Ingoti yekuphelelwa yimali
Litfuba lekulahlekelwa yiyo yonkhe imali yakho yekubheja ngembi kwekufinyelela umgomo.
Ekubhejeni lokulingana nemali, ingoti yekuphelelwa yimali ilandzela ifomula yekuphelelwa yimali kwemgembuli (gambler’s ruin). Nangabe unemali yekubheja lengu-$500, ubheja $10 futsi umgomo ngu-$600, ufinyelela umgomo cishe ku-57% wetikhatsi futsi uphelelwa yimali kuletinye.
Umbuto
Unemayunithi langu-aimaliLiyunithiLinani lelibhejwako lelisisekelo luhlelo noma umdlali lasebenta ngalo. Kwenyuswa kwelinani kuchazwa ngemayunithi kute kusebente kunoma ngumuphi litafula.Fundza konkhe → emalini yekubhejaimaliImali yekubhejaImali yonkhe lebekelwe kudlala. Kuphatsa imali yekubheja kusho kunquma kutsi ungafaka engcupheni lengakanani kuko kubheja ngakunye nakuyo iseshini ngayinye.Fundza konkhe → futsi ufuna kufinyelela emayunithi langu-a + b, ubheja liyunithi linye ngesikhatsi ekubhejeni lokulingana nemalikubhejaKubheja lokulingana nemaliLokubovu/lokumnyama, lengalingani/lelinganako, phansi/etulu. Tinombolo letingu-18, kukhokha 1:1.Fundza konkhe → lokunelitfubatibaloLitfubaLitfuba lekutsi umphumela wenteke, kusukela ku-0 kuya ku-1 noma ku-0% kuya ku-100%. Inombolo yinye: 1/37 = 2.70%.Fundza konkhe → lekuwina lelingu-p = 18/37 nelitfuba lekulahlekelwa lelingu-q = 19/37. Lingakanani litfuba lekutsi ufinyelele umgomo ngembi kwekutsi imali yakho iphele nya? Imphendvulo yatfolwa nguPascal, Fermat naHuygens nga-1650s futsi ingulomunye wemiphumela lemidzala kakhulu etibalweni tematfuba.
Ifomula yekuphelelwa yimali kwemgembuli
P(kufinyelela umgomo) = (1 − (q/p)ᵃ) / (1 − (q/p)ᵃ⁺ᵇ). Ingoti yekuphelelwa yimalitibaloIngoti yekuphelelwa yimaliLitfuba lekulahlekelwa yimali yonkhe yekubheja ngaphambi kwekufika emgomeni noma enanini lekujikeleta.Fundza konkhe → linani lelisalako nangabe loko kususwa kulokuphelele. Nangabe q/p = 19/18 ≈ 1.0556, silinganiso sikhula ngekushesha lokukhulu (exponentially) ngekwelinani lemayunithi, ngako ifomula ijezisa kakhulu emayunithi lamancane: lapho kubheja lokudzingekako kute ufinyelele umgomo kunyenti, kulapho intsela lengu-2.70% ikhokhwa khona tikhatsi letinyenti endleleni.
Kukufundza
Emayunithi lamancane ayalimata. Kuzama kuphindza kabili $500 ngekubheja $10 kuphumelela ku-6% wetikhatsi; ngekubheja kunye kwa-$500 kuphumelela ku-48.6% wetikhatsi. Kudlala ngesibindi, kubheja lokumbalwa nalokukhulu, kwandzisa kakhulu litfuba lekufinyelela umgomo emdlalweni lonelinani lelilindzelekile lelibi (negative expectation), ngobe kunciphisa linani letikhatsi inzuzo yelikhasino lesetjentiswa ngato. Kuphindze kwandzise kakhulu kugucugucukatibaloKugucugucukaSilinganiso sekutsi imiphumela isabalele kangakanani etungeleta linani lelilindzelekile. Kukhulu ku-straight up, kuncane ekubhejeni lokulingana nemali.Fundza konkhe → kwaloko lokwenteka kuwe, futsi kucedza busuku ngekushesha. Lombono (theorem) ubitwa ngekutsi “kudlala ngesibindi kuncono kakhulu” futsi wafakazelwa nguDubins naSavage nga-1965.
Lapho inkinga yacala khona
Lombuto mdzala kune-roulette. Nga-1656 Pascal waniketa Fermat liphazili: badlali lababili baphosa emadayisi lamatsatfu, ngamunye acala ngetintfo tekubala letingu-12; kuphosa lokungu-11 kuhambisa intfo yekubala ngendlela yinye, kuphosa lokungu-14 ngalenye. Bobabili bayicombulula, futsi Huygens, lowayiva ngencwadzi levela kusati setibalo Pierre de Carcavi, wayishicilela nga-1657 njengenkinga yesihlanu encwadzini yekucala ngematfuba, kanye nemphendvulo kodvwa ngaphandle kwebufakazi. Lishumi nakunye lingaphoswa ngetindlela letingu-27 kantsi lishumi nakune ngaletingu-15 kuphela, ngako intfo yekubala ngayinye ihamba ngendlela yemdlali wekucala tikhatsi letingu-9 ku-14, futsi ifomula lengenhla, netintfo tekubala letingu-12 ngamunye, imenta abe nelitfuba lelicishe liphindvwe ka-1,157 lekuwina konkhe kunekulahlekelwa ngiko konkhe. Inzuzo yelikhasino lengu-2.70% incane kakhulu, kodvwa ifomula lefanako ikhombisa kutsi yentani ekubhejeni lokunyenti.
Kubheja kwangempela ngesibindi
Ngenyanga yaMabasa 2004 Ashley Revell, lijaha laseNgilandi, watsengisa cishe yonkhe intfo labenayo, kuhlanganise netingubo takhe, wahamba na-$135,300 waya e-Plaza e-Las Vegas. Ngemuva kwekubheja lokuncane wabeka yonkhe leyo mali kulokubovukubhejaBovuKubheja lokulingana nemali etinombolweni letingu-18 letibovu. NgesiFulentji: rouge.Fundza konkhe →, kanye. LibholatinsitaLibholaLibhola lelincane leliphoswa emzileni lihamba ngakulolunye luhlangotsi kune-rotor. Emabhola alamuhla ayi-ivorine noma i-Teflon, 18–21 mm.Fundza konkhe → lawela ku-7 lobovu futsi waphuma na-$270,600. Elisondvweni lelinelicandzalisondvoLicandzaUmgodzi munye loluhlata longambonjwa kubheja lokulingana nemali, kwelidazini noma kwelikholamu; umtfombo wenzuzo yelikhasino. Kuphindze kutsiwe: licandza linye, 0.Fundza konkhe → lelikabili loko kujikeleta kunye bekulitfuba lelingu-47.37% futsi kwamlahlekisela $7,121 ngesilinganiso, inzuzo yelikhasino lengu-5.26% ekubhejeni kunye. Nangabe kusakatwe ekubhejeni kwa-$10, umgomo lofanako bewutawucishe ungabi nalitsemba. Kudlala ngesibindi akwenti kubheja kube kuhle; kwenta kube kufishane ngangekwenteka.
Ingoti yekuphelelwa yimali ngaphandle kwemgomo
Nangabe umane udlala uze uphelelwe yimali noma uyeke ngemuva kwekujikeleta lokungu-N, umbuto uba “lingakanani litfuba lekutsi imali yami yekubheja iphele nya ekujikeleteni lokungu-N?”. Ayikho ifomula lelula (closed form) yanoma nguliphi linani la-N kodvwa tilingisi kulelisayithi tiyakubala: imali yekubheja lengu-$500 nga-$10 kulokubovu cishe ayisoze yaphela ekujikeleteni lokungu-100 (ngaphansi kwa-1%), iphela cishe ku-9% wetikhatsi ekujikeleteni lokungu-500, futsi cishe ku-95% wetikhatsi ekujikeleteni lokungu-5,000. Nangabe kute umtsetfo wekuyeka litfuba litsambekela ku-100%, lokuyinguculo yesikhatsi lesidze yenzuzo yelikhasinotibaloInzuzo yelikhasinoIncenye yelinani ngalinye lelibhejiwe leligcinwa likhasino ngesilinganiso: 2.70% ku-roulette yaseYurophu.Fundza konkhe →.
- p10 −$500
- p25 −$500
- phakatsi −$500
- p75 +$0
- p90 +$350
Kuhlangana ngekuhamba kwesikhatsi: Umtsetfo wetinombolo letinkhulu ku-roulette
Sikhatsi lesingakanani, futsi embili kangakanani
Leminye imiphumela lemibili yakadzeni iphendvula imibuto badlali labayibutako ngempela. Nangabe kute umgomo, kubheja lokulingana nemali ngelinani linye kuhlala ngesilinganiso kujikeleta lokungu-37 kuliyunithi ngalinye lemali yekubheja elisondvweni laseYurophu na-19 kulelaseMelika, ngobe kujikeleta ngakunye kutsatsa 1/37 weliyunithi ngesilinganiso (1/19 elisondvweni laseMelika): emayunithi langu-100 ahlala kujikeleta lokungu-3,700 ngesilinganiso, nanoma lesigamu setiseshini letinjalo tiphela ngekhatsi kwalokungu-3,134 (buka likhasi Budze beseshini nelibito layo). Futsi noma ngabe imali yekubheja inkhulu kangakanani, litfuba elisondvweni laseYurophu lekuke ube embili ngemayunithi langu-k lingu-(18/19)ᵏ. Loko kungu-95% kuliyunithi linye na-58% kumayunithi lalishumi, kodvwa ayikho imali yekubheja, noma ngabe ijulile kangakanani, leniketa litfuba lelilinganako lekuke ube embili ngemayunithi langu-13; elisondvweni laseMelika litfuba lingu-(9/10)ᵏ futsi lehla ngaphansi kwesigamu kumayunithi langu-7.
