Isu le-Fibonacci ku-roulette
Esuini le-Fibonacci ku-roulette, amanani abhejwayo alandela u-1, 1, 2, 3, 5, 8, 13… Ya phambili isinyathelo esisodwa ngemuva kokuhlulwa, bese ubuyela emuva izinyathelo ezimbili ngemuva kokuwina.
Alilehluli isondo; alukho uhlelo lwamanani abhejwayo olukwenