Ekipimo ky'Enjawukana mu Roulette
Ekipimo ky'enjawukana mu roulette, ekikolo kya kubiri eky'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 →, bwe bbanga erya bulijjo wakati w'ekivuddemu n'ekyo ekisuubirwa.
Ku buli $1 esibiddwa, σ eri 5.84 ku straight up ne 1.00 ku mmyufu. Kubisaamu ssente za zzaala n'ekikolo kya kubiri eky'omuwendo gw'okwetooloola okufuna ogw'ekiseera ky'okuzannya.
Etteeka ery'okwanguyirwa
Ebitundu nga bibiri ku bisatu eby'ebiseera by'okuzannya bigwa munda wa σ emu okuva ku kisuubirwa ate 95% munda wa bbiri. Ku kwetooloola 100 okw'emmyufuzzaalaEmmyufuZzaala ya emu ku emu ku nnamba 18 emmyufu. Mu Lufalansa: rouge.Soma byonna → ku $10 (ekisuubirwa −$27, σ = $100), ebiseera by'okuzannya ebisinga bigwa wakati wa −$127 ne +$73, era kumpi byonna wakati wa −$227 ne +$173. Ekivuddemu ebweru w'ekkomo eryo tekiba bujulizi bwa kintu kyonna, okuggyako nti ekiseera ky'okuzannya kimu ku abiri kikikola.
Lwaki √N
Okufiirwa okusuubirwaokubalaOkufiirwa okusuubirwaOmuwendo ogusuubirwa nga gukubisiddwamu ssente zonna ezisibiddwa; ssente ez'okufiirwa ku kigero mu kiseera ky'okuzannya oba mu kiseera ekimu.Soma byonna → kukula mu kigero kya N; okusaasaana kukula mu kigero kya √N. Ku N entono okusaasaana kwe kusinga, era ebiseera by'okuzannya biba ng'okukasuka ssente ng'okwekubiira katono. Ku N ennene okufiirwa kusinga okusaasaana. Ekifo we bisisinkana, okufiirwa okusuubirwa we kwenkana ekipimo ky'enjawukanaokubalaEkipimo ky'enjawukanaEkikolo kya kkubo bbiri eky'enjawulo y'ebivaamu; ebbanga ery'abulijjo ekivuddemu we kiba okuva ku muwendo ogusuubirwa.Soma byonna → kimu, kiri ku N = (σ/enkizo)² = (1/0.027)² ≈ okwetooloola 1,370 ku zzaala ya emu ku emu ne (5.84/0.027)² ≈ 46,800 ku straight upzzaalaStraight upEnnamba emu yokka, esasula 35:1.Soma byonna →. Wansi w'emiwendo egyo, omukisa gwe gusalawo; waggulu waagyo, enkizo ya kaasino y'esalawo.
Engeri y'okukikozesa
Okumanya oba ekiseera ky'okuzannya kyali kya njawulo, bala (ekivuddemu − EV)/σ. Omuzannyi asiba $10 ku mmyufu amaliriza okwetooloola 100 ku +$150 aba ku (150 + 27)/100 = 1.77σ, ekivaamu ekibaawo omulundi gumu ku 25: omukisa, so si kyewuunyo. Omuzannyi wa straight up ku +$150 ze zimu aba ku 0.3σ: ekiro kya bulijjo. Ekivuddemu kye kimu mu ddoola kitegeeza ebintu eby'enjawulo ku zzaala ez'enjawulo.
Ensobi y'ekipimo ey'ekitundu
Okubala kwe kumu kukubuulira okwetooloola kumeka okwetaagisa okulaba enkizo ya kaasino mu bibalo. Ensobi y'ekipimo ey'ekitundu ky'okuwangula ekirabiddwa eri √(p(1 − p)/N). Ku mmyufu nga N = 1,000: √(0.4865 × 0.5135 / 1000) ≈ 1.6%. Enjawulo wakati w'okukasuka ssente okw'obwenkanya n'emmyufu eri 1.35%, kale oluvannyuma lw'okwetooloola 1,000 okyali tosobola kubyawula na bukakafu. Oluvannyuma lwa 10,000, ensobi y'ekipimo eba 0.5% era osobola. Eno y'ensonga era lwaki okuzuula okusosola kwa nnamuziga kwetaaga okwetooloola kungi bwe kutyo.
