Izibalo ze-roulette · Ukusetshenziswa · imizuzu 13

Ingozi yokuphelelwa yimali

Q: Ingabe ukwenyuswa kwenani kwehlisa ingozi yokuphelelwa yimali?

I-Martingale iyayehlisa emaseshinini amafushane futhi iyikhuphula kakhulu emaseshinini amade. Ukubheja ngenani elingaguquki ngeyunithi elikhulu yindlela eqotho yokuyehlisa.

Amathuba okulahlekelwa yiyo yonke imali yakho yokubheja ngaphambi kokufinyelela umgomo.

Impendulo emfushane

Ekubhejeni okulingana nemali, ingozi yokuphelelwa yimali ilandela ifomula yokuphelelwa yimali komgembuli (gambler’s ruin). Uma unemali yokubheja engu-$500, ubheja u-$10 futhi umgomo ungu-$600, ufinyelela umgomo cishe ku-57% wezikhathi futhi uphelelwa yimali kwezinye.

ifomula

ukuphelelwa yimali komgembuli

p (okulingana nemali)

18/37

q/p

1.0556

umphumela omdala kunayo yonke

Pascal–Fermat, 1656

Umbuzo

Unamayunithi angu-aimaliIyunithiInani elibhejwayo eliyisisekelo uhlelo noma umdlali asebenza ngalo. Ukwenyuswa kwenani kuchazwa ngamayunithi ukuze kusebenze kunoma yiliphi itafula.Funda konke → emali yokubhejaimaliImali yokubhejaInani lonke lemali ebekelwe ukudlala. Ukuphatha imali yokubheja kusho ukunquma ukuthi ingakanani yayo ozoyibeka engcupheni ekubhejeni ngakunye nasesheshini ngayinye.Funda konke → futhi ufuna ukufinyelela amayunithi angu-a + b, ubheja iyunithi elilodwa ngesikhathi ekubhejeni okulingana nemaliukubhejaUkubheja okulingana nemaliBomvu/mnyama, engalingani/elinganayo, phezulu/phansi. Izinombolo eziyi-18, kukhokha u-1:1.Funda konke → okunamathubaizibaloAmathubaIthuba lomphumela, kusukela ku-0 kuya ku-1 noma ku-0% kuya ku-100%. Inombolo eyodwa: 1/37 = 2.70%.Funda konke → okuwina angu-p = 18/37 namathuba okuhlulwa angu-q = 19/37. Angakanani amathuba okuthi ufinyelele umgomo ngaphambi kokuthi imali yakho iphele nya? Impendulo yatholwa ngu-Pascal, Fermat no-Huygens ngama-1650 futhi ingenye yemiphumela emidala kakhulu kwezamathuba.

Blaise Pascal: Inganekwane yesondo le-roulette

Ifomula yokuphelelwa yimali komgembuli

P(ukufinyelela umgomo) = (1 − (q/p)ᵃ) / (1 − (q/p)ᵃ⁺ᵇ). Ingozi yokuphelelwa yimaliizibaloIngozi yokuphelelwa yimaliAmathuba okulahlekelwa yimali yokubheja yonke ngaphambi kokufinyelela umgomo noma inani lokujikeleza.Funda konke → iyinani elisalayo uma lokho kususwa kokuphelele. Uma u-q/p = 19/18 ≈ 1.0556, isilinganiso sikhula ngokushesha okukhulu (exponentially) ngokwenani lamayunithi, ngakho ifomula ijezisa kakhulu amayunithi amancane: lapho ukubheja okudingekayo ukuze ufinyelele umgomo kukuningi, kulapho intela engu-2.70% ikhokhwa khona izikhathi eziningi endleleni.

imali yokubhejaiyunithiumgomoukubheja kuze kufinyelelwe umgomop(ukufinyelela umgomo)ingozi yokuphelelwa yimali

$500$10$60010≈ 57%≈ 43%

$500$50$6002≈ 79%≈ 21%

$500$10$1,00050≈ 6%≈ 94%

$500$100$1,0005≈ 43%≈ 57%

$500$500$1,000148.6%51.4%

$100$10$20010≈ 37%≈ 63%

Ukubheja okulingana nemali, inani elingaguquki, ngaphandle kwe-la partage. Isibali sengozi yokuphelelwa yimali senza izibalo zanoma yimaphi amanani.

Ukukufunda

Amayunithi amancane ayalimaza. Ukuzama ukuphinda kabili u-$500 ngokubheja u-$10 kuphumelela ku-6% wezikhathi; ngokubheja okukodwa kuka-$500 kuphumelela ku-48.6% wezikhathi. Ukudlala ngesibindi, ukubheja okumbalwa nokukhulu, kwandisa kakhulu amathuba okufinyelela umgomo emdlalweni onenani elilindelekile elibi (negative expectation), ngoba kunciphisa inani lezikhathi inzuzo yekhasino esetshenziswa ngazo. Kuphinde kwandise kakhulu ukuguquguqukaizibaloUkuguquguqukaIsilinganiso sokuthi imiphumela ihlakazeke kangakanani ezungeze inani elilindelekile. Kuphezulu ku-straight up, kuphansi ekubhejeni okulingana nemali.Funda konke → kwalokho okwenzeka kuwe, futhi kuqeda ubusuku ngokushesha. Lo mbono (theorem) ubizwa ngokuthi “ukudlala ngesibindi kungcono kakhulu” futhi wafakazelwa ngu-Dubins no-Savage ngo-1965.

Amathuba okuguqula u-$500 abe ngu-$1,000 kokubomvu%

ukubheja okukodwa kuka-$500

48.6%

ukubheja kuka-$100

≈ 43%

ukubheja kuka-$50

≈ 37%

ukubheja kuka-$20

≈ 21%

ukubheja kuka-$10

≈ 6%

ukubheja kuka-$5

≈ 0.5%

024.3048.6%

Lapho ukubheja okudingekayo kukuningi, inzuzo yekhasino ikhokhwa kaningi. Ukudlala ngokwesaba kuyabiza.

Lapho inkinga yaqala khona

Lo mbuzo mdala kune-roulette. Ngo-1656 u-Pascal wanika u-Fermat iphazili: abadlali ababili baphonsa amadayisi amathathu, ngamunye eqala ngezinto zokubala ezingu-12; ukuphonsa okungu-11 kuhambisa into yokubala ngendlela eyodwa, ukuphonsa okungu-14 ngenye. Bobabili bayixazulula, futhi u-Huygens, owezwa ngayo ngencwadi evela kusazi sezibalo u-Pierre de Carcavi, wayinyathelisa ngo-1657 njengenkinga yesihlanu encwadini yokuqala ngamathuba, kanye nempendulo kodwa ngaphandle kobufakazi. Ishumi nanye lingaphonswa ngezindlela ezingu-27 kanti ishumi nane ngezingu-15 kuphela, ngakho into yokubala ngayinye ihamba ngendlela yomdlali wokuqala izikhathi ezingu-9 ku-14, futhi ifomula engenhla, nezinto zokubala ezingu-12 ngamunye, imenza abe namathuba acishe aphindwe ka-1,157 okuwina konke kunokulahlekelwa yikho konke. Inzuzo yekhasino engu-2.70% incane kakhulu, kodwa ifomula efanayo ikhombisa ukuthi yenzani ekubhejeni okuningi.

Ephazilini ka-Pascal, ukuphonsa ngakunye kwamadayisi amathathu kuhambisa into eyodwa yokubala phakathi kwabadlali.

