Blaise Pascal: roulette ƒe ʋuafɔ ƒe gli
Akɔntabula si wogblɔna zi geɖe be eyae wɔ ʋuafɔ la, evɔ nu bubu wònɔ agbagba dzem be yeawɔ.
Pascal (1623–1662) do mɔ̃ siwo atrɔ ɖaa evɔ ŋusẽ aɖeke mehiã na wo o la kpɔ le ƒe 1650-awo me. Ʋuafɔ si trɔna kple ŋɔŋɔ sue aɖe ko si wotsɔna na eya la ate ŋu anye roulette rotor ƒe tɔgbuiwo dometɔ ɖeka; gake kɔnyinya ko wònye, womeŋlɔe ɖi le nuŋlɔɖi aɖeke me o.
Akɔntabula la
Blaise Pascal wɔ akɔntabumɔ̃ aɖe esime wòxɔ ƒe wuiasieke, eɖo kpeɖodzi geometry ƒe nyawo dzi esime wònye ɖekakpui, ewɔ gɔmeɖoanyi dɔ ɖe tetedeanyi kple nuɖeɖekpekpe ŋu, eye le ƒe 1654 me, le agbalẽ siwo wòŋlɔ ɖo ɖe Pierre de Fermat me la, eɖe “akɔntawo ƒe mamã ƒe kuxi” la me: aleke woama bɛtga si le fefe aɖe si wotso le titina me la dzɔdzɔe. Woƒe ŋuɖoɖoe nye be woama ga la ɖe fefewɔla ɖe sia ɖe ƒe mɔnukpɔkpɔakɔntabubuMɔnukpɔkpɔMɔnukpɔkpɔ be emetsonu aɖe nadzɔ, tso 0 va ɖo 1 alo tso 0% va ɖo 100%. Xexlẽdzesi ɖeka: 1/37 = 2.70%.Xlẽe blibo → be yeaɖu dzi ne woyi fefe la dzi la nu, eye afi sia ye asixɔxɔ si wokpɔ mɔ naakɔntabubuAsixɔxɔ si wokpɔ mɔ naEmetsonu le titina me le bɛt ɖe sia ɖe me le ɣeyiɣi didi me. −1/37 le bɛtga me na Europa bɛt gbadza ɖe sia ɖe.Xlẽe blibo → tso. EV akɔntabubu ɖe sia ɖe le nyatakakadzraɖoƒe sia dzi tso agbalẽ mawo me.
Ɖe Blaise Pascal ƒe roulette mɔ̃ aɖe nɔ anyi a?
Le ƒe 1650-awo ƒe titina me la, Pascal wɔ dɔ ɖe mɔ̃ si atrɔ ɖaa ŋu, eye wogblɔ be ewɔ ʋuafɔ aɖe si ƒe kpekpeme sɔ nyuie si trɔ ɣeyiɣi didi kple ŋɔŋɔ sue aɖe ko. Ŋutinyagbalẽ geɖe gblɔna be ʋuafɔ sia zu roulette rotordɔwɔnuRotorƲuafɔ la ƒe akpa si trɔna eye dowo le edzi.Xlẽe blibo →, gake gɔmeɖoanyi nuŋlɔɖi aɖeke meɖoe kpe o. Ate ŋu anye be tsieƒe-duwo me dɔwɔlawo le ƒe alafa 18lia me zã ŋkɔ la tsɔ do ŋgɔ na woƒe fefe. Numekuƒe la mate ŋu axɔe se le kpeɖodzi siwo li nu o.
Mɔnukpɔkpɔ, le eya ŋutɔ ƒe nyawo kple mía tɔwo me
Agbalẽ siwo woŋlɔ le ƒe 1654 me meyɔ roulette o, elabena menɔ anyi haɖe o. Wobia be: fefewɔla eve hiã akɔnta etɔ̃ hafi aɖu ga la dzi; wotso le 2–1; aleke woama ga la? Pascal ƒe ŋuɖoɖo zã nu si míeyɔna egbe be asixɔxɔ si wokpɔ mɔ na le nɔnɔme aɖe me, kple susu si yia ɖe ati si ɖe mɔ siwo fefe la ate ŋu ato la fia ƒe alɔwo me. Huygens xlẽ agbalẽawo eye le ƒe 1657 me eta sukugbalẽ gbãtɔ si ku ɖe nu si wokpɔ mɔ na ŋu. Nya “expectation” la, eya ye wɔe.
Pascal kple Fermat ɖe akɔntawo ƒe mamã ƒe kuxi la me: asixɔxɔ si wokpɔ mɔ na abe nɔnɔme aɖe ƒe asi dzɔdzɔe ene.
Huygens, De Ratiociniis in Ludo Aleae: agbalẽ gbãtɔ si wota si ƒo nu tso nu si wokpɔ mɔ na ŋu.
Jakob Bernoulli, Ars Conjectandi: xexlẽdzesi gãwo ƒe se.
Woƒo nu tso roulette ŋu le Paris. Fetu ɖe sia ɖe nye 36/n − 1: EV = −1/37 (alo −2/38).
Pearson ƒe chi-square dodokpɔ, si woɖe fia kple roulette trɔtrɔwo.
Esiawo katã, le nyatakakadzraɖoƒe sia dzi, le browser me.
Bɛt la
Pascal ƒe susu si ku ɖe bɛtɖoɖo ŋu si wonya wu la meku ɖe roulette ŋu o, ke boŋ ɖe Mawu ŋu: “bɛt” si le Pensées me si tsɔ xɔse sɔ kple bɛt si ƒe fetu nye nu si nu mewuna o. Asixɔxɔ si wokpɔ mɔ na ƒe susu wònye, eye zi gbãtɔe nye esi ame aɖe zã nyametsotso ƒe nufiafia tsɔ ɖo kpe nya aɖe dzi. Roulette fefewɔla siwo yɔa Pascal ɖe ʋuafɔ la ta la, Pascal si mele vevie o ŋue wole nu ƒom tsoe; ame si le vevie la nye esi ɖe aleke woakpɔ gafefe ƒe asi fia.
Nukunu la
Pascal ye wɔ roulette ƒe ʋuafɔ gbãtɔ alo menye eyae o hã la, fefe la ɖe eƒe dɔ ŋutɔŋutɔ fia nyuie: mɔ̃ si tso ame si ɖee fia be màte ŋu akpɔ nane ɖe nu maɖekemaɖekeo ta o (mɔ̃ si atrɔ ɖaa medzea edzi o; nu si wokpɔ mɔ na metrɔna o) gbɔ, si wozãna tsɔ ɖea nu ma ke fiana fefewɔla miliɔn ʋɛ aɖewo ƒe sia ƒe.
Nyabiasewo
Ezɔ le gafefelawo dome le Paris le ƒe 1650-awo ƒe gɔmedzedze, eye nenemae akɔntawo ƒe mamã ƒe kuxi la va ɖo egbɔ to Chevalier de Méré dzi. Nuŋlɔɖi aɖeke meli si fia be efe gafefe vevie kple ga o.
Elabena enye ŋutinya nyui eye ƒe alafa 19lia ƒe kasinowo ƒe ŋkɔxɔlawo lɔ̃e. Gbugbɔe gblɔ, gake ŋlɔ eƒe dzɔtsoƒe ɖe te.
Nukokoe sue
Eɖee fia be màte ŋu akpɔ nane ɖe nu maɖekemaɖekeo ta o. Emegbe ame aɖe tu kasino ɖe edzi.
Nunyaƒewo
- Pascal, B. & Fermat, P. Correspondence on the problem of points.
- Huygens, C. De Ratiociniis in Ludo Aleae.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.