Enjawulo y'ebivaamu
Lwaki straight up ne zzaala ku mmyufu ezirina okufiirwa okusuubirwaokubalaOkufiirwa okusuubirwaOmuwendo ogusuubirwa nga gukubisiddwamu ssente zonna ezisibiddwa; ssente ez'okufiirwa ku kigero mu kiseera ky'okuzannya oba mu kiseera ekimu.Soma byonna → kwe kumu ziwulikika ng'emizannyo egy'enjawulo.
Enjawulo y'ebivaamu epima ebivaamu bwe bisaasaana okwetooloola omuwendo ogusuubirwa. Ku buli yuniti esibiddwa eri nga 34 ku straight up ne nga 1 ku mmyufu.
Ensengekera ya zzaala emu
Ku zzaala esasula W ku 1 n'obusobokaokubalaObusobokaObusoboka bw'ekivaamu, okuva ku 0 okutuuka ku 1 oba 0% okutuuka ku 100%. Ennamba emu: 1/37 = 2.70%.Soma byonna → p, ekivaamu ku buli yunitissenteYunitiSsente za zzaala ez'entandikwa enkola oba omuzannyi z'akozesa. Okulinnyisa zzaala kunnyonnyolwa mu yuniti kusobole okukola ku mmeeza yonna.Soma byonna → kiba +W n'obusoboka p ne −1 n'obusoboka 1 − p. 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 → guba pW − (1 − p) = −1/37. Enjawulo y'ebivaamuokubalaEnjawulo y'ebivaamuEkipimo ky'engeri ebivaamu gye bisaasaanamu okwetooloola omuwendo ogusuubirwa. Kinene ku straight up, kitono ku zzaala za emu ku emu.Soma byonna → eba E[X²] − EV² = pW² + (1 − p) − (1/37)². Ku straight upzzaalaStraight upEnnamba emu yokka, esasula 35:1.Soma byonna →: (1/37)(1225) + 36/37 − 0.0007 ≈ 34.08. Ku mmyufuzzaalaEmmyufuZzaala ya emu ku emu ku nnamba 18 emmyufu. Mu Lufalansa: rouge.Soma byonna →: 18/37 + 19/37 − 0.0007 ≈ 0.999.
Kye kitegeeza eri ekiseera ky'okuzannya
Enjawulo y'ebivaamu egattibwa ku kwetooloola okwetongoddeokubalaOkwetooloola okwetongoddeBuli kwetooloola kulina obusoboka bwe bumu k'abe ebyayita bwe biri. Gwe musingi gwa buli kubala ku mukutu guno.Soma byonna →, kale mu kwetooloola N ku ssente za zzaala ezitakyuka, enjawulo y'ebivaamu ey'omugatte eba N × ssente za zzaala² × σ², ate ekipimo ky'enjawukanaokubalaEkipimo ky'enjawukanaEkikolo kya kkubo bbiri eky'enjawulo y'ebivaamu; ebbanga ery'abulijjo ekivuddemu we kiba okuva ku muwendo ogusuubirwa.Soma byonna → kiba σ × ssente za zzaala × √N. Okwetooloola 100 ku $10: ekipimo ky'enjawukana kiba nga $584 ku straight up ne $100 ku mmyufu, okwetooloola −$27 ze zimu ezisuubirwa. Omuzannyi omu alaba ebivaamu nga bikyukakyuka mu bikumi; omulala alaba okuseeyeeya okugonvu. Bombi basasula omuwendo gwe gumu.
Enjawulo y'ebivaamu n'enkola za zzaala
Okulinnyisa zzaalaenteekateekaOkulinnyisa zzaalaEtteeka lyonna erikyusa ssente za zzaala okusinziira ku bivuddemu emabega. Okulinnyisa oluvannyuma lw'okufiirwa kuzirinnyisa ng'ofiiriddwa, okulinnyisa oluvannyuma lw'okuwangula kuzirinnyisa ng'owangudde.Soma byonna → tekukyusa EV ku buli yuniti esibiddwa naye kukyusa byombi, ssente ezisibiddwa n'engeri ebivaamu gye bigabanyizibwamu. MartingaleenteekateekaMartingaleOkulinnyisa zzaala okukubisaamu zzaala bbiri oluvannyuma lwa buli kufiirwa. Laba ekitundu ky'Enteekateeka za Zzaala okumanya ky'ekola ne ky'etakola.Soma byonna → ekendeeza enjawulo y'ebivaamu ey'ebiseera by'okuzannya ebisinga (okuwangula okutono kungi) n'eyongerako omukira omunene (okufiirwa okunene okutatera kubaawo); enjawulo y'ebivaamu ey'omugatte mu biseera by'okuzannya byonna esinga eya zzaala ey'omuwendo gumuenteekateekaZzaala ey'omuwendo gumuOkusiba ssente ze zimu buli kwetooloola. Kye kipimo buli kulinnyisa zzaala kwe kugeraageranyizibwako.Soma byonna → olw'omukira ogwo. ParolienteekateekaParoliOkulinnyisa oluvannyuma lw'okuwangula: kubisaamu emirundi ebiri ng'owangudde, ddayo ku ntandikwa ng'ofiiriddwa oba ng'owangudde emirundi esatu egiddiriŋŋana. Era eyitibwa: Martingale ey'ekifuulannenge.Soma byonna → ekola ekikontana. Okulonda enkola ya zzaala kwe kulonda engeri y'enjawulo y'ebivaamu; ekigero tekiri ku lukalala lw'oyinza okulonda.