Ukubheja kwangempela ngesibindi

Ngo-Ephreli 2004 u-Ashley Revell, insizwa yaseNgilandi, wathengisa cishe yonke into ayenayo, kuhlanganise nezingubo zakhe, wahamba no-$135,300 waya e-Plaza e-Las Vegas. Ngemuva kokubheja okuncane wabeka yonke leyo mali kokubomvuukubhejaBomvuUkubheja okulingana nemali ezinombolweni eziyi-18 ezibomvu. NgesiFulentshi: rouge.Funda konke →, kanye. IbholaokokusebenzaIbholaIbhola elincane eliphonswa emzileni libheke ngakolunye uhlangothi lwe-rotor. Amabhola esimanje enziwa nge-ivorine noma nge-Teflon, angu-18–21 mm.Funda konke → lawela ku-7 obomvu futhi waphuma no-$270,600. Esondweni leqandaisondoIqandaIgodi elilodwa eliluhlaza elingambozwa ukubheja okulingana nemali, okwedazini noma okwekholamu; umthombo wenzuzo yekhasino. Kubuye kuthiwe: iqanda elilodwa, 0.Funda konke → eliphindiwe lokho kujikeleza okukodwa kwakuyithuba elingu-47.37% futhi kwamlahlekisela u-$7,121 ngokwesilinganiso, inzuzo yekhasino engu-5.26% ekubhejeni okukodwa. Uma kusakazwe ekubhejeni kuka-$10, umgomo ofanayo ubungacishe ungabi nathemba. Ukudlala ngesibindi akwenzi ukubheja kube kuhle; kwenza kube kufushane ngangokunokwenzeka.

Yonke imali yokubheja ka-Ashley Revell ibekwe ekujikelezeni okukodwa kwesondo leqanda eliphindiwe.

Ingozi yokuphelelwa yimali ngaphandle komgomo

Uma umane udlala uze uphelelwe yimali noma uyeke ngemuva kokujikeleza okungu-N, umbuzo uba “angakanani amathuba okuthi imali yami yokubheja iphele nya ekujikelezeni okungu-N?”. Ayikho ifomula elula (closed form) yanoma yiliphi inani lika-N kodwa izilingisi kule sayithi ziyakubala: imali yokubheja engu-$500 ngo-$10 kokubomvu cishe ayilokothi iphele ekujikelezeni okungu-100 (ngaphansi kuka-1%), iphela cishe ku-9% wezikhathi ekujikelezeni okungu-500, futhi cishe ku-95% wezikhathi ekujikelezeni okungu-5,000. Uma kungekho mthetho wokuyeka amathuba athambekela ku-100%, okuyinguqulo yesikhathi eside yenzuzo yekhasinoizibaloInzuzo yekhasinoIngxenye yenani ngalinye elibhejwayo ikhasino eyigcinayo ngokwesilinganiso: ama-2.70% ku-roulette yaseYurophu.Funda konke →.

Amaseshini ayishumi, imali yokubheja engu-$500, $25 kokubomvu, ukujikeleza okungu-200umphumela uqhathaniswa nesiqalo

amaseshini angu-1,000 × ukujikeleza okungu-500 · okunsomi p10/p25/p75/p90, okuluhlaza okwesibhakabhaka okukhanyayo phakathi, amasampula angu-81 afiphele · hambisa phezu kweshadi ukuze ubone ama-quantile ekujikelezeni

p10 −$500
p25 −$500
phakathi −$500
p75 +$0
p90 +$350

amaseshini angu-1,000 × ukujikeleza okungu-500 · i-y-axis inqunyelwe ku-percentile yoku-1–99 (okweqisayo −$500 kuya ku-+$1,500) · ukujikeleza okungu-500 · isisekelo $25 · okulingana nemali

Imigqa ethinta phansi isiphelelwe yimali. Ngeyunithi elincane ibingahlala isikhathi eside futhi igcine endaweni efanayo.

Ukuhlangana ngokuhamba kwesikhathi: Umthetho wezinombolo ezinkulu ku-roulette

Isikhathi esingakanani, futhi phambili kangakanani

Eminye imiphumela emibili yakudala iphendula imibuzo abadlali abayibuzayo ngempela. Uma kungekho mgomo, ukubheja okulingana nemali ngenani elingaguquki kuhlala ngokwesilinganiso ukujikeleza okungu-37 eyunithini ngayinye yemali yokubheja esondweni laseYurophu no-19 kwelaseMelika, ngoba ukujikeleza ngakunye kuthatha u-1/37 weyunithi ngokwesilinganiso (1/19 esondweni laseMelika): amayunithi angu-100 ahlala ukujikeleza okungu-3,700 ngokwesilinganiso, nakuba ingxenye yamaseshini anjalo iphela ngaphakathi kokungu-3,134 (bheka ikhasi elithi Ubude beseshini nezindleko). Futhi noma ngabe imali yokubheja inkulu kangakanani, amathuba esondweni laseYurophu okuke ube phambili ngamayunithi angu-k angu-(18/19)ᵏ. Lokho kungu-95% eyunithini eyodwa no-58% kumayunithi ayishumi, kodwa ayikho imali yokubheja, noma ngabe ijule kangakanani, enikeza amathuba alinganayo okuke ube phambili ngamayunithi angu-13; esondweni laseMelika amathuba angu-(9/10)ᵏ futhi ehla ngaphansi kwengxenye kumayunithi angu-7.

