Blaise Pascal: tatsuniyar dabaran roulette

Masanin lissafi

Blaise Pascal ya gina na'urar lissafi ta inji yana ɗan shekara goma sha tara, ya tabbatar da sakamako a fannin projective geometry tun yana matashi, ya yi aikin tushe kan matsi da wofi (vacuum), kuma a 1654, a cikin wasiƙu da Pierre de Fermat, ya warware “matsalar maki” (problem of points): yadda za a raba kuɗin caca na wasan sa'a da aka katse cikin adalci. Amsarsu, wato a raba bisa ga yiwuwarlissafiYiwuwaDamar faruwar wani sakamako, daga 0 zuwa 1 ko daga 0% zuwa 100%. Lamba ɗaya: 1/37 = 2.70%.Karanta gaba ɗaya → kowane ɗan wasa na yin nasara da a ce an ci gaba da wasan, ita ce asalin ƙimar da ake tsammanilissafiƘimar da ake tsammaniMatsakaicin sakamako a kowace caca a cikin dogon lokaci. −1/37 na kuɗin caca a kowace cacar Turai ta yau da kullum.Karanta gaba ɗaya →. Kowane lissafin EV a wannan shafin ya samo asali daga waɗannan wasiƙu.

Shin akwai na'urar roulette ta Blaise Pascal?

A tsakiyar shekarun 1650 Pascal ya yi aiki kan na'urar motsi na dindindin, kuma ana cewa ya gina dabaran da aka daidaita sosai wanda ya daɗe yana juyawa da ƙaramar gogayya. Labarin cewa wannan dabaran ya zama rotorkayan aikiRotorƁangaren dabaran da ke juyawa wanda ke ɗauke da ramuka.Karanta gaba ɗaya → na roulette ana maimaita shi a cikin littattafan tarihi da yawa, amma babu ɗaya daga cikin tushen farko da ya rubuta shi. Yana yiwuwa masu gudanar da caca a garuruwan maɓuɓɓugan ruwa a ƙarni na 18 sun yi amfani da sunan don jawo kwastomomi. Ba abu ne da Ɗakin gwajinmu zai karɓa bisa ga hujjojin da ake da su ba.

Yiwuwa, a kalmominsa da namu

Wasiƙun 1654 ba su ambaci roulette ba, domin a lokacin bai wanzu ba tukuna. Tambayarsu ita ce: ʼyan wasa biyu suna buƙatar maki uku don cin tukunyar kuɗi; sun tsaya a 2–1; ta yaya za a raba kuɗin? Amsar Pascal tana amfani da abin da yau za mu kira conditional expectation da hujja mai maimaita kanta a kan bishiyar yiwuwar ci gaban wasan. Huygens ya karanta wasiƙun kuma a 1657 ya wallafa littafin karatu na farko kan abin da ake tsammani. Kalmar “expectation” tasa ce.

Cacar Pascal

Shahararriyar hujjar Pascal game da caca ba ta roulette ba ce, ta Allah ce: “wager” a cikin littafin Pensées wanda ke ɗaukar imani a matsayin caca mai lada marar iyaka. Hujja ce ta ƙimar da ake tsammani, kuma ita ce karo na farko da wani ya yi amfani da ka'idar yanke shawara (decision theory) don kare wani ra'ayi. ʼYan wasan roulette da ke kiran sunan Pascal don dabaran suna kiran Pascal ɗin da bai dace ba; wanda ke da muhimmanci shi ne wanda ya nuna yadda ake ƙimanta farashin caca.

Abin mamaki

Ko Pascal ne ya gina dabaran roulette na farko ko a'a, wasan kyakkyawan misali ne na aikinsa na gaskiya: na'ura daga mutumin da ya tabbatar cewa ba za a samu wani abu ba tare da biyan komai ba (motsi na dindindin ba ya aiki; abin da ake tsammani ba ya ɓacewa), wadda ake amfani da ita don nuna wannan abu ga ʼyan wasa miliyoyi a kowace shekara.

Tambayoyi