Budze beseshini nelibito layoLisondvo nemitsetfo ye-roulette yaseMelika
Imali yekubheja yelitfuba lelilinganako
Phendvula umbuto: kufanele ulete malini kute ube lokungenani nelitfuba lelilinganako lekuwina linani lelitsite ngembi kwekulahlekelwa ngiko konkhe? Ekuwineni lokuncane, akukhulu. Ekuwineni lokukhulu imali yekubheja ledzingekako inyuka kakhulu, futsi nangabe sekwendlule liphuzu lelitsite ayikho imali yekubheja leyenele, ngobe ngisho nalengapheli iniketa litfuba lelingaphansi kwalelilinganako lekuke ube embili kangako. Taylor (2021) ukubeka ngalenye indlela: elisondvweni laseMelika, kute ube nelitfuba lelilinganako lekufinyelela emayunithi langu-100 kufanele ucale ngalangu-94, ubeke engotini langu-94 kute uwine langu-6. Elisondvweni laseYurophu bewutawudzinga langu-88.
Sifundvo lesisebentako
Ncuma kutsi utama kwentani. Nangabe umgomo kukuwina lokutsite, bheja emanani lamakhulu tikhatsi letimbalwa. Nangabe umgomo kubusuku lobudze, bheja emanani lamancane futsi wemukele kutsi inzuzo yelikhasino itawutsatsa 2.70% wayo emalini lenkhulu yonkhe lebhejiweimaliImali yonkhe lebhejiweLinani lonkhe lelibhejwe ngesikhatsi seseshini noma ngesikhatsi lesitsite, kubalwa nemali lewiniwe lephindze yabhejwa. Kuphindze kutsiwe: handle, action.Fundza konkhe →. Nangabe umgomo kuko kokubili, kukhona lokufanele kuyekwe, futsi kuvame kuba ngumgomo.
Lifomula
Imibuto
I-MartingalelisuMartingaleKwenyuswa kwelinani lokuphindza kubheja kabili ngemuva kwekulahlekelwa ngakunye. Buka sigaba semasu kute ubone kutsi kwentani nekutsi akwenti ini.Fundza konkhe → iyayehlisa etiseshinini letimfishane futsi iyikhuphula kakhulu etiseshinini letindze. Kubheja ngelinani linyelisuKubheja ngelinani linyeKubheja linani lelifanako kuko konkhe kujikeleta. Lizinga lesisekelo lekucatsaniswa nalo konkhe kwenyuswa kwelinani.Fundza konkhe → ngeliyunithi lelikhulu yindlela leticotfo yekuyehlisa.
Ifomula lengenhla ngeyekubheja lokulingana nemali. Ekubhejeni lokunekugucugucuka lokukhulu kuphelelwa yimali kunelitfuba lelikhulu ngemanani lamancane futsi umgomo ufinyelelwa ngendlela lengalingani; sebentisa ikhaliketha.
Sinyatselo ngasinye lesiya emgomweni sinelitfuba lelincane kancane kunesinyatselo ngasinye lesiya ekuphelelweni yimali; silinganiso siyanchwabelana ngekwelinani letinyatselo.
Bumnandi betibalo
Zama loku ngekwakho kucala. Sixazululo ngasinye sifihliwe; sivule nawukulungele.
Une-$100 futsi ufuna $1,000, ubheja kulokubovukubhejaBovuKubheja lokulingana nemali etinombolweni letingu-18 letibovu. NgesiFulentji: rouge.Fundza konkhe → kuphela. Licebo lekucala: bheja $1 ngesikhatsi. Licebo lesibili: bheja konkhe lonako uze wendlule $500, bese ubheja lokwanele kuphela kutsi ufike ku-$1,000. Nguliphi licebo lelincono, futsi ngalokungakanani?
