Blaise Pascal: Umugani w'Uruziga rwa Roulette
Umuhanga mu mibare ukunze kwitirirwa uruziga, wageragezaga gukora ikindi kintu.
Pascal (1623–1662) yakoze amagerageza ku bikoresho bigenda iteka (perpetual motion) mu myaka ya 1650. Uruziga ruzenguruka nta guterana kunini rumwitirirwa rushobora kuba sekuruza wa rotor ya roulette; ariko uko kwitirirwa ni umugani wa rubanda, ntikugaragazwa n'inyandiko.
Umuhanga mu mibare
Blaise Pascal yakoze mubazi ikoreshwa n'imashini afite imyaka cumi n'icyenda, agaragaza ibisubizo muri jewometiri ya projective akiri ingimbi, akora ubushakashatsi bw'ibanze ku muvuduko w'umwuka (pressure) n'ubusa (vacuum), maze mu 1654, mu mabaruwa yandikiranye na Pierre de Fermat, akemura “ikibazo cy'amanota”: uko amafaranga yategewe mu mukino w'amahirwe wahagaritswe yagabanywa mu buryo buboneye. Igisubizo cyabo, kugabana hakurikijwe amahirweimibareAmahirweAmahirwe y'igisubizo, kuva kuri 0 kugeza kuri 1 cyangwa kuva kuri 0% kugeza kuri 100%. Umubare umwe: 1/37 = 2,70%.Soma byose → buri mukinnyi yari afite yo gutsinda iyo umukino ukomeza, ni yo nkomoko y'agaciro gateganyijweimibareAgaciro gateganyijweIgisubizo mpuzandengo kuri buri tega mu gihe kirekire. −1/37 y'itega kuri buri tega risanzwe ry'i Burayi.Soma byose →. Buri bara rya EV kuri uru rubuga rikomoka kuri ayo mabaruwa.
Ese Blaise Pascal yaba yarakoze imashini ya roulette?
Hagati mu myaka ya 1650 Pascal yakoze ku mashini igenda iteka, kandi bivugwa ko yakoze uruziga ruringaniye neza rwazengurukaga igihe kirekire nta guterana kunini. Inkuru y'uko urwo ruziga rwabaye rotoribikoreshoRotorIgice cy'uruziga kizenguruka gitwaye utuzu.Soma byose → ya roulette isubirwamo mu bitabo byinshi by'amateka ariko ntiboneka mu nyandiko n'imwe y'ibanze. Birashoboka ko abacungaga kazino zo mu mijyi y'amazi ashyushye mu kinyejana cya 18 bakoreshaga iryo zina mu kwamamaza. Ntabwo ari ikintu Laboratwari yakwemera hashingiwe ku bimenyetso.
Amahirwe, mu magambo ye no mu yacu
Amabaruwa yo mu 1654 ntavuga roulette, kuko yari itarabaho. Abaza ikibazo iki: abakinnyi babiri bakeneye amanota atatu ngo batsindire amafaranga yose; bahagarara ari 2–1; ayo mafaranga yagabanywa ate? Igisubizo cya Pascal gikoresha icyo ubu twakwita agaciro gateganyijwe gashingiye ku kindi (conditional expectation) n'impamvu isubiramo imanuka ku giti cy'uburyo bwose umukino wari gukomeza. Huygens yasomye ayo mabaruwa maze mu 1657 asohora igitabo cya mbere cyigisha agaciro gateganyijwe. Ijambo “expectation” ni irye.
Pascal na Fermat bakemura ikibazo cy'amanota: agaciro gateganyijwe nk'igiciro kiboneye cy'aho umukinnyi ageze.
Huygens, De Ratiociniis in Ludo Aleae: inyandiko ya mbere icapwe ku gaciro gateganyijwe.
Jakob Bernoulli, Ars Conjectandi: itegeko ry'imibare minini.
Roulette isobanurwa i Paris. Buri bwishyu ni 36/n − 1: EV = −1/37 (cyangwa −2/38).
Ikizamini cya chi-square cya Pearson, kigaragazwa ku mazunguruka ya roulette.
Ibyo byose biri hejuru, kuri uru rubuga, muri mushakisha.
Itega rya Pascal
Igitekerezo cya Pascal kizwi cyane ku gutega ntikivuga roulette ahubwo kivuga Imana: “itega” riri muri Pensées rifata kwemera nk'itega rifite ubwishyu butagira iherezo. Ni igitekerezo gishingiye ku gaciro gateganyijwe, kandi ni ubwa mbere umuntu yakoresheje theory y'ifatwa ry'ibyemezo (decision theory) ngo agaragaze ikintu icyo ari cyo cyose. Abakinnyi ba roulette bitabaza Pascal ku bijyanye n'uruziga bitabaza Pascal utari we; ufite agaciro ni uwagaragaje uko urusimbi rugenerwa igiciro.
Igitangaje
Yaba Pascal yarakoze uruziga rwa mbere rwa roulette cyangwa atarakoze, umukino ni urugero rwiza rw'ubushakashatsi bwe nyabwo: igikoresho cyaturutse ku muntu wagaragaje ko udashobora kubona ikintu utatanze ikindi (imashini igenda iteka ntishoboka; agaciro gateganyijwe ntikiyongera), gikoreshwa kwereka ikintu kimwe abakinnyi miliyoni nkeya buri mwaka.
Ibibazo
Mu ntangiriro z'imyaka ya 1650 yagendanaga n'abakina urusimbi i Paris, ari na ko ikibazo cy'amanota cyamugezeho binyuze kuri Chevalier de Méré. Nta nyandiko ivuga ko yakinaga ku mafaranga by'ukuri.
Kuko ari inkuru nziza kandi abamamazaga kazino mu kinyejana cya 19 barayikundaga. Yisubiremo, ariko uyiherekeze n'icyitonderwa cy'inkomoko.
Akanya k'urwenya
Yagaragaje ko nta kintu ubona ku busa. Hanyuma umuntu ayubakiraho kazino.
Inkomoko
- 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.