Blaise Pascal: di stori bɔt di rulɛt wil
Di matimatishan we pipul kin se mek di wil, we bin de tray fɔ bil sɔntin ɔda.
Pascal (1623–1662) bin de tray mashin dɛn fɔ muv sote go na di 1650 dɛn. Di wil we de tɔn wit lɛk nɔ fraykshɔn, we pipul se na in mek am, kin bi di gran-gran fɔ di rulɛt rotɔ; bɔt da tin de na stori we pipul de tɛl, nɔ na pepa we pruv am.
Di matimatishan
Blaise Pascal bil wan kalkuleta we de wok wit mashin we i gɛt nayntin ia, i pruv tin dɛn na projɛktiv jiomɛtri we i stil yɔŋ, i du fawndeshɔn wok pan prɛshɔ ɛn vakyum, ɛn na 1654, insay lɛta dɛn wit Pierre de Fermat, i sɔlv di “prɔblɛm fɔ pɔynt dɛn”: aw fɔ sheb di bɛt mɔni fɔ chans gem we stɔp fɔ ɔf, wit fɛrnɛs. Dɛn ansa, fɔ sheb am akɔdin to di prɔbabilitimatematiksPrɔbabilitiDi chans fɔ wan rizɔlt, frɔm 0 to 1 ɔ frɔm 0% to 100%. Wan nɔmba: 1/37 = 2.70%.Rid ɔl → we ɛni pleya bin gɛt fɔ win if di gem bin kɔntinyu, na usay valyu we fɔ ɛkspɛktmatematiksValyu we fɔ ɛkspɛktDi avrej rizɔlt fɔ ɛni bɛt if yu ple lɔng tɛm. −1/37 fɔ di bɛt mɔni fɔ ɛni nɔmal Yuropian bɛt.Rid ɔl → bigin. Ɛni EV kalkyuleshɔn na dis sayt kɔmɔt frɔm dɛn lɛta dɛn de.
Blaise Pascal bin ɛva gɛt rulɛt mashin?
Midul di 1650 dɛn, Pascal bin de wok pan mashin fɔ muv sote go, ɛn pipul se i bil wil we balans fayn we tɔn fɔ lɔng tɛm wit smɔl fraykshɔn. Di stori se dis wil tɔn di rulɛt rotɔikwipmɛntRotɔDi pat fɔ di wil we de tɔn ɛn we kɛr di pɔkit dɛn.Rid ɔl → de insay bɔku istri buk, bɔt nɔ wan pan di fɔs-an sɔs dɛn nɔ rayt am. I pɔsibul se di wan dɛn we bin de rɔn gem na di spa tɔŋ dɛn na di 18 sɛnchri bin yuz di nem fɔ sɛl. I nɔto sɔntin we di Lab go gri pan wit dis pruf.
Prɔbabiliti, insay in wɔd dɛn ɛn wi yon
Di lɛta dɛn frɔm 1654 nɔ tɔk bɔt rulɛt, bikɔs rulɛt nɔ bin de yet. Dɛn de aks: tu pleya nid tri pɔynt fɔ win di mɔni; dɛn stɔp na 2–1; aw dɛn fɔ sheb di mɔni? Pascal in ansa yuz wetin wi go kɔl tide kɔndishɔnal ɛkspɛkteshɔn ɛn wan agyumɛnt we de go dɔŋ ɛni rod we di gem bin fɔ kɔntinyu. Huygens rid di lɛta dɛn ɛn na 1657 i pablish di fɔs tɛks buk bɔt wetin fɔ ɛkspɛkt. Di wɔd “expectation” na in yon.
Pascal ɛn Fermat sɔlv di prɔblɛm fɔ pɔynt dɛn: valyu we fɔ ɛkspɛkt as di fɛr prays fɔ wan pozishɔn.
Huygens, De Ratiociniis in Ludo Aleae: di fɔs buk we dɛn print bɔt wetin fɔ ɛkspɛkt.
Jakob Bernoulli, Ars Conjectandi: di lɔ fɔ big nɔmba.
Pipul rayt bɔt rulɛt na Paris. Ɛni pe na 36/n − 1: EV = −1/37 (ɔ −2/38).
Pearson in chi-skwɛ tɛst, we i sho wit rulɛt spin dɛn.
Ɔl wetin de ɔp, na dis sayt, insay brawza.
Di bɛt
Pascal in agyumɛnt bɔt bɛt we pipul sabi pas ɔl nɔto bɔt rulɛt, na bɔt Gɔd: di “wager” insay di Pensées we se fɔ biliv na lɛk bɛt we in pe nɔ gɛt ɛnd. Na agyumɛnt bɔt valyu we fɔ ɛkspɛkt, ɛn na di fɔs tɛm we ɛnibɔdi yuz disizhɔn tiori fɔ agyu fɔ ɛni tin. Rulɛt pleya dɛn we de kɔl Pascal nem fɔ di wil de kɔl di rɔng Pascal; di wan we impɔtant na di wan we sho aw fɔ prays gambul.
Di tin we fɔni
Ilɛk Pascal bil di fɔs rulɛt wil ɔ i nɔ bil am, di gem na fayn ɛgzampul fɔ in rial wok: mashin frɔm man we pruv se yu nɔ kin gɛt sɔntin fɔ natin (mashin fɔ muv sote go nɔ de wok; wetin fɔ ɛkspɛkt nɔ de chenj), we dɛn de yuz fɔ sho di sem tin to sɔm milyɔn pleya ɛvri ia.
Kwɛstyɔn dɛn
I bin de waka wit gambul pipul na Paris na di fɔs ia dɛn fɔ di 1650 dɛn, ɛn na so di prɔblɛm fɔ pɔynt dɛn rich am tru di Chevalier de Méré. Nɔ rɛkɔd nɔ de se i bin ple fɔ mɔni siriɔs wan.
Bikɔs na fayn stori ɛn bikɔs di wan dɛn we bin de advataiz kasino na di 19 sɛnchri bin lɛk am. Tɛl am bak, bɔt put nɔt ɔnda am.
Smɔl jok fɔ ɛz di maynd
I pruv se yu nɔ kin gɛt sɔntin fɔ natin. Dɔn sɔmbɔdi bil kasino pan am.
Usay wi gɛt am frɔm
- Pascal, B. & Fermat, P. Lɛta dɛn bɔt di prɔblɛm fɔ pɔynt dɛn.
- Huygens, C. De Ratiociniis in Ludo Aleae.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.