Khombisa sixazululo
Imphendvulo Licebo lesibili, kakhulu. Lifika ku-$1,000 cishe ku-9.0% wesikhatsi, eduze ne-10% lolinganako. Licebo lekucala liphumelela cishe tikhatsi letingu-7 ku-10²².
Emdlalweni lolinganakotibaloUmdlalo lolinganakoUmdlalo lapho kute luhlangotsi lolunenzuzo: konkhe kubheja kunelinani lelilindzelekile lelingu-zero.Fundza konkhe → bewutawufika ku-$1,000 usuka ku-$100 kanye kulokulishumi nobe ngabe wentani, ngobe linani lesilinganiso lemali yakho lihlala ku-$100.
Inzuzo yelikhasino itsatsa 2.70% kukho konkhe kubheja, ngako nawubheja kancane esewonkhe, uhlala useduze nalokunye kulokulishumi. Licebo lesibili linguma ludzaba ngekubheja lokumbalwa: $100 uba $200, $400, $800, bese $200 uyenela. Liphumelela cishe ku-9.0% wesikhatsi. Licebo lekucala litsatsa kubheja lokutinkhulungwane ngaphambi kwekutsi luhambo luphele, futsi inzuzo yelikhasino, lencane kukho ngakunye, ihlangana ibe ngulokucishe kube kuphelelwa yimali lokucinisekile.
Lona ngumphumela we-Dubins–Savage ngendlela yawo lelula kakhulu (Epstein, 2013): emdlalweni lovuna likhasino, bheja lokukhulu njengoba udzinga, tikhatsi letimbalwa njengoba ungakhona.
Une-$500 futsi ufuna $1,000, uyema nawusawutfolile. Ukhetsa luhlobo lunye lwekubheja bese uluphindza kuze kuwine kanye nobe imali iphele. Nguluphi luhlobo loluniketa litfuba lelincono kakhulu?
Khombisa sixazululo
Imphendvulo Kubheja kunye kwe-$500 kulokubovu: 48.6%. Onkhe emacebo lahlakata imali ekubhejeni lokuncane enta kabi kakhulu.
Khetsa linani ngalinye lelibhejwako kutsi kuwina kunye kwanele: $30 ku-straight upkubhejaI-straight upInombolo yinye, kukhokha 35:1.Fundza konkhe → kuwina $1,050, $60 ku-splitkubhejaI-splitTinombolo letimbili leyakhelene, kukhokha 17:1.Fundza konkhe → kuwina $1,020, njalo njalo. Bese ubala litfuba lekutsi lokungenani kubheja kunye kuwine ngaphambi kwekutsi imali iphele. Ti-straight up letilishumi nesitfupha te-$30 tonkhe tiphutsa ngelitfuba la-(36/37)¹⁶ = 64.5%, ngako tifika ku-$1,000 ku-35.5% wesikhatsi.
Litafula likhombisa kubheja ngakunye. Lokubovu kwenta kahle kakhulu ngobe kufika lapho ngekubheja kunye, ngako inzuzo yelikhasino ikhokhwa kanye, ku-$500. I-six linekubhejaI-six lineTinombolo letisitfupha emigceni lemibili leyakhelene, kukhokha 5:1. NgesiFulentji: sixain.Fundza konkhe → ingeyesibili ngobe idzinga kubheja lokutsatfu kuphela. Kubheja kunye kwelidazinikubhejaLidazini1–12, 13–24 noma 25–36, kukhokha 2:1.Fundza konkhe → kubi kakhulu, litfuba la-12/37; nanoma kudlalwa ngemayunithiimaliLiyunithiLinani lelibhejwako lelisisekelo luhlelo noma umdlali lasebenta ngalo. Kwenyuswa kwelinani kuchazwa ngemayunithi kute kusebente kunoma ngumuphi litafula.Fundza konkhe → e-$250 uze ube ne-$1,000 nobe ngetulu, lidazini lifika lapho ku-46.4% wesikhatsi kuphela.
Bollman (2024) wakha litafula lelifanako lelisondvo laseMelika. Umugca wakhe welidazini unephutsa: kufanele ufundzeke 12/38 = 31.6%.
kubhejalinani lelibhejwako × linani lekubhejalitfuba lekufika ku-$1,000I-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%Lidazini$500 × 132.4%Bovu$500 × 148.6%Ubheja liyunithi linye kulokubovu, kujikeleta ngemuva kwekujikeleta, ngemali yekubhejaimaliImali yekubhejaImali yonkhe lebekelwe kudlala. Kuphatsa imali yekubheja kusho kunquma kutsi ungafaka engcupheni lengakanani kuko kubheja ngakunye nakuyo iseshini ngayinye.Fundza konkhe → lengapheli. Ngemuva kwekujikeleta kwekucala usetulu ngeliyunithi linye nobe usephansi ngeliyunithi linye. Litfuba lini lekutsi uyophindze ulingane ncamashi?
