{"id":14681,"date":"2016-10-01T12:39:24","date_gmt":"2016-10-01T09:39:24","guid":{"rendered":"http:\/\/109.232.216.219\/~bilimvegelecek\/?p=14681"},"modified":"2017-12-19T12:54:19","modified_gmt":"2017-12-19T09:54:19","slug":"bu-oyunu-oynar-misiniz","status":"publish","type":"post","link":"https:\/\/bilimvegelecek.com.tr\/index.php\/2016\/10\/01\/bu-oyunu-oynar-misiniz","title":{"rendered":"Bu oyunu oynar m\u0131s\u0131n\u0131z?"},"content":{"rendered":"<p>Bu yaz\u0131da basit ama olduk\u00e7a ilgin\u00e7 bir yaz\u0131 tura oyununu ele al\u0131yoruz. Bu oyunu kumarhaneye kar\u015f\u0131 oynar m\u0131s\u0131n\u0131z, yani \u201cuzun vadede\u201d kazanabilir misiniz? Bu soruyu s\u0131ra d\u0131\u015f\u0131, \u015f\u0131k bir \u00e7\u00f6z\u00fcmle sezgilerimizden ba\u011f\u0131ms\u0131z olarak yan\u0131tlayaca\u011f\u0131z. \u00c7\u00f6z\u00fcm, matematiksel yarat\u0131c\u0131l\u0131\u011f\u0131n s\u00fcrpriz zarafetine g\u00fczel bir \u00f6rnek. Merakl\u0131 okurun ilgisini \u00e7ekece\u011fini umuyorum.<\/p>\n<p><strong>Dokuz at\u0131\u015fta yaz\u0131 tura oyunu. <\/strong>Oyuncu yaz\u0131 ya da turadan birini se\u00e7ti\u011fini a\u00e7\u0131klar ve hilesiz bir madeni paray\u0131 dokuz kez atar. Diyelim ki oyuncu yaz\u0131y\u0131 se\u00e7ti. Oyun boyunca her at\u0131\u015f sonras\u0131 yaz\u0131lar\u0131n say\u0131s\u0131 turalar\u0131n say\u0131s\u0131ndan b\u00fcy\u00fckse oyuncu kazan\u0131r, ortaya koydu\u011fu her 10 lira i\u00e7in 60 lira al\u0131r. E\u011fer her at\u0131\u015f sonras\u0131 yaz\u0131lar\u0131n say\u0131s\u0131 turalar\u0131n say\u0131s\u0131ndan k\u00fc\u00e7\u00fck ya da e\u015fitse oyuncu ortaya koydu\u011fu 10 liray\u0131 kaybeder.<\/p>\n<p>Oyuncunun kazanma olas\u0131l\u0131\u011f\u0131 ve <em>beklenti say\u0131s\u0131<\/em> ka\u00e7t\u0131r?<\/p>\n<p><strong>\u00c7\u00f6z\u00fcm. <\/strong>\u00d6nce, her at\u0131\u015f sonras\u0131 yaz\u0131lar\u0131n say\u0131s\u0131n\u0131n turalardan b\u00fcy\u00fck olmas\u0131n\u0131 dikkate almayal\u0131m. Bu durumda dokuz at\u0131\u015f sonunda yaz\u0131 say\u0131s\u0131n\u0131n tura say\u0131s\u0131ndan fazla oldu\u011fu olas\u0131 se\u00e7enekler \u015funlard\u0131r: 9 yaz\u0131 0 tura, 8 yaz\u0131 1 tura, 7 yaz\u0131 2 tura, 6 yaz\u0131 3 tura, 5 yaz\u0131 4 tura.<\/p>\n<p>\u015eimdi, yukar\u0131daki be\u015f se\u00e7enekten birini ele alal\u0131m, \u00f6rne\u011fin 6 yaz\u0131 3 tura. Bu durum i\u00e7in sorunun bizden istedi\u011fi olas\u0131l\u0131\u011f\u0131 bulmaya \u00e7al\u0131\u015faca\u011f\u0131z, daha sonra ayn\u0131 y\u00f6ntemle di\u011fer se\u00e7enekleri de hesaplay\u0131p oyuncunun kazanma olas\u0131l\u0131\u011f\u0131na ula\u015faca\u011f\u0131z.