Amathuba ochungechunge ku-roulette
Uchungechunge olude lombala owodwa luvamile. Futhi alusho lutho ngokujikeleza okulandelayo.
Ezinhlanu ezibomvu ngokulandelana: 2.7%. Eziyishumi: 0.074%. Eseshini yokujikeleza okungu-200 uchungechunge lwesithupha lombala owodwa luvela kaningi kunokuba lungaveli.
Uchungechunge lokuhlulwa luza kangaki
Ukubheja okulingana nemali esondweni elineqanda elilodwa kuhlulwa ekujikelezeni okungu-19 kwangu-37. Umugqa ngamunye ungamathuba okuthi uchungechunge oluthile lokujikeleza luhlulwe lonke, nokuthi umdlali we-Martingale, ophinda kabili ngemuva kokuhlulwa ngakunye, usuvele ulahlekelwe yimali engakanani ngaleso sikhathi.
| ukuhlulwa ngokulandelana | amathuba | cishe 1 kwangu- | okulahlekile kuze kube manje | ukubheja okulandelayo |
|---|---|---|---|---|
| 1 | 51.4% | 2 | $1 | $2 |
| 2 | 26.4% | 4 | $3 | $4 |
| 3 | 13.5% | 7 | $7 | $8 |
| 4 | 7.0% | 14 | $15 | $16 |
| 5 | 3.6% | 28 | $31 | $32 |
| 6 | 1.8% | 55 | $63 | $64 |
| 7 | 0.94% | 106 | $127 | $128 |
| 8 | 0.48% | 207 | $255 | $256 |
| 9 | 0.25% | 403 | $511 | $512 |
| 10 | 0.13% | 784 | $1,023 | $1,024 |
| 11 | 0.065% | 1527 | $2,047 | $2,048 |
| 12 | 0.034% | 2974 | $4,095 | $4,096 |
| 13 | 0.017% | 5792 | $8,191 | $8,192 |
| 14 | 0.0089% | 11279 | $16,383 | $16,384 |
| 15 | 0.0046% | 21965 | $32,767 | $32,768 |
Amathuba ngu-19/37 ophindaphindwe ngokwawo kanye ngokuhlulwa ngakunye, kubalwa kusukela ekujikelezeni okuthile okukodwa. Iseshini ende inokujikeleza okuningi lapho uchungechunge olunjalo lungaqala khona, ngakho ebusuku bonke lungenzeka kakhulu kunalokho okuphakanyiswa umugqa owodwa.
Uchungechunge olulodwa
AmathubaizibaloAmathubaIthuba lomphumela, kusukela ku-0 kuya ku-1 noma ku-0% kuya ku-100%. Inombolo eyodwa: 1/37 = 2.70%.Funda konke → okuthi ukujikeleza okungu-k okulandelayo konke kube okubomvuukubhejaBomvuUkubheja okulingana nemali ezinombolweni eziyi-18 ezibomvu. NgesiFulentshi: rouge.Funda konke → angu-(18/37)ᵏ. Okubili: 23.7%. Okuhlanu: 2.7%. Okuyishumi: 0.074%, cishe u-1 ku-1,350. Okungamashumi amabili: u-1 ezigidini ezingu-1.8. Okungamashumi amabili nesithupha, irekhodi lase-Monte Carlo: u-1 ezigidini ezingu-137. Lawa ngamathuba ochungechunge oluthile oluqala ekujikelezeni okuthile, okuwumbuzo cishe kungekho muntu owubuzayo ngempela.
Eseshini
Umbuzo abantu abawushoyo uthi “ingabe uchungechunge lwe-k luzovela kwenye indawo eseshini yami?”, futhi impendulo inkulu kakhulu kuno-(18/37)ᵏ ngoba iseshini yokujikeleza okungu-200 inikeza cishe izindawo ezingu-200 lapho uchungechunge lungaqala khona. Uchungechunge lwesithupha noma ngaphezulu lombala ofanayo, obomvu noma omnyamaukubhejaMnyamaUkubheja okulingana nemali ezinombolweni ezimnyama eziyi-18. NgesiFulentshi: noir.Funda konke →, luvela eseshini yokujikeleza okungu-200 cishe ku-94% wezikhathi; olwesishiyagalombili noma ngaphezulu cishe ku-47%; olweshumi noma ngaphezulu cishe ku-14%. Uma uqamba umbala kusengaphambili amathuba ayehla, acishe abe ngu-75%, 27% no-7%. Umdlali ohlala kusihlwa wonke uzobona uchungechunge olude njalo kusihlwa.