amayunithi phambili, nganoma yisiphi isikhathiYaseYurophuYaseMelika

194.7%90.0%

576.3%59.0%

1058.2%34.9%

1349.5%25.4%

2033.9%12.2%

506.7%0.5%

1000.45%0.003%

Ukubheja okulingana nemali, inani elingaguquki, imali yokubheja enkulu ngokwanele ukuthi ingapheli neze. Amathuba angu-(18/19)ᵏ esondweni leqanda elilodwa no-(9/10)ᵏ kwelamaqanda amabili.

Ubude beseshini nezindleko Isondo nemithetho ye-roulette yaseMelika

Imali yokubheja yamathuba alinganayo

Phendula umbuzo: kumele ulethe malini ukuze ube okungenani namathuba alinganayo okuwina inani elithile ngaphambi kokulahlekelwa yikho konke? Ekuwineni okuncane, akukhulu. Ekuwineni okukhulu imali yokubheja edingekayo inyuka kakhulu, futhi uma sekudlule iphuzu elithile ayikho imali yokubheja eyanele, ngoba ngisho nengapheli inikeza amathuba angaphansi kwalawo alinganayo okuke ube phambili kangako. U-Taylor (2021) ukubeka ngenye indlela: esondweni laseMelika, ukuze ube namathuba alinganayo okufinyelela amayunithi angu-100 kumele uqale ngangu-94, ubeke engcupheni angu-94 ukuze uwine angu-6. Esondweni laseYurophu ubungadinga angu-88.

ukuwinaYaseYurophuYaseMelika

iyunithi e-122

amayunithi angu-233

amayunithi angu-345

amayunithi angu-468

amayunithi angu-5712

amayunithi angu-6921

amayunithi angu-712ayikho imali yokubheja eyanele

amayunithi angu-815ayikho imali yokubheja eyanele

amayunithi angu-1024ayikho imali yokubheja eyanele

amayunithi angu-1246ayikho imali yokubheja eyanele

amayunithi angu-13 noma ngaphezuluayikho imali yokubheja eyaneleayikho imali yokubheja eyanele

Imali yokubheja encane kakhulu, ngamayunithi, enikeza okungenani amathuba alinganayo okuwina inani ngaphambi kokulahlekelwa yimali yokubheja, ngokubheja okulingana nemali ngenani elingaguquki. Isibalo sethu esisuka efomuleni engenhla.

Isifundo esisebenzayo

Nquma ukuthi uzama ukwenzani. Uma umgomo kuwukuwina okuthile, bheja amanani amakhulu izikhathi ezimbalwa. Uma umgomo kuwubusuku obude, bheja amanani amancane futhi wamukele ukuthi inzuzo yekhasino izothatha u-2.70% wayo emalini enkulu ephelele ebhejiweimaliImali yonke ebhejiweInani lonke elibhejwe phakathi neseshini noma esikhathini esithile, kubalwa nemali ewiniwe ephinde yabhejwa. Kubuye kuthiwe: handle, action.Funda konke →. Uma umgomo kungukho kokubili, kukhona okumele kuyekwe, futhi kuvame ukuba ngumgomo.

Ifomula

P(umgomo) = (1 − (q/p)ᵃ) / (1 − (q/p)ᵃ⁺ᵇ)

ingozi yokuphelelwa yimali = 1 − P(umgomo)

q/p = 19/18 ekubhejeni okulingana nemali

isilinganiso sokujikeleza kuze kuphele imali, ngaphandle komgomo = 37 × amayunithi

P(ukuke ube phambili ngamayunithi angu-k) = (18/19)ᵏ

Imibuzo

Ingabe ukwenyuswa kwenani kwehlisa ingozi yokuphelelwa yimali?