<\/p>\n<p>Dokuz at\u0131\u015fta 6 yaz\u0131 3 tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak olduk\u00e7a basit:\u00a0 m\u00fcmk\u00fcn haller say\u0131s\u0131 2<sup>9<\/sup>=512 , uygun haller say\u0131s\u0131 9\u2019un 6\u2019l\u0131 kombinasyonu,\u00a0 ve 6 yaz\u0131 3 tura gelme olas\u0131l\u0131\u011f\u0131 84\/512.<\/p>\n<p>Tabii ki bulmak istedi\u011fimiz olas\u0131l\u0131k yukar\u0131daki sonu\u00e7 de\u011fil, \u00e7\u00fcnk\u00fc biz her at\u0131\u015f sonras\u0131 yaz\u0131 say\u0131s\u0131n\u0131n tura say\u0131s\u0131ndan fazla olmas\u0131n\u0131 istiyoruz. Bunun i\u00e7in 84 se\u00e7enek i\u00e7inden istemedi\u011fimiz durumlar\u0131n say\u0131s\u0131n\u0131 \u00e7\u0131kar\u0131rsak geriye her at\u0131\u015f sonras\u0131 yaz\u0131lar\u0131n say\u0131s\u0131n\u0131n turalar\u0131n say\u0131s\u0131ndan b\u00fcy\u00fck oldu\u011fu durumlar kalacak.<\/p>\n<p><strong>Ak\u0131l dolu bir hamle: \u015eah mat!<\/strong><\/p>\n<p>Az sonra istemedi\u011fimiz durumlar\u0131n say\u0131s\u0131n\u0131 ak\u0131l dolu bir yolla bularak probleme beyaz bayrak sallataca\u011f\u0131z.<\/p>\n<p>Yaz\u0131lar\u0131n daima \u00f6nde gidebilmesi ilk iki at\u0131\u015fta yaz\u0131 gelmesine ba\u011fl\u0131, \u00e7\u00fcnk\u00fc (YT), (TY) veya (TT) gelmesi durumunda oyuncu kaybediyor, kumarhane kazan\u0131yor.<\/p>\n<p>\u015eimdi, 6 yaz\u0131 3 tura i\u00e7inden rastgele bir durumu ele alal\u0131m. \u00d6rne\u011fin (YYTTTYYYY) se\u00e7ene\u011fine bakal\u0131m: Oyuncu kaybeder, \u00e7\u00fcnk\u00fc d\u00f6rd\u00fcnc\u00fc at\u0131\u015fta yaz\u0131 say\u0131s\u0131 tura say\u0131s\u0131na e\u015fit oluyor.<\/p>\n<p>Bu a\u015famaya dikkat! Say\u0131lar\u0131 geometriyle bulu\u015fturuyoruz. Her bir at\u0131\u015f i\u00e7in koordinat d\u00fczleminde g\u00f6sterece\u011fimiz noktalar\u0131n bile\u015fenlerini belirleyece\u011fiz. \u015e\u00f6yle ki: Birinci bile\u015fen at\u0131\u015f say\u0131, ikinci bile\u015fense her at\u0131\u015f sonras\u0131 yaz\u0131lar\u0131n turalardan ne kadar fazla ya da eksik oldu\u011funu g\u00f6steren say\u0131 olacak. \u00d6rne\u011fin be\u015f at\u0131\u015fl\u0131k (YYTTT) durumuna kar\u015f\u0131l\u0131k gelen be\u015f noktan\u0131n ilki (1, 1) olur \u00e7\u00fcnk\u00fc at\u0131\u015f say\u0131s\u0131 1, yaz\u0131 say\u0131s\u0131 1. Ayn\u0131 \u015fekilde ikinci nokta (2, 2), \u00fc\u00e7\u00fcnc\u00fc (3, 1), d\u00f6rd\u00fcnc\u00fc (4, 0), be\u015finci nokta (5, -1). Dikkat edilirse, d\u00f6rd\u00fcnc\u00fc at\u0131\u015f sonunda yaz\u0131 say\u0131s\u0131 tura say\u0131s\u0131ndan \u00e7\u0131kar\u0131l\u0131rsa sonu\u00e7 s\u0131f\u0131r oldu\u011fundan d\u00f6rd\u00fcnc\u00fc noktan\u0131n ikinci bile\u015feni s\u0131f\u0131r oluyor. Ayn\u0131 \u015fekilde be\u015finci at\u0131\u015f sonras\u0131nda yaz\u0131lar turalardan \u00e7\u0131kar\u0131ld\u0131\u011f\u0131nda elde edilen sonu\u00e7 -1, be\u015finci noktan\u0131n ikinci bile\u015feni oluyor.