Khombisa sixazululo
Imphendvulo 36 ku-37, 97.3%. Elisondvweni laseMelika ngu-36 ku-38, 94.7%.
Nangabe kujikeleta kwekucala kuwina (tikhatsi letingu-18 ku-37), usetulu ngeliyunithi linye, futsi inzuzo yelikhasino idvonsela phansi yonkhe iseshini lengapheli, ngako ngelinye lilanga uyabuyela ekulinganeni: loko kucinisekile. Nangabe kulahlekelwa (tikhatsi letingu-19 ku-37), kufanele ukhuphuke ngeliyunithi linye, futsi litfuba lekutsi uyoke wandlule ngeliyunithi linye ngu-18/19 (buka litafula lelingenhla).
Kanyekanye: 18/37 + 19/37 × 18/19 = 18/37 + 18/37 = 36/37.
Ngalokujwayelekile litfuba ngu-1 kususa umehluko emkhatsini wematfuba ekuwina nekulahlekelwa ekujikeleteni: 1 − 1/37 elisondvweni laseYurophu, 1 − 2/38 elisondvweni laseMelika. Emdlalweni lote licandzalisondvoLicandzaUmgodzi munye loluhlata longambonjwa kubheja lokulingana nemali, kwelidazini noma kwelikholamu; umtfombo wenzuzo yelikhasino. Kuphindze kutsiwe: licandza linye, 0.Fundza konkhe → umehluko awukho futsi litfuba ngu-1: emaphuzu ahlala abuyela ekulinganeni. Epstein (2013) unika umtsetfo lojwayelekile.
Inkinga ya-Pascal ya-1656: badlali lababili baphosa emadayisi lamatsatfu, ngamunye acala ngemathokheni langu-12. Ngamunye we-11 udlulisela lithokheni kumdlali wekucala, ngamunye we-14 udlulisela linye kulowesibili; kuphosa lokunye akubalwa. Kungenteka kangakanani kutsi umdlali wekucala awine wonkhe langu-24? Futsi nangabe esikhundleni saloko ubheja liyunithi lelingu-1 kulokubovu kujikeleta ngakunye ngekumelana nemngani lodlala njengelibhange, emayunithi langu-12 ngamunye, kungenteka kangakanani kutsi uwine onkhe langu-24?
Khombisa sixazululo
Imphendvulo Umdlali wekucala uwina cishe tikhatsi letingu-1,157 ku-1,158. Wena, kulokubovu, uwina onkhe emayunithi langu-24 cishe ku-34% wesikhatsi kuphela.
Emadayisi lamatsatfu enta 11 ngetindlela letingu-27 na-14 ngetindlela letingu-15, ngako lithokheni ngalinye lelidlulako liya kumdlali wekucala tikhatsi letingu-27 ku-42, tikhatsi letingu-9 ku-14. Nangabe luhlangotsi ngalunye lucala ku-12, litfuba lekutsatsa konkhe ngu-1/(1 + r¹²), lapho r kulinganiselwa kwelitfuba lelinye luhlangotsi kulelakho.
Kumdlali wekucala r = 5/9, futsi (5/9)¹² ≈ 0.00086, ngako litfuba licishe libe ngu-0.99914: ematfuba la-9¹² ku-5¹², nobe 282,429,536,481 ku-244,140,625, cishe 1,157 ku-1. Huygens washicilela tona leto tinombolo ngo-1657.
Kulokubovu, r = 19/18 ngenca yelicandza, futsi (19/18)¹² ≈ 1.913: litfuba lakho ngu-1/2.913 ≈ 34.3%. Luhlamvu lwemali belutawunika 50%. Inzuzo yelikhasino ya-2.70% kukubheja ngakunye iyahlangana, ekubhejeni lokunyenti lokudzingekako, ibe ngumehluko wemaphuzu langu-16.
Lokuhlekisako
Kudlala ngesibindi kuncono kakhulu. Futsi kuphela ngekushesha.
Imitfombo
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.
- Carcavi, P. de. Incwadzi leya ku-Huygens, 28 Inyoni 1656, mayelana nenkinga Pascal layibeka ku-Fermat.
- Huygens, C. De Ratiociniis in Ludo Aleae.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Reuters. “Briton bets it all on roulette spin, and wins.”
- Las Vegas Sun. “Man wagers life’s worth.”