Kungani lokhu kubalulekile ku-Martingale
Konke ukwenyuswa kwenaniisuUkwenyuswa kwenaniNoma yimuphi umthetho oshintsha inani elibhejwayo ngokusekelwe emiphumeleni yangaphambili. Ukwenyuswa kwenani ngemuva kokuhlulwa kulikhuphula ngemuva kokulahlekelwa, ukwenyuswa kwenani ngemuva kokuwina kulikhuphula ngemuva kokuwina.Funda konke → ngemuva kokuhlulwa kunobude bochungechunge obukwaphulayo: ukuhlulwa okuyisithupha kusukela ku-$10 oyisisekelo emkhawulweni ka-$500, okuyishumi ku-FibonacciisuFibonacciUkwenyuswa kwenani okulandela uchungechunge 1, 1, 2, 3, 5, 8, 13…: isinyathelo esisodwa phambili ngemuva kokuhlulwa, izinyathelo ezimbili emuva ngemuva kokuwina.Funda konke →, okuhlanu uma uphinda kathathu emadazininiukubhejaIdazini1–12, 13–24 noma 25–36, kukhokha u-2:1.Funda konke →. Amathuba ochungechunge lokuhlulwa okuyisithupha ekubhejeni okulingana nemali angu-(19/37)⁶ ≈ 1.8% emzamweni ngamunye, futhi iseshini yokujikeleza okungu-200 iqukethe mhlawumbe imizamo engu-100, ngakho ukwaphuka kufika cishe emaseshinini amane kwamahlanu alobo bude. Amathuba ochungechunge ku-roulette yisizathu sokuthi lokho kuwela eweni kungeyona into engavamile.
Izinombolo ezishisayo nezibandayo
Izibalo ezifanayo zisebenza ku-straight upukubhejaI-straight upInombolo eyodwa, kukhokha u-35:1.Funda konke →. Ekujikelezeni okungu-300 inani elilindelekile lenombolo ngayinye lingu-8.1; ukuchezuka okujwayelekileizibaloUkuchezuka okujwayelekileImpande yesikwele yokuguquguquka (variance); ibanga elivamile lomphumela ukusuka enanini elilindelekile.Funda konke → kucishe kube ngu-2.8. Enye inombolo izophuma izikhathi ezingu-15 kanti enye izikhathi ezi-2 ngenhlanhla nje, njalo. Ibhodi lemiphumela eligqamisa izinombolo “ezishisayo” ligqamisa phezulu kokusabalala okujwayelekile. ILabhorethri ye-roulette ichaza ukuthi kudingeka ukujikeleza okungakanani ngaphambi kokuba inombolo eshisayoinganekwaneInombolo eshisayoInombolo evele kaningi kunalokho obekulindelekile muva nje. Esondweni elingenzeleli ayibikezeli lutho.Funda konke → isho okuthile (izinkulungwane, esondweni elilodwa elaziwayo).
Ukuzimela kuyiphuzu lonke
Uchungechunge lwezibomvu eziyishumi alwenzi okumnyama kube namathuba amakhulu, futhi alwenzi nokubomvu kube namathuba amakhulu. Kokubili kungu-18/37. Uchungechunge luwuphawu lokulandelana okungahleliwe futhi bekungaba yinto esolisayo uma lungekho: ukulandelana kokujikeleza okungu-200 kungenalo uchungechunge oludlula olune bekungaba wubufakazi obunamandla kakhulu bokuphazanyiswa kunalokho okunochungechunge lweshumi nambili.
Ifomula
Imibuzo
Uchungechunge oludumile yilolo lwezimnyama ezingu-26 e-Monte Carlo ngomhla ka-18 Agasti 1913. Ezibomvu ezingu-32 ngokulandelana zabikwa ekhasino yaseMelika ngo-1943. Kokubili kuyahambisana nenhlanhla uma ucabanga ukuthi amakhasino ajikelezisa isondo kangaki.
Kungu-18/37 noma kunjani. Bheja lokho okushiwo yicebo lakho, noma ungabheji lutho.
