Blaise Pascal: Olugero lwa Nnamuziga wa Roulette
Omukugu mu kubala atera okuweebwa ekitiibwa kya nnamuziga, eyali agezaako okuzimba ekintu ekirala.
Pascal (1623–1662) yagezesa ebyuma ebyetooloola awatali kukoma mu myaka gya 1650. Nnamuziga eyetooloola kumpi awatali kukwatagana gw'agambibwa okukola ayinza okuba jjajja wa rotor ya roulette; naye ekyo kya nnono, so si kiwandiikiddwa mu bujulizi.
Omukugu mu kubala
Blaise Pascal yazimba ekyuma ekibala ng'alina emyaka kkumi n'omwenda, n'alaga ebyava mu geometry ya projective ng'akyali muvubuka, n'akola omulimu ogw'omusingi ku puleesa n'ekifo ekitaliimu mpewo, era mu 1654, mu bbaluwa ne Pierre de Fermat, n'agonjoola “ekizibu ky'obubonero”: engeri y'okugabanya mu bwenkanya ssente za zzaala ez'omuzannyo gw'omukisa ogusalibwako. Eky'okuddamu kyabwe, okugabanya okusinziira ku busobokaokubalaObusobokaObusoboka bw'ekivaamu, okuva ku 0 okutuuka ku 1 oba 0% okutuuka ku 100%. Ennamba emu: 1/37 = 2.70%.Soma byonna → bwa buli muzannyi okuwangula singa omuzannyo gwali gugenda mu maaso, ye ntandikwa y'omuwendo ogusuubirwaokubalaOmuwendo ogusuubirwaEkivaamu eky'omu makkati ku buli zzaala mu bbanga eddene. −1/37 ya ssente za zzaala ku buli zzaala eya bulijjo eya Bulaaya.Soma byonna →. Buli kubala kwa EV ku mukutu guno kuva mu bbaluwa ezo.
Waaliwo ekyuma kya roulette ekya Blaise Pascal?
Wakati mu myaka gya 1650 Pascal yakola ku kyuma ekyetooloola awatali kukoma, era kigambibwa nti yazimba nnamuziga eyenkanankana obulungi eyetooloolanga okumala ebbanga ddene nga tekwatagana nnyo. Olugero nti nnamuziga oyo yafuuka rotorebikozesebwaRotorEkitundu kya nnamuziga ekyetooloola ekirimu ebinnya.Soma byonna → ya roulette luddibwamu mu byafaayo bingi naye teruwandiikiddwa mu nsibuko yonna ey'olubereberye. Kisoboka nti abaddukanya kaasino mu bibuga by'amazzi ag'ebbugumu mu kyasa 18 baakozesa erinnya eryo okusikiriza abantu. Si kintu Laabu kye yandikkirizza ku bujulizi obwo.
Obusoboka, mu bigambo bye ne mu byaffe
Bbaluwa za 1654 teziyogera ku roulette, eyali tennabaawo. Zibuuza: abazannyi babiri beetaaga obubonero busatu okuwangula ssente; bayimirira ku 2–1; ssente zigabanyizibwa zitya? Eky'okuddamu kya Pascal kikozesa kye twandiyise leero okusuubira okw'obukwakkulizo n'okulowooza okuddiŋŋana ku muti gw'engeri omuzannyo gye gwandigenzemu. Huygens yasoma bbaluwa ezo era mu 1657 n'afulumya ekitabo ekisooka eky'okusomesa ku kusuubira. Ekigambo “expectation” kikye.
Pascal ne Fermat bagonjoola ekizibu ky'obubonero: omuwendo ogusuubirwa ng'omuwendo ogw'obwenkanya ogw'embeera.
Huygens, De Ratiociniis in Ludo Aleae: ekiwandiiko ekisooka ekyakubibwa ku kusuubira.
Jakob Bernoulli, Ars Conjectandi: etteeka ly'emiwendo eminene.
Roulette ennyonnyolwa e Paris. Buli nsasula eri 36/n − 1: EV = −1/37 (oba −2/38).
Okugezesa kwa chi-square okwa Pearson, okulagibwa ku kwetooloola kwa roulette.
Byonna waggulu, ku mukutu guno, mu browser.
Zzaala ye
Endowooza ya Pascal esinga okumanyika ku kusiba zzaala si ku roulette wabula ku Katonda: “zzaala” mu Pensées etwala okukkiriza nga zzaala erina empeera etaliiko kkomo. Ndowooza ya muwendo ogusuubirwa, era gwe mulundi ogusooka omuntu yenna okukozesa endowooza y'okusalawo okuwagira ekintu kyonna. Abazannyi ba roulette abayita Pascal ku lwa nnamuziga bayita Pascal omukyamu; omukulu ye oyo eyalaga engeri y'okuteeka omuwendo ku zzaala.
Ekyewuunyisa
Ka Pascal abe nga ye yazimba nnamuziga wa roulette eyasooka oba nedda, omuzannyo gwe kyokulabirako ekirungi eky'omulimu gwe ogwa nnamaddala: ekyuma okuva ku musajja eyalaga nti tosobola kufuna kintu nga tobaddeko ky'owaayo (ekyuma ekyetooloola awatali kukoma kirema; okusuubira tekukyuka), ekikozesebwa okulaga ekintu kye kimu eri abazannyi obukadde obutonotono buli mwaka.
Ebibuuzo
Yatambulanga mu bibiina by'abasiba zzaala e Paris ku ntandikwa y'emyaka gya 1650, era bwe kityo ekizibu ky'obubonero bwe kyamutuukako okuyita mu Chevalier de Méré. Tewali kiwandiiko kiraga nti yazannyanga ssente mu bunene.
Kubanga lugero lulungi era kubanga abatumbula kaasino mu kyasa 19 baalwagala. Luddemu ng'oteekako ekijuliziddwamu.
Eky'okusesa
Yalaga nti tosobola kufuna kintu nga tewali ky'owaddeyo. Awo omuntu n'azimba kaasino ku kyo.
Ensibuko
- 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.