I-MartingaleisuMartingaleUkwenyuswa kwenani okuphinda kabili inani elibhejwayo ngemuva kokuhlulwa ngakunye. Bheka isigaba esithi “Amasu okubheja ku-roulette” ukuze ubone ukuthi kwenzani nokuthi yini engakwenzi.Funda konke → iyayehlisa emaseshinini amafushane futhi iyikhuphula kakhulu emaseshinini amade. Ukubheja ngenani elingaguqukiisuUkubheja ngenani elilodwaUkubheja inani elifanayo kukho konke ukujikeleza. Isisekelo okuqhathaniswa naso konke ukwenyuswa kwenani.Funda konke → ngeyunithi elikhulu yindlela eqotho yokuyehlisa.

Kuthiwani ngokubheja kwe-straight up?

Ifomula engenhla eyokubheja okulingana nemali. Ekubhejeni okunokuguquguquka okuphezulu ukuphelelwa yimali kunamathuba amakhulu ngamanani amancane futhi umgomo ufinyelelwa ngendlela engalingani; sebenzisa isibali.

Kungani u-q/p eyinani elibalulekile?

Isinyathelo ngasinye esiya emgomweni sinamathuba amancane kancane kunesinyathelo ngasinye esiya ekuphelelweni yimali; isilinganiso siyanqwabelana ngokwenani lezinyathelo.

Ubumnandi bezibalo

Zama lezi ngokwakho kuqala. Isixazululo ngasinye sifihliwe; sivule uma usukulungile.

