Blaise Pascal: di story bout di roulette wheel
Di mathematician weh people mostly gi di credit fi di wheel, an im did a try build sumting else.
Pascal (1623–1662) did a experiment wid perpetual-motion machine inna di 1650s. Di wheel weh spin wid almost nuh friction, weh people seh a fi im, coulda be a ancestor a di roulette rotor; but dat a tradition, nuh paper nuh prove it.
Di mathematician
Blaise Pascal build a mechanical calculator wen im did nineteen, prove result inna projective geometry wen im did a teenager, do foundation work pon pressure an vacuum, an inna 1654, inna letter wid Pierre de Fermat, im solve di “problem a points”: ow fi share di stake dem fair wen a game a chance stop haffway. Dem ansa, fi share it by how much probabilitymathsProbabilityDi chance fi a result, fram 0 to 1 or 0% to 100%. One numba: 1/37 = 2.70%.Read di whole ting → evry playa did have fi win if di game did keep gwaan, a weh expected valuemathsExpected valueDi average result pon evry bet inna di long run. −1/37 a di stake fi evry standard European bet.Read di whole ting → come fram. Evry EV calculation pon dis site come dung fram dem letter deh.
Blaise Pascal did have a roulette machine fi true?
Inna di middle a di 1650s, Pascal did a work pon a perpetual-motion machine, an people seh im build a wheel weh balance nice an spin long time wid likkle friction. Di story seh dat wheel tun di roulette rotorgearRotorDi part a di wheel weh spin an carry di pocket dem.Read di whole ting →; nuff history book repeat it, but nuh primary source nuh show it. It coulda be seh di people weh run game inna di spa town dem inna di 18th century use di name fi sell di game. Di Lab woulda neva accept it pon dat evidence.
Probability, inna im word dem an fi wi
Di 1654 letter dem nuh talk bout roulette, cause roulette neva exist yet. Dem ask: two playa need tree point fi win a pot; dem stop at 2–1; ow dem fi share di pot? Pascal ansa use wah wi woulda call conditional expectation today, an a argument weh go dung di tree a evry way di game coulda continue. Huygens read di letter dem an inna 1657 im put out di fus textbook pon expectation. Di word “expectation” a fi im.
Pascal an Fermat solve di problem a points: expected value as di fair price a a position.
Huygens, De Ratiociniis in Ludo Aleae: di fus print work pon expectation.
Jakob Bernoulli, Ars Conjectandi: di law a big numba.
Smaddy describe roulette inna Paris. Evry payout a 36/n − 1: EV = −1/37 (or −2/38).
Pearson chi-square test, show pon roulette spin dem.
All a dem ting up deh, pon dis site, inna a browser.
Di wager
Pascal mos famous argument bout bettin nuh bout roulette, but bout God: di “wager” inna di Pensées weh show belief like a bet wid a payoff weh nuh have nuh end. A expected-value argument dat, an a di fus time smaddy use decision theory fi argue fi anyting. Roulette playa weh call pon Pascal fi di wheel a call di wrong Pascal; di one weh matter a di one weh show ow fi put a price pon a gamble.
Di irony
Wedda Pascal build di fus roulette wheel or no, di game show im real work nice: a machine fram a man weh prove seh yuh cyaan get sumting fi nutten (perpetual motion fail; expectation stay di same), an now dem use it fi show di same ting to a few million playa evry year.
Question dem
Im did move wid gamblin people inna Paris inna di early 1650s, an a suh di problem a points reach im, tru di Chevalier de Méré. Nuh record nuh show seh im play fi money serious.
Cause a good story, an cause casino promoter dem inna di 19th century did like it. Tell it, but put a footnote.
Sumting fi laugh
Im prove seh yuh cyaan get sumting fi nutten. Den smaddy build a casino pon it.
Source dem
- Pascal, B. & Fermat, P. Letter dem pon di problem a points.
- Huygens, C. De Ratiociniis in Ludo Aleae.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.