<\/p>\n<p>\u015eimdi, yukar\u0131da rasgele se\u00e7ti\u011fimiz (YYTTTYYYY) durumuna bir kez daha bakal\u0131m ve dokuz at\u0131\u015f i\u00e7in dokuz noktay\u0131 s\u0131ras\u0131yla belirleyelim: (1, 1), (2, 2), (3, 1), (4, 0), (5, -1), (6, 0), (7, 1), (8, 2), (9, 3).<\/p>\n<p>Yukar\u0131da belirledi\u011fimiz dokuz noktay\u0131 koordinat d\u00fczleminde g\u00f6sterip, bu noktalar\u0131n birle\u015ftirilmesinden olu\u015fan grafi\u011fi \u00e7izelim.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-14683 size-full\" src=\"https:\/\/bilimvegelecek.com.tr\/wp-content\/uploads\/2017\/12\/mat-sohbet-152-1.jpg\" alt=\"\" width=\"632\" height=\"279\" srcset=\"https:\/\/bilimvegelecek.com.tr\/wp-content\/uploads\/2017\/12\/mat-sohbet-152-1.jpg 632w, https:\/\/bilimvegelecek.com.tr\/wp-content\/uploads\/2017\/12\/mat-sohbet-152-1-600x265.jpg 600w, https:\/\/bilimvegelecek.com.tr\/wp-content\/uploads\/2017\/12\/mat-sohbet-152-1-300x132.jpg 300w\" sizes=\"auto, (max-width: 632px) 100vw, 632px\" \/><\/p>\n<p>Oyuncunun kazanabilmesi i\u00e7in grafi\u011fin (1, 1) noktas\u0131ndan ba\u015flay\u0131p (9, 3)\u2019te bitmesi gerekiyor, ama bu yeterli de\u011fil, ayr\u0131ca grafi\u011fin <em>x<\/em> eksenini kesmemesi (ikinci bile\u015fen negatif oldu\u011funda turalar yaz\u0131lardan \u00e7ok oluyor), hatta <em>x<\/em> eksenine u\u011framamas\u0131 gerekiyor ( ikinci bile\u015fen s\u0131f\u0131r oldu\u011funda yaz\u0131 say\u0131s\u0131 tura say\u0131s\u0131na e\u015fit oluyor, oyuncu kaybediyor). O halde biz (1, 1)\u2019de ba\u015flay\u0131p (9, 3)\u2019de biten ve <em>x <\/em>eksenini kesmeyen grafiklerin say\u0131s\u0131n\u0131 bulmal\u0131y\u0131z.<\/p>\n<p>\u00d6te yandan 6 yaz\u0131 3 turaya kar\u015f\u0131l\u0131k gelen toplam 84 tane grafi\u011fin oldu\u011funu biliyoruz.\u00a0 Bu 84 grafi\u011fin ba\u015flang\u0131\u00e7 noktas\u0131 (1, 1) ya da (1, -1) olacak. Oyunun her a\u015famas\u0131nda yaz\u0131lar\u0131n \u00f6nde olmas\u0131 i\u00e7in ba\u015flang\u0131\u00e7 noktas\u0131 (1, 1) olmal\u0131d\u0131r elbette.<\/p>\n<p>(1, 1)\u2019den ba\u015flay\u0131p <em>x<\/em> eksenine u\u011frayarak (9, 3)\u2019e giden grafiklerin say\u0131s\u0131yla (1, -1)\u2019den ba\u015flayan (9, 3)\u2019e giden grafiklerin say\u0131s\u0131n\u0131 toplay\u0131p 84\u2019ten \u00e7\u0131kar\u0131rsak <em>x<\/em> eksenine u\u011framadan (9, 3)\u2019e giden grafiklerin say\u0131s\u0131n\u0131 bulmu\u015f olaca\u011f\u0131z.