Uno-$100 futhi ufuna u-$1,000, ubheja ku-bomvuukubhejaBomvuUkubheja okulingana nemali ezinombolweni eziyi-18 ezibomvu. NgesiFulentshi: rouge.Funda konke → kuphela. Uhlelo lokuqala: bheja u-$1 ngesikhathi. Uhlelo lwesibili: bheja konke onakho uze udlule u-$500, bese ubheja okwanele kuphela ukufinyelela ku-$1,000. Yiluphi uhlelo olungcono, futhi ngokungakanani?
Bonisa isixazululo
Impendulo Uhlelo lwesibili, ngokude. Lufinyelela ku-$1,000 cishe ku-9.0% wezikhathi, eduze no-10% olungile. Uhlelo lokuqala luphumelela cishe izikhathi ezingu-7 ku-10²².
Ku-mdlalo olungileizibaloUmdlalo olinganayoUmdlalo lapho kungekho hlangothi olunenzuzo: konke ukubheja kunenani elilindelekile eliyiqanda.Funda konke → ubungafinyelela ku-$1,000 usuka ku-$100 kanye kweziyishumi noma ngabe wenzani, ngoba inani elimaphakathi lemali yakho lihlala ku-$100.
Inzuzo yekhasino ithatha u-2.70% kukho konke ukubheja, ngakho uma ubheja imali encane isiyonke, usondela kakhulu kokukodwa kweziyishumi. Uhlelo lwesibili luqeda udaba ngokubheja okumbalwa: u-$100 uba ngu-$200, $400, $800, bese u-$200 eyanela. Luphumelela cishe ku-9.0% wezikhathi. Uhlelo lokuqala luthatha izinkulungwane zokubheja ngaphambi kokuba uhambo luphele, futhi inzuzo yekhasino, encane ekubhejeni ngakunye, iyahlangana ibe yincithakalo ecishe iqinisekile.
Lona ngumphumela we-Dubins–Savage esimweni sawo esilula kakhulu (Epstein, 2013): emdlalweni othanda ikhasino, bheja okuningi ngangokuba udinga, izikhathi ezimbalwa ngangokunokwenzeka.
Uno-$500 futhi ufuna u-$1,000, ume ngokushesha nje uma usunawo. Ukhetha uhlobo olulodwa lokubheja bese uluphinda luze luwine kanye noma imali iphele. Yiluphi uhlobo olunikeza amathuba amahle kakhulu?
Bonisa isixazululo
Impendulo Ukubheja okukodwa kwe-$500 kokubomvu: 48.6%. Lonke uhlelo olusabalalisa imali ekubhejeni okuncane lwenza kabi kunalokho.
Khetha inani ngalinye elibhejwayo ukuze ukuwina okukodwa kwanele: u-$30 ku-straight upukubhejaI-straight upInombolo eyodwa, kukhokha u-35:1.Funda konke → uwina u-$1,050, u-$60 ku-splitukubhejaI-splitIzinombolo ezimbili ezingomakhelwane, kukhokha u-17:1.Funda konke → uwina u-$1,020, njalo njalo. Bese ubala amathuba okuthi okungenani ukubheja okukodwa kuwine ngaphambi kokuba imali iphele. Ama-straight up ayishumi nesithupha ka-$30 wonke aphuthelwa ngamathuba angu-(36/37)¹⁶ = 64.5%, ngakho afinyelela ku-$1,000 ku-35.5% wezikhathi.
Ithebula libonisa ukubheja ngakunye. Okubomvu kwenza kangcono ngoba kufika lapho ngokubheja okukodwa, ngakho inzuzo yekhasino ikhokhwa kanye, ku-$500. I-six lineukubhejaI-six lineIzinombolo eziyisithupha emigqeni emibili engomakhelwane, kukhokha u-5:1. NgesiFulentshi: sixain.Funda konke → iza yesibili ngoba idinga ukubheja okuthathu kuphela. Ukubheja okukodwa edazininiukubhejaIdazini1–12, 13–24 noma 25–36, kukhokha u-2:1.Funda konke → yikho okubi kakhulu, amathuba angu-12/37; ngisho kudlalwa ngamayunithiimaliIyunithiInani elibhejwayo eliyisisekelo uhlelo noma umdlali asebenza ngalo. Ukwenyuswa kwenani kuchazwa ngamayunithi ukuze kusebenze kunoma yiliphi itafula.Funda konke → ka-$250 uze ube no-$1,000 noma ngaphezulu, idazini lifika lapho ku-46.4% kuphela wezikhathi.
U-Bollman (2024) wakha ithebula elifanayo esondweni laseMelika. Umugqa wakhe wedazini unephutha: kufanele ufundeke ngokuthi 12/38 = 31.6%.
ukubhejainani elibhejwayo × inani lokubhejaamathuba okufinyelela ku-$1,000
I-straight up$30 × 1635.5%
I-split$60 × 835.9%
I-street$90 × 534.5%
I-corner$125 × 436.7%
I-six line$166, $166, $16841.2%
Idazini$500 × 132.4%
Bomvu$500 × 148.6%
Ubheja iyunithi elilodwa kokubomvu, ukujikeleza emva kokujikeleza, ngemali yokubhejaimaliImali yokubhejaInani lonke lemali ebekelwe ukudlala. Ukuphatha imali yokubheja kusho ukunquma ukuthi ingakanani yayo ozoyibeka engcupheni ekubhejeni ngakunye nasesheshini ngayinye.Funda konke → engapheli. Ngemuva kokujikeleza kokuqala usuphambili ngeyunithi elilodwa noma usemuva ngeyunithi elilodwa. Ayini amathuba okuthi uzophinde ulingane ncamashi?