Cha. Ukuchema kubonakala ngokuthi amagodiokokusebenzaIgodiEsinye sezikhala ezingu-37 ezinezinombolo ku-rotor. Kubuye kuthiwe: slot, cup.Funda konke → athile aphuma kaningi ekujikelezeni okuyizinkulungwane, hhayi ngochungechunge lombala.
Ubumnandi bezibalo
Zama lezi ngokwakho kuqala. Isixazululo ngasinye sifihliwe; sivule uma usukulungile.
Esondweni laseYurophu kudingeka ukujikeleza okungakanani, ngokwesilinganiso, ngaphambi kokuthi zonke izinombolo ezingu-37 ziphume okungenani kanye?
Bonisa isixazululo
Impendulo Cishe ukujikeleza okungu-155 ngokwesilinganiso; i-median (inani eliphakathi) ingu-147.
Bala isikhathi sokulinda inombolo entsha eyodwa ngesikhathi. Ukujikeleza kokuqala kuhlala kubonisa inombolo entsha. Uma usubone inombolo engu-1, amagodiokokusebenzaIgodiEsinye sezikhala ezingu-37 ezinezinombolo ku-rotor. Kubuye kuthiwe: slot, cup.Funda konke → angu-36 kwangu-37 amasha, ngakho inombolo entsha elandelayo ithatha ukujikeleza okungu-37/36 ngokwesilinganiso. Uma usubone izinombolo ezingu-k, kuthatha u-37/(37 − k).
Hlanganisa izikhathi zokulinda: 37/37 + 37/36 + 37/35 + … + 37/1 = 37 × (1 + 1/2 + 1/3 + … + 1/37) ≈ 37 × 4.20 = 155.5 wokujikeleza.
Iningi lalokho kusekugcineni. Inombolo yokugcina iyodwa ithatha ukujikeleza okungu-37 ngokwesilinganiso, kuthi ezinhlanu zokugcina zithathe cishe okungu-85. Esondweni laseMelika isibalo esifanayo sinikeza cishe u-161. Lena yinkinga yomqoqi wamakhuphoni (coupon collector’s problem); isilinganiso esifanayo sivela esibalweni esijwayelekile.
Ekujikelezeni okungu-37 kwesondo laseYurophu, ukujikeleza okukodwa egodini ngalinye, kufanele ulindele ukubona izinombolo ezehlukene ezingaki?
Bonisa isixazululo
Impendulo Cishe u-23.6. Cishe ingxenye yesithathu yezinombolo, cishe u-13, aziphumi nhlobo.
Thatha inombolo eyodwa, isibonelo u-17. Ekujikelezeni ngakunye ayiphumi ngamathuba angu-36/37, ngakho iphuthelwa yikho konke ukujikeleza okungu-37 ngamathuba angu-(36/37)³⁷ ≈ 0.363.
Yonke inombolo inamathuba afanayo, ngakho ngokwesilinganiso izinombolo ezingu-37 × 0.363 ≈ 13.4 azikho, kuthi ezingu-37 − 13.4 ≈ 23.6 ziphume, eziningi zazo kabili noma ngaphezulu.
Abadlali be-roulette bakubiza ngokuthi umthetho wengxenye yesithathu (law of thirds). Akuwona umthetho, kumane kuyizibalo zokuphindaphindeka: ochungechungeni olude njengesondo, cishe ingxenye yesithathu yezinombolo ayiphumi, esondweni elilungile njengakwelinye. Emagodini angu-38 ingxenye ingu-(37/38)³⁸ ≈ 0.363 nayo; esondweni elikhulu izinza eduze no-1/e ≈ 0.368.
Umngane wakho ukukhombisa izinhlu ezimbili zemibala engu-50, bomvuukubhejaBomvuUkubheja okulingana nemali ezinombolweni eziyi-18 ezibomvu. NgesiFulentshi: rouge.Funda konke → noma mnyamaukubhejaMnyamaUkubheja okulingana nemali ezinombolweni ezimnyama eziyi-18. NgesiFulentshi: noir.Funda konke →, okuthiwa ngayinye ivela esondweni lapho amaqandaisondoIqandaIgodi elilodwa eliluhlaza elingambozwa ukubheja okulingana nemali, okwedazini noma okwekholamu; umthombo wenzuzo yekhasino. Kubuye kuthiwe: iqanda elilodwa, 0.Funda konke → engabalwanga. Olunye lushintsha umbala izikhathi ezingu-25 futhi uchungechunge lwalo olude kakhulu luyisithupha. Olunye lushintsha izikhathi ezingu-35 futhi aludluli kwezintathu ngokulandelana. Yiluphi oluqanjiwe?
