Blaise Pascal: Labari Keke Ruletbe
Malam lissafibe, keke saba-ye suro yinzəna, ade kəla gade gərjin-ro kawojin.
Pascal (1623–1662) shekarawa 1650-lan na'urawa motsi daimbe gwajin. Keke juyima, ganyi gogewa sharu, suro yinzəna rotor ruletbe kakan dijin mbeji; amma suro yin ade labar gargajiyabe, rubutulan tabbatanyi.
Malam lissafibe
Blaise Pascal shekara mewu-a lekar-alan kalkuleta na'urabe gərjin, saurayi ro lokte geometry projective-lan nətijawa nəmjin, aiki asal matsawa-a fanko-a dijin, kuru 1654-lan, wasikawa Pierre de Fermat-a-lan, “matsala rabo lambawabe”-ga warwarjin: wasa damabe dəga yaksəna-lan kudi cacabe dagu adalcilan rabojin. Amsa sowa, wasa dəwozənadəlan wasama tilo tilo damalissafiDamaDama nətija tilobe, 0-lan 1-ro au 0%-lan 100%-ro. Lamba tilo: 1/37 = 2.70%.Samma karatuwo → nasarabe-ye rabo, ade asal kima matsakaicilissafiKima matsakaiciNətija matsakaici caca tilobe lokte kuralan. Caca Turaibe standard samma-lan kudi cacabe-be −1/37.Samma karatuwo →-be. Lissafi EV samma shafi adelan wasikawa ade-lan ga ishin.
Na'ura rulet Blaise Pascal-be mbeji-a?
Tsakiya shekarawa 1650-lan Pascal na'ura motsi daimbe-lan aiki dijin, kuru labarzəna keke daidaima, lokte kura ganyi gogewa sharu juyima, gərjin. Labar keke ade rotorna'uraRotorBangare kekebe juyijinma, ramiwa səkkəjinma.Samma karatuwo → ruletbe tajin tarikhwa ngəwulan wartəjin, amma manazarta asalbe tilolan rubutuzənyi. Mbeji: karni 18-ntənlan masu kasino garuwa ruwa maganinbe suga talla-ro amfani dijin. Bincikeye shaida ade-lan karbajinnyi.
Dama, magana sobe-a inyibe-a
Wasikawa 1654-be rulet-ga gulnyi, sabab lokte ade rulet bago. Su tambajin: wasama ndi kudi gənaro lamba yasge rakkajin; 2–1-lan yakkajin; kudiga dagu rabojin? Amsa Pascal-be ago ade-lan kima matsakaici sharaditin gulzəna-ga amfani dijin, hujja wartə-wartəbe-a bishiya hanyawa wasa gaderobe-a. Huygens wasikawaga karatujin, 1657-lan kitawu awal kima matsakaibe fitəjin. Kalma “expectation” (kima matsakaici) sobe.
Pascal-a Fermat-a matsala rabo lambawabe warwarjin: kima matsakaici ade kima adalci matsayibe.
Huygens, De Ratiociniis in Ludo Aleae: kitawu buga dijinzəna awal kima matsakaibe.
Jakob Bernoulli, Ars Conjectandi: doka lambawa kurabe.
Rulet Paris-lan bayanzəna. Biya samma 36/n − 1: EV = −1/37 (au −2/38).
Gwaji chi-square Pearson-be, juyiwa ruletbelan nəmzəna.
Fuwunbe samma, shafi adelan, burauzalan.
Caca
Hujja Pascal-be shahara kura samma cacalan rulet-ga gənyi, Kalkalu-ga: “caca” Pensées-lan, imaniga caca biya iyaka bagoma-a ruma. Ade hujja kima matsakaibe, kuru kəlo awal kam ilimi zabebe-ga kəla tilo-ro hujjaro amfani dijin. Wasamawa ruletbe Pascal-ga keke-ro gulma Pascal kəribe gənyi gulzəna; Pascal muhimmi ade caca-ga kima dagu yinmaga nəmjinma.
Ajab
Pascal keke rulet awal gərjin-a, gərjinnyi-a, wasa ade aiki sobe gaskiya-ga nəmjin: na'ura kam tilobe, kam kəla sha bago kəla gənjinnyi nəmjinma (motsi daimbe dəwonyi; kima matsakaici kərgajin), wasamawa miliyon kəlaro shekara tilolan kəla ade-ga nəmro amfani dijin.
Tambayawa
Shekarawa 1650 awal-lan kamwa cacama Paris-be-a lejin, kuru adelan matsala rabo lambawabe Chevalier de Méré-lan ga suro isəna. Kudi gaskiyabe-a dəlan wasa dijin rubutu bago.
Sabab labar ngəla, kuru masu talla kasinobe karni 19-ntənbe suga nəngajin. Gulwo, amma bayan manazartabe-a.
Dariya kəlabe
Kam kəla sha bago kəla gənjinnyi nəmjin. Baya-lan kam tilo kasino ade-lan gərjin.
Majiyawa
- Pascal, B. & Fermat, P. Wasikawa matsala rabo lambawabe-lan.
- Huygens, C. De Ratiociniis in Ludo Aleae.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.