<\/p>\n<p>\u00d6nce, (-1, 1)\u2019den ba\u015flay\u0131p (9, 3)\u2019e giden grafiklerin say\u0131s\u0131n\u0131 bulal\u0131m: Bir grafik (-1, 1)\u2019den ba\u015flad\u0131ysa ilk at\u0131\u015f tura gelmi\u015f demektir. Grafi\u011fin (9, 3)\u2019e gidebilmesi i\u00e7in ilk at\u0131\u015ftan sonraki sekiz at\u0131\u015f\u0131n alt\u0131s\u0131n\u0131n yaz\u0131 ikisinin tura olmas\u0131 gerekiyor. O halde (-1, 1)\u2019den ba\u015flay\u0131p (9, 3)\u2019e giden grafiklerin say\u0131s\u0131 \u2019dir.<\/p>\n<p>\u015eimdi de (1, 1)\u2019den ba\u015flay\u0131p <em>x<\/em> eksenine u\u011frayarak (9, 3)\u2019e giden grafiklerin say\u0131s\u0131n\u0131 bulal\u0131m. Bu say\u0131 da 28, yani (-1, 1)\u2019den ba\u015flay\u0131p (9, 3)\u2019e giden grafiklerin say\u0131s\u0131na e\u015fit! Ho\u015f bir s\u00fcrpriz! \u015e\u00f6yle ki: Yukar\u0131da grafi\u011fini \u00e7izdi\u011fimiz (YYTTTYYYY) se\u00e7ene\u011finde yaz\u0131lar\u0131 tura, turalar\u0131 yaz\u0131 yaparsak (TTYYYTTTT) olur. Bu durumun grafi\u011fi a\u015fa\u011f\u0131daki gibidir.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-14684 size-full\" src=\"https:\/\/bilimvegelecek.com.tr\/wp-content\/uploads\/2017\/12\/mat-sohbet-152-2.jpg\" alt=\"\" width=\"638\" height=\"331\" srcset=\"https:\/\/bilimvegelecek.com.tr\/wp-content\/uploads\/2017\/12\/mat-sohbet-152-2.jpg 638w, https:\/\/bilimvegelecek.com.tr\/wp-content\/uploads\/2017\/12\/mat-sohbet-152-2-600x311.jpg 600w, https:\/\/bilimvegelecek.com.tr\/wp-content\/uploads\/2017\/12\/mat-sohbet-152-2-300x156.jpg 300w\" sizes=\"auto, (max-width: 638px) 100vw, 638px\" \/><\/p>\n<p>\u0130lk grafikle yukar\u0131daki kar\u015f\u0131la\u015ft\u0131r\u0131l\u0131rsa grafiklerin <em>x<\/em> eksenini ilk u\u011frad\u0131klar\u0131 noktan\u0131n solunda birbirlerinin <em>x<\/em> eksenine g\u00f6re simetri\u011fi olduklar\u0131 g\u00f6r\u00fcl\u00fcr. O halde her bir se\u00e7enek i\u00e7in yaz\u0131lar\u0131 tura, turalar\u0131 yaz\u0131 yaparsak (-1, 1)\u2019den ba\u015flay\u0131p (9, 3)\u2019e giden grafiklerin say\u0131s\u0131yla (1, 1)\u2019den ba\u015flay\u0131p <em>x<\/em> eksenine u\u011frayarak (9, 3)\u2019e giden grafiklerin say\u0131s\u0131n\u0131n e\u015fit oldu\u011fu g\u00f6r\u00fcl\u00fcr. B\u00f6ylece (1, 1)\u2019den ba\u015flay\u0131p <em>x<\/em> eksenine u\u011framadan (9, 3)\u2019e giden grafiklerin say\u0131s\u0131 84 \u2013 28 \u2013 28 =28 olur.<\/p>\n<p>Art\u0131k istedi\u011fimiz olas\u0131l\u0131\u011f\u0131, yani dokuz at\u0131\u015f boyunca yaz\u0131 say\u0131s\u0131n\u0131n tura say\u0131s\u0131ndan b\u00fcy\u00fck olma olas\u0131l\u0131\u011f\u0131n\u0131 bulabiliriz: 28\/512.<\/p>\n<p>Bundan sonra, di\u011fer durumlar ( 9 yaz\u0131 0 tura, 8 yaz\u0131 1 tura, 7 yaz\u0131 2 tura, 5 yaz\u0131 4 tura) i\u00e7in de ayn\u0131 y\u00f6ntemle olas\u0131l\u0131klar\u0131 hesaplayabiliriz.