Bonisa isixazululo
Impendulo Olwesibili. Uhlu lwangempela lushintsha cishe izikhathi ezingu-24 noma ezingu-25. Uhlu olunokushintsha okungu-35 luvela cishe kanye ezinhlwini ezingu-500, kanti olungenalo uchungechunge olude kunezintathu luvela cishe kabili ezinhlwini ezingu-100.
Umbala omusha ngamunye uphinda owandulele noma ushintshe, ingxenye nengxenye, ngakho amathuba angu-49 okushintsha anikeza ukushintsha okungu-24.5 ngokwesilinganiso, kungaba ngaphezulu noma ngaphansi ngo-3.5. Amashumi amathathu nanhlanu ayizinyathelo ezintathu ezinjalo ngaphezu kwesilinganiso; isondo elilungile likhiqiza ukushintsha okungaka cishe kanye ezinhlwini ezingu-500.
Izichungechunge zitshela indaba efanayo. Uhlu lwangempela lwemibala engu-50 lunochungechunge lwezine noma ngaphezulu cishe ku-98% wezikhathi, futhi uchungechunge lwalo olude kakhulu luvame ukuba yizinhlanu noma eziyisithupha.
Abantu abacelwa ukuthi baqambe uhlu olungahleliwe bashintsha kaningi kakhulu, ngoba uchungechunge lwezine noma ezinhlanu kubo lubukeka njengephethini. U-Taylor (2021) ubonisa uphawu olufanayo ezinhlwini zokuphonsa uhlamvu lwemali eziqanjwe abafundi: ukungahleleki kwangempela kunezichungechunge eziningi kunalokho abantu abakulindele.
Incwadi yezindaba zekhasino ilandisa ngomdlali inombolo yakhe eyaphuma izikhathi ezinhlanu ngokulandelana futhi ikubiza ngokuthi irekhodi. Lokho kuyivelakancane kangakanani esondweni laseYurophu? Futhi kufanele kwenzeke kangaki endaweni ethile ekhasino eyodwa enamatafula angu-20, ngalinye lijikeleza izikhathi ezingu-40 ngehora, imini nobusuku?
Bonisa isixazululo
Impendulo Inombolo eqanjwe kusengaphambili iphuma izikhathi ezinhlanu ngokulandelana: 1 ku-69 wezigidi. Noma iyiphi inombolo iphinda izikhathi ezine ngemuva kokuphuma kwayo okokuqala: 1 ku-1.87 wezigidi. Leyo khasino ijikeleza cishe izikhathi eziyizigidi ezingu-7 ngonyaka, ngakho kufanele ibone uchungechunge lwezinhlanu kathathu noma kane ngonyaka.
Inombolo eqanjiwe iphuma ngamathuba angu-1/37 ekujikelezeni ngakunye, ngakho ezinhlanu ngokulandelana zinamathuba angu-(1/37)⁵ = 1 ku-69,343,957. Kodwa akekho oqamba inombolo kusengaphambili. Noma yini ephuma kuqala, ukujikeleza okune okulandelayo kumele kuyiphinde: (1/37)⁴ = 1 ku-1,874,161.
Amatafula angu-20 × ukujikeleza okungu-40 × amahora angu-24 × izinsuku ezingu-365 = ukujikeleza okungu-7,008,000 ngonyaka. Ukujikeleza ngakunye kungaqala uchungechunge, ngakho ikhasino ilindele izichungechunge zezinhlanu ezingu-7,008,000/1,874,161 ≈ 3.7 ngonyaka.
Alikho irekhodi elisemthethweni lalolu hlobo, futhi akudingeki: into engavamile etafuleni elilodwa iyinto ejwayelekile ekhasino yonke, futhi izindaba zixoxwa ngetafula lapho kwenzeke khona. Indaba, ku-Goldman (2007), yenzeka esondweni elinamaqanda amabili, lapho izibalo zingu-1 ku-79 wezigidi no-1 ku-2.09 wezigidi.
Okokuhlekisa
Uchungechunge olude yindlela okungahleliwe okubukeka ngayo.
Imithombo
- 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.