Okulabula ku kukyama
Ebivaamu bya straight up tebigabanyizibwa nga normal mu kiseera ky'okuzannya ekimpi: ebiseera by'okuzannya ebisinga biba −$10 buli kwetooloola obutakyuka nga oluusi wabaawo okubuuka kwa +$350. Etteeka lya ±1σ linnyonnyola bulungi okusaasaana naye bubi engeri, okutuusa N lw'eba mu bikumi. Ku zzaala ya emu ku emuzzaalaZzaala ya emu ku emuEmmyufu/enzirugavu, ezitagabanyizika/ezigabanyizika, ennene/entono. Ennamba 18, esasula 1:1.Soma byonna →, okusemberera kwa normal kulungi okuva ku kwetooloola nga 30.
Ensengekera
Ebibuuzo
Bwe bujulizi nti wazannya ebiseera by'okuzannya nga 40, oba nti wali mu kimu ku amakumi ana eky'omukisa. Kiddemu.
Kikyukakyuka kitono nnyo buli lukya: ensobi y'ekipimo ey'ekigero eri σ/√N. Ku N = 10,000 eba 1% ya ssente za zzaala.
Okwesanyusa n'Okubala
Gezaako bino ggwe kennyini okusooka. Buli kugonjoola kuzingiddwa; kuggulewo ng'oli mwetegefu.
Mu kwetooloola 100 okwa nnamuziga wa Bulaaya, yunitissenteYunitiSsente za zzaala ez'entandikwa enkola oba omuzannyi z'akozesa. Okulinnyisa zzaala kunnyonnyolwa mu yuniti kusobole okukola ku mmeeza yonna.Soma byonna → emu ku mmyufuzzaalaEmmyufuZzaala ya emu ku emu ku nnamba 18 emmyufu. Mu Lufalansa: rouge.Soma byonna → eba mu magoba n'okuwangula waakiri 51, ate yuniti emu ku straight upzzaalaStraight upEnnamba emu yokka, esasula 35:1.Soma byonna → eba mu magoba singa ennamba yaayo ejja waakiri emirundi 3. Kozesa bell curve okuteebereza obusoboka bwombi, oluvannyuma obugerageranye n'eby'okuddamu ebituufu.
Laga okugonjoola
Eky'okuddamu Emmyufu: bell curve ewa 35.6% ate eky'okuddamu ekituufu kiri 35.5%. Straight up: bell curve ewa 55.0% ate eky'okuddamu ekituufu kiri 50.9%. Ekkubo eddala likola ku mmyufu naye lisubwa ku nnamba emu.
Emmyufu: okuwangula kuba 100 × 18/37 = 48.6 ku kigero, n'okusaasaana kwa √(100 × 18/37 × 19/37) = 5.0. Okuba mu magoba kitegeeza 51 oba okusingawo; akabonero ak'ekitundu, 50.5, kali okusaasaana 0.37 waggulu w'ekigero, era bell curve eteeka 35.6% waggulu waako. Okugatta obusoboka obutuufu obw'okuwangula 51, 52 … 100 kuwa 35.5%.
Straight up: okujja kuba 100/37 = 2.70 ku kigero, n'okusaasaana kwa √(100 × 1/37 × 36/37) = 1.62. Okujja kusatu oba okusingawo kitegeeza waggulu wa 2.5, okusaasaana 0.12 wansi w'ekigero: 55.0% okusinziira ku bell curve. Mu butuufu, buli 1 ng'oggyeko obusoboka bw'okujja 0, 1 ne 2, 6.5% + 17.9% + 24.7%, ekisigaza 50.9%.
Bell curve yeetaaga ebivaamu bingi ku njuyi zombi ez'ekigero. Emmyufu ebirina oluvannyuma lw'okwetooloola 100; ennamba ejja emirundi egitasukka esatu ku kigero tebirina. Curve ewa ne 8.7% ku “tewali kujja”, so ng'obusoboka obutuufu buli 6.5%. Taylor (2021) ateeka binomial ne bell curve okumpi n'okumpi mu ngeri y'emu.
Eky'okusesa
Ekiseera ky'okuzannya kimu ku abiri kiri ebweru wa sigma bbiri. Bulijjo waliwo omuntu ku mukira.
Ensibuko
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.