 etkileyebiliyor. \u00d6rne\u011fin bir yat\u0131r\u0131mc\u0131, “bu hisse son be\u015f g\u00fcnd\u00fcr d\u00fc\u015f\u00fcyor, art\u0131k y\u00fckselmesi gerekir” diye d\u00fc\u015f\u00fcn\u00fcrse, kumarbaz\u0131n yan\u0131lg\u0131s\u0131na d\u00fc\u015fm\u00fc\u015f olur \u2014 piyasa hareketleri, \u00f6nceki g\u00fcnlerin “dengelenmesi” gerekti\u011fini bilmiyor. Ama ayn\u0131 yat\u0131r\u0131mc\u0131, “k\u0131sa vadeli dalgalanmalara bakmak yerine uzun vadeli ortalama getiriye bakmal\u0131y\u0131m” derse, B\u00fcy\u00fck Say\u0131lar Yasas\u0131’n\u0131 do\u011fru uygulam\u0131\u015f olur.<\/p>\n\n\n\n

Bu t\u00fcr yanl\u0131\u015f yorumlamalar\u0131n bir ba\u015fka kuzeni de ortalama yalan s\u00f6yleyebilir yaz\u0131m\u0131zda<\/a> bahsetti\u011fimiz durumlar; bir ortalaman\u0131n tek ba\u015f\u0131na yan\u0131lt\u0131c\u0131 olabilece\u011fini biliyoruz, ama B\u00fcy\u00fck Say\u0131lar Yasas\u0131 bize ayn\u0131 zamanda \u015funu da hat\u0131rlat\u0131yor: yeterince b\u00fcy\u00fck ve rastgele bir \u00f6rneklemde, o ortalama ger\u00e7ekten g\u00fcvenilir bir referans noktas\u0131na d\u00f6n\u00fc\u015f\u00fcyor. Mesele, \u00f6rneklemin b\u00fcy\u00fckl\u00fc\u011f\u00fc ve rastgeleli\u011fi.<\/p>\n\n\n\n

Spor ve Oyun D\u00fcnyas\u0131ndan \u00d6rnekler<\/h2>\n\n\n\n

B\u00fcy\u00fck Say\u0131lar Yasas\u0131, spor istatistiklerinde de s\u00fcrekli kar\u015f\u0131m\u0131za \u00e7\u0131k\u0131yor. Bir basketbolcunun serbest at\u0131\u015f y\u00fczdesi, tek bir ma\u00e7ta y\u00fczde 100 ya da y\u00fczde 0 olabilir \u2014 ama sezon boyunca binlerce at\u0131\u015f birikince, bu oran oyuncunun ger\u00e7ek yetene\u011fine \u00e7ok daha yak\u0131n bir say\u0131ya oturur. Bu y\u00fczden analistler, k\u00fc\u00e7\u00fck \u00f6rneklemlere (tek bir ma\u00e7, birka\u00e7 at\u0131\u015f) dayanarak “bu oyuncu art\u0131k iyi de\u011fil” gibi sonu\u00e7lar \u00e7\u0131karmaktan ka\u00e7\u0131n\u0131yor; as\u0131l g\u00fcvenilir resim, yeterince b\u00fcy\u00fck bir \u00f6rneklem birikince ortaya \u00e7\u0131k\u0131yor.<\/p>\n\n\n\n

Bu mant\u0131k, Bayes\u00e7i d\u00fc\u015f\u00fcnme yakla\u015f\u0131m\u0131yla da yak\u0131ndan ili\u015fkili; yeni kan\u0131tlar geldik\u00e7e inanc\u0131m\u0131z\u0131 nas\u0131l g\u00fcncellememiz gerekti\u011fini Bayes teoremi yaz\u0131m\u0131zda<\/a> ele alm\u0131\u015ft\u0131k. B\u00fcy\u00fck Say\u0131lar Yasas\u0131 da benzer bir \u015fekilde, “yeterince veri topland\u0131\u011f\u0131nda ger\u00e7ek \u00f6r\u00fcnt\u00fc ortaya \u00e7\u0131kar” ilkesine dayan\u0131yor \u2014 ikisi de sab\u0131rl\u0131 ve veri temelli d\u00fc\u015f\u00fcnmenin \u00f6nemini vurguluyor.<\/p>\n\n\n\n

Resmi ve Akademik Kaynak<\/h2>\n\n\n\n

Bu konunun matematiksel temelini ve tarihini daha derinlemesine incelemek istersen, Britannica’n\u0131n B\u00fcy\u00fck Say\u0131lar Yasas\u0131 maddesine<\/a> g\u00f6z atabilirsin; Bernoulli’nin orijinal ispat\u0131ndan g\u00fcn\u00fcm\u00fczdeki uygulamalar\u0131na kadar konuyu kapsaml\u0131 bir \u015fekilde ele al\u0131yor.<\/p>\n\n\n\n

Son S\u00f6z<\/h2>\n\n\n\n

B\u00fcy\u00fck Say\u0131lar Yasas\u0131 ile kumarbaz\u0131n yan\u0131lg\u0131s\u0131 aras\u0131ndaki fark, asl\u0131nda istatistiksel d\u00fc\u015f\u00fcnmenin en g\u00fczel derslerinden biri: rastgelelik k\u0131sa vadede kaotik g\u00f6r\u00fcn\u00fcr, ama yeterince \u00e7ok g\u00f6zlemle sab\u0131rla topland\u0131\u011f\u0131nda, alt\u0131nda yatan ger\u00e7ek \u00f6r\u00fcnt\u00fc ortaya \u00e7\u0131kar. Sorun, bu sabr\u0131 beklemeden, k\u0131sa vadeli sapmalara anlam y\u00fcklemeye \u00e7al\u0131\u015fmakta.<\/p>\n","protected":false},"excerpt":{"rendered":"

Bir madeni paray\u0131 10 kez att\u0131\u011f\u0131n\u0131zda 7 kez tura gelebilir \u2014 bu, hi\u00e7 de \u015fa\u015f\u0131rt\u0131c\u0131 de\u011fil. Ama ayn\u0131 paray\u0131 10 milyon kez att\u0131\u011f\u0131n\u0131zda, tura gelme oran\u0131n\u0131n neredeyse tam olarak y\u00fczde 50’ye yakla\u015faca\u011f\u0131ndan emin olabilirsiniz. Bu basit ama derin g\u00f6zlem, istatisti\u011fin en temel prensiplerinden birinin \u00f6zeti: B\u00fcy\u00fck Say\u0131lar Yasas\u0131. Ne var ki bu yasa, kumarbaz\u0131n yan\u0131lg\u0131s\u0131 … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-74","post","type-post","status-publish","format-standard","hentry","category-istatistik-olasilik"],"_links":{"self":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/74","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=74"}],"version-history":[{"count":1,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/74\/revisions"}],"predecessor-version":[{"id":75,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/74\/revisions\/75"}],"wp:attachment":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=74"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=74"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=74"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}