<\/p>\n<p>5 yaz\u0131 4 tura i\u00e7in istenilen olas\u0131l\u0131k, (9, 5) &#8211; 2 x (8, 5) \/\u00a02<sup>9<\/sup>=14\/512<br \/>\nolur. Ayn\u0131 \u015fekilde hesaplan\u0131rsa, 7 yaz\u0131 2 tura i\u00e7in 20\/512, 8 yaz\u0131 1 tura i\u00e7in 7\/512, 9 yaz\u0131 0 tura i\u00e7in 1\/512 bulunur.<\/p>\n<p>Ba\u015flang\u0131\u00e7taki 6 yaz\u0131 3 tura i\u00e7in buldu\u011fumuz 28\/512 say\u0131s\u0131yla yukar\u0131daki say\u0131lar\u0131 toplarsak oyuncunun kazanma olas\u0131l\u0131\u011f\u0131n\u0131 buluyoruz: 28+14+20+7+1\/512=35\/256<\/p>\n<p>Dokuz at\u0131\u015f boyunca yaz\u0131lar\u0131n say\u0131s\u0131n\u0131n turalar\u0131n say\u0131s\u0131ndan b\u00fcy\u00fck olma, yani oyuncunun kazanma olas\u0131l\u0131\u011f\u0131 35\/256. Kaybetme olas\u0131l\u0131\u011f\u0131 ise 1-35\/256 = 221\/256 olur.<\/p>\n<p>\u015eimdi, beklenti say\u0131s\u0131n\u0131 bularak bu oyunun uzun vadede kazan\u0131l\u0131p kazan\u0131lamayaca\u011f\u0131na karar verelim.<\/p>\n<p>Oyuncu kazand\u0131\u011f\u0131nda ortaya koydu\u011fu her 10 lira i\u00e7in kumarhaneden 60 lira al\u0131yor. Bu durumda oyunun <em>beklenti say\u0131s\u0131: <\/em>35\/256 x 60 \u2013 221\/256 x 10 = -55\/128<\/p>\n<p>Beklenti say\u0131s\u0131 negatif \u00e7\u0131kt\u0131, oyuncu kaybeder, oynamamal\u0131!<\/p>\n<p><strong>D\u00fczeltme:<\/strong> Ge\u00e7en say\u0131daki yaz\u0131da sayfa 76\u2019daki e\u015fitlikte 5\/8 yaz\u0131lm\u0131\u015f, -5\/8 olmal\u0131. Ayr\u0131ca sayfa 77\u2019de P(z)+P(z)=1\u00a0yaz\u0131lm\u0131\u015f, \u00a0P(z)+P(g)=1 olmal\u0131. Teknik nedenlerden kaynaklanan bu d\u00fczeltmeler i\u00e7in \u00f6z\u00fcr diliyoruz.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu yaz\u0131da basit ama olduk\u00e7a ilgin\u00e7 bir yaz\u0131 tura oyununu ele al\u0131yoruz. Bu oyunu kumarhaneye kar\u015f\u0131 oynar m\u0131s\u0131n\u0131z, yani \u201cuzun vadede\u201d kazanabilir misiniz? Bu soruyu s\u0131ra d\u0131\u015f\u0131, \u015f\u0131k bir \u00e7\u00f6z\u00fcmle sezgilerimizden ba\u011f\u0131ms\u0131z olarak yan\u0131tlayaca\u011f\u0131z. \u00c7\u00f6z\u00fcm, matematiksel yarat\u0131c\u0131l\u0131\u011f\u0131n s\u00fcrpriz zarafetine g\u00fczel bir \u00f6rnek. Merakl\u0131 okurun ilgisini \u00e7ekece\u011fini umuyorum. Dokuz at\u0131\u015fta yaz\u0131 tura oyunu. Oyuncu yaz\u0131 ya [&hellip;]<\/p>\n","protected":false},"author":375,"featured_media":14682,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[189,25,514],"tags":[208,1668,1530,1667],"class_list":["post-14681","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-152-sayi","category-matematik","category-matematik-sohbetleri","tag-matematik","tag-olasilik","tag-sayilar","tag-yazi-tura"],"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.8 - aioseo.com -->\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"Ali T\u00f6r\u00fcn\"\/>\n\t<link