- p10 −$500
- p25 −$500
- wakati −$500
- p75 +$40
- p90 +$1,120
Enteekateeka ya Zzaala ey'Omuwendo Gumu mu RouletteEnteekateeka ya Paroli mu Roulette (Martingale ey'Okukyusa)
Lwaki kikulu eri omuzannyi
Enjawulo y'ebivaamu y'efuula ebiseera by'okuzannya ebimpi obutategeerekeka n'ebiwanvu okutegeerekeka. Nga σ = $100 ne EV = −$27 mu kwetooloola 100, enkizo ya kaasino kye kimu kya kuna eky'okutabukatabuka, era ekiseera ky'okuzannya eky'amagoba kya bulijjo. Mu kwetooloola 10,000, EV eba −$2,700 ne σ eba $1,000; kati enkizo ya kaasino kumpi esinga okutabukatabuka emirundi esatu, era okuwangula okuddiŋŋana kintu kya sigma ssatu. Enjawulo y'ebivaamu mukwano gw'omuzannyi mu kiseera ekimpi era gwa kaasino mu kiseera ekiwanvu.
Enjawulo y'ebivaamu ey'okugatta zzaala
Ku zzaala eziwera ku kwetooloola kumu, ebivaamu bikwatagana (okujja ku 17 era kwe kujja ku nzirugavuzzaalaEnzirugavuZzaala ya emu ku emu ku nnamba 18 enzirugavu. Mu Lufalansa: noir.Soma byonna → ne ku dazenizzaalaDazeni1–12, 13–24 oba 25–36, esasula 2:1.Soma byonna → ey'okubiri), kale enjawulo z'ebivaamu tezigattibwa bugattibwa. Ekikozesebwa Ekizimba Zzaala kibala engabanya entuufu ku cipussenteCipuAkabonero akakiikirira omuwendo ogutakyuka, akateekebwa ku mmeeza ya zzaala okusiba zzaala. Era kayitibwa: check.Soma byonna → zonna ng'kibala ebivaamu byonna 37, eyo y'engeri yokka entuufu ey'okukikola.
Ensengekera
Ebibuuzo
Nedda. Buli zzaala erina omuwendo ogusuubirwa gwe gumu. Enjawulo y'ebivaamu ennene kitegeeza okukyukakyuka okugazi okwetooloola omuwendo ogwo.
Zzaala ya emu ku emuzzaalaZzaala ya emu ku emuEmmyufu/enzirugavu, ezitagabanyizika/ezigabanyizika, ennene/entono. Ennamba 18, esasula 1:1.Soma byonna →, ku σ ≈ 1 ku buli yuniti. Ekka n'okusingawo ne la partageetteekaLa partageEtteeka ery'e Bufalansa: zeero bw'ejja, ekitundu kya ssente za zzaala ya emu ku emu kizzibwayo. Likendeeza enkizo ya kaasino ku zzaala ezo ku kitundu, okutuuka ku 1.35%.Soma byonna →, era nayo erongoosa ekigero.
Amagoba agasuubirwa ge gamu ku buli ddoola; enjawulo y'ebivaamu ekwata ku ngeri ennyingiza ya kaasino gy'ejja mu bitole, era kaasino erina abazannyi nkumi na nkumi abagigonza.
Okwesanyusa n'Okubala
Gezaako bino ggwe kennyini okusooka. Buli kugonjoola kuzingiddwa; kuggulewo ng'oli mwetegefu.
Abazannyi babiri buli omu asiba $1 buli kwetooloola okumala okwetooloola 100 ku nnamuziga wa Bulaaya, omu bulijjo ku mmyufuzzaalaEmmyufuZzaala ya emu ku emu ku nnamba 18 emmyufu. Mu Lufalansa: rouge.Soma byonna →, omulala bulijjo ku 17. Ani asinga obusoboka okuba mu magoba ku nkomerero?
Laga okugonjoola
Eky'okuddamu Omuzannyi ku 17: 50.9%, so nga 35.5% ku mmyufu. Bombi bafiirwa $2.70 ku kigero.
Emmyufu: omuzannyi aba mu magoba n'okuwangula 51 oba okusingawo ku 100, buli kumu n'obusobokaokubalaObusobokaObusoboka bw'ekivaamu, okuva ku 0 okutuuka ku 1 oba 0% okutuuka ku 100%. Ennamba emu: 1/37 = 2.70%.Soma byonna → bwa 18/37. Binomial distribution ewa 35.5%, era okuwangula 50 kwokka, okwenkanankana, 7.7% endala.
Ennamba 17: buli kuwangula kukomyawo $36, kale okuwangula kubiri (−$28) tekumala ate okusatu (+$8) kumala. Obusoboka bw'okujja kusatu oba okusingawo mu kwetooloola 100 ku 1/37 buli 50.9%.
Omuzannyi wa straight up aba mu magoba emirundi mingi, naye ebivaamu bikyukakyuka nnyo: okujja kumu okwongerako oba okukendeezaako kukyusa ekivuddemu ku $36, era abazannyi abali mu kufiirwa batera okuba emabega ennyo. Bollman (2024) awa emiwendo gya Amerika, 26.5% ne 49.2%.
Eky'okusesa
Okufiirwa okusuubirwa kwe kumu. Emu ku zo ekikubuulira mu ddoboozi ery'omwanguka.
Ensibuko
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.