Bonisa isixazululo
Impendulo 36 ku-37, 97.3%. Esondweni laseMelika kungu-36 ku-38, 94.7%.
Uma ukujikeleza kokuqala kuwina (izikhathi ezingu-18 kwezingu-37), usuphambili ngeyunithi elilodwa, futhi inzuzo yekhasino idonsela phansi yonke iseshini engapheli, ngakho ngokushesha noma kamuva uzodlula futhi ekulinganeni: lokho kuqinisekile. Uma kuhlulwa (izikhathi ezingu-19 kwezingu-37), kumele ukhuphuke ngeyunithi elilodwa, futhi amathuba okuke ube phambili ngeyunithi elilodwa angu-18/19 (bheka ithebula elingenhla).
Konke ndawonye: 18/37 + 19/37 × 18/19 = 18/37 + 18/37 = 36/37.
Ngokuvamile amathuba angu-1 kususwe umehluko phakathi kwamathuba okuwina nawokuhlulwa ekujikelezeni: 1 − 1/37 esondweni laseYurophu, 1 − 2/38 esondweni laseMelika. Emdlalweni ongenalo iqandaisondoIqandaIgodi elilodwa eliluhlaza elingambozwa ukubheja okulingana nemali, okwedazini noma okwekholamu; umthombo wenzuzo yekhasino. Kubuye kuthiwe: iqanda elilodwa, 0.Funda konke → umehluko awukho futhi amathuba angu-1: amaphuzu ahlala ebuyela ekulinganeni. U-Epstein (2013) unikeza umthetho ojwayelekile.
Iphazili ka-Pascal yango-1656: abadlali ababili baphonsa amadayisi amathathu, ngamunye aqale ngama-counter (izibalo zokudlala) angu-12. Njalo uma kuphuma u-11 kudluliselwa i-counter eyodwa kumdlali wokuqala, njalo uma kuphuma u-14 kudluliselwa eyodwa kowesibili; okunye ukuphonsa akubalwa. Ayini amathuba okuthi umdlali wokuqala awine zonke ezingu-24? Futhi uma esikhundleni salokho ubheja iyunithi elingu-1 kokubomvu ekujikelezeni ngakunye ubhekene nomngane odlala njengebhange, amayunithi angu-12 ngamunye, ayini amathuba okuthi uwine zonke ezingu-24?
Bonisa isixazululo
Impendulo Umdlali wokuqala uwina cishe izikhathi ezingu-1,157 kwezingu-1,158. Wena, kokubomvu, uwina wonke amayunithi angu-24 cishe ku-34% kuphela wezikhathi.
Amadayisi amathathu enza u-11 ngezindlela ezingu-27 no-14 ngezindlela ezingu-15, ngakho i-counter ngayinye edlulayo iya kumdlali wokuqala izikhathi ezingu-27 kwezingu-42, izikhathi ezingu-9 kwezingu-14. Uma uhlangothi ngalunye luqala ngo-12, amathuba okuthatha konke angu-1/(1 + r¹²), lapho u-r engumlinganiselo wamathuba ohlangothi olunye kwawakho.
Kumdlali wokuqala r = 5/9, futhi (5/9)¹² ≈ 0.00086, ngakho amathuba acishe abe ngu-0.99914: amathuba angu-9¹² ku-5¹², noma 282,429,536,481 ku-244,140,625, cishe 1,157 ku-1. U-Huygens wanyathelisa lezo zinombolo ncamashi ngo-1657.
Kokubomvu, r = 19/18 ngenxa yeqanda, futhi (19/18)¹² ≈ 1.913: amathuba akho angu-1/2.913 ≈ 34.3%. Uhlamvu lwemali belungapha u-50%. Inzuzo yekhasino engu-2.70% ekubhejeni ngakunye iyahlangana, ekubhejeni okuningi okudingekayo, ibe yigebe lamaphuzu angu-16.

Okokuhlekisa

$Ukudlala ngesibindi kungcono kakhulu. Futhi kuphela ngokushesha.$

Ukudlala ngesibindi kungcono kakhulu. Futhi kuphela ngokushesha.

Imithombo

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, uhlelo lwesi-3, 1968. Ukuphelelwa yimali komgembuli (gambler’s ruin), isahluko XIV.
Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed. Academic Press, 2013.
Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021.
Carcavi, P. de. Incwadi eya ku-Huygens, 28 Septemba 1656, mayelana nenkinga u-Pascal ayibeka ku-Fermat. Œuvres complètes de Christiaan Huygens, vol. 1, 1888, pp. 492–494.
Huygens, C. De Ratiociniis in Ludo Aleae. 1657. Incazelo yokuqala enyatheliswe ngenani elilindelekile.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Isahluko 13, i-roulette.
Reuters. “Briton bets it all on roulette spin, and wins.” Ephreli 2004.
Las Vegas Sun. “Man wagers life’s worth.” 12 Ephreli 2004.

kubuyekezwe ngo-2026-09-28imodeli: yaseYurophu, iqanda elilodwaindlela yokusebenza ↗imithombo ↗