rel=\"canonical\" href=\"https:\/\/bilimvegelecek.com.tr\/index.php\/2016\/10\/01\/bu-oyunu-oynar-misiniz\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 4.9.8\" \/>\n\t\t<meta property=\"og:locale\" content=\"tr_TR\" \/>\n\t\t<meta property=\"og:site_name\" content=\"Bilim ve Gelecek\" \/>\n\t\t<meta property=\"og:type\" content=\"article\" \/>\n\t\t<meta property=\"og:title\" content=\"Bu oyunu oynar m\u0131s\u0131n\u0131z? | Bilim ve Gelecek\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/bilimvegelecek.com.tr\/index.php\/2016\/10\/01\/bu-oyunu-oynar-misiniz\" \/>\n\t\t<meta property=\"fb:app_id\" content=\"2104805563100892\" \/>\n\t\t<meta property=\"fb:admins\" content=\"1250955469\" \/>\n\t\t<meta property=\"og:image\" content=\"https:\/\/bilimvegelecek.com.tr\/wp-content\/uploads\/2017\/12\/yazi-tura-atmak.jpg\" \/>\n\t\t<meta property=\"og:image:secure_url\" content=\"https:\/\/bilimvegelecek.com.tr\/wp-content\/uploads\/2017\/12\/yazi-tura-atmak.jpg\" \/>\n\t\t<meta property=\"og:image:width\" content=\"800\" \/>\n\t\t<meta property=\"og:image:height\" content=\"450\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2016-10-01T09:39:24+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2017-12-19T09:54:19+00:00\" \/>\n\t\t<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/bilimvegelecekdergisi\/\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n\t\t<meta name=\"twitter:site\" content=\"@bilimvegelecek\" \/>\n\t\t<meta name=\"twitter:title\" content=\"Bu oyunu oynar m\u0131s\u0131n\u0131z? | Bilim ve Gelecek\" \/>\n\t\t<meta name=\"twitter:image\" content=\"https:\/\/bilimvegelecek.com.tr\/wp-content\/uploads\/2017\/12\/yazi-tura-atmak.jpg\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/bilimvegelecek.com.tr\\\/index.php\\\/2016\\\/10\\\/01\\\/bu-oyunu-oynar-misiniz#article\",\"name\":\"Bu oyunu oynar m\\u0131s\\u0131n\\u0131z? | Bilim ve Gelecek\",\"headline\":\"Bu oyunu oynar m\\u0131s\\u0131n\\u0131z?\",\"author\":{\"@id\":\"https:\\\/\\\/bilimvegelecek.com.tr\\\/index.php\\\/author\\\/atorun#author\"},\"publisher\":{\"@id\":\"https:\\\/\\\/bilimvegelecek.com.tr\\\/#organization\"},\"image\":{\"@type\":\"ImageObject\",\"url\":\"https:\\\/\\\/bilimvegelecek.com.tr\\\/wp-content\\\/uploads\\\/2017\\\/12\\\/yazi-tura-atmak.jpg\",\"width\":800,\"height\":450},\"datePublished\":\"2016-10-01T12:39:24+03:00\",\"dateModified\":\"2017-12-19T12:54:19+03:00\",\"inLanguage\":\"tr-TR\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/bilimvegelecek.com.tr\\\/index.php\\\/2016\\\/10\\\/01\\\/bu-oyunu-oynar-misiniz#webpage\"},\"isPartOf\":{\"@id\":\"https:\\\/\\\/bilimvegelecek.com.tr\\\/index.php\\\/2016\\\/10\\\/01\\\/bu-oyunu-oynar-misiniz#webpage\"},\"articleSection\":\"152. 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