Blaise Pascal: Nthano ya Gudumu la Roulette

Katswiri wa masamu

Blaise Pascal anapanga makina owerengera ali ndi zaka khumi ndi zisanu ndi zinayi, anatsimikizira mfundo za projective geometry ali mnyamata, anagwira ntchito yofunika pa kukakamiza kwa mpweya ndi malo opanda mpweya, ndipo mu 1654, m’makalata ndi Pierre de Fermat, anathetsa “vuto la mapointi”: momwe angagawire mwachilungamo ndalama zobetcha za masewera amwayi oimitsidwa pakati. Yankho lawo, kugawa molingana ndi kuthekeramasamuKuthekeraMwayi wa zotsatira, kuchokera 0 mpaka 1 kapena 0% mpaka 100%. Nambala imodzi: 1/37 = 2.70%.Werengani yonse → kwa wosewera aliyense kupambana masewerawo akanapitirira, ndilo chiyambi cha mtengo woyembekezekamasamuMtengo woyembekezekaZotsatira zapakati pa betcha lililonse pa nthawi yayitali. −1/37 ya ndalama zobetcha pa betcha lililonse la ku Ulaya wamba.Werengani yonse →. Kuwerengera kulikonse kwa EV patsamba lino kumachokera m’makalata amenewo.

Kodi panali makina a roulette a Blaise Pascal?

Chapakati pa m’ma 1650 Pascal ankagwira ntchito pa makina oyenda kosatha ndipo akuti anapanga gudumu lolinganizidwa bwino limene linkazungulira nthawi yaitali ndi kukangana kochepa. Nkhani yoti gudumu limeneli linakhala rotorzipangizoRotorGawo lozungulira la gudumu limene limanyamula tibowo.Werengani yonse → ya roulette imabwerezedwa m’mabuku ambiri a mbiri koma siilembedwa m’gwero loyambirira lililonse. N’zotheka kuti oyendetsa juga m’matauni a akasupe m’zaka za zana la 18 ankagwiritsa ntchito dzinali kukopa makasitomala. Labu silingavomereze zimenezi pa umboni umene ulipo.

Kuthekera, m’mawu ake ndi m’mawu athu

Makalata a 1654 sanena za roulette, imene inali isanakhalepo. Amafunsa kuti: osewera awiri akufunika mapointi atatu kuti apambane ndalama zonse; aima pa 2–1; kodi ndalamazo zigawidwe bwanji? Yankho la Pascal limagwiritsa ntchito chimene lero tingachitche chiyembekezo chokhala ndi chikhalidwe (conditional expectation) ndi mfundo yobwerezabwereza yotsika mumtengo wa njira zonse zimene masewera akanapitirira. Huygens anawerenga makalatawo ndipo mu 1657 anafalitsa buku loyamba la maphunziro onena za chiyembekezo. Mawu oti “chiyembekezo” (expectation) ndi ake.

Kubetcha kwa Pascal

Mfundo yotchuka kwambiri ya Pascal yokhudza kubetcha si ya roulette koma ya Mulungu: “kubetcha” (wager) m’buku la Pensées kumene kumaona chikhulupiriro ngati betcha la malipiro opanda malire. Ndi mfundo ya mtengo woyembekezeka, ndipo ndi nthawi yoyamba imene wina aliyense anagwiritsa ntchito chiphunzitso cha kupanga zisankho kuti atsimikizire chinthu. Osewera roulette amene amatchula Pascal pa nkhani ya gudumu akutchula Pascal wolakwika; wofunika ndi amene anasonyeza momwe angaikire mtengo pa juga.

Chodabwitsa chake

Kaya Pascal anapanga gudumu loyamba la roulette kapena ayi, masewerawa ndi chitsanzo chabwino cha ntchito yake yeniyeni: chida chochokera kwa munthu amene anatsimikizira kuti sungapeze kanthu popanda kupereka kanthu (makina oyenda kosatha amalephera; chiyembekezo sichisintha), chimene chimagwiritsidwa ntchito kusonyeza chinthu chomwecho kwa osewera mamiliyoni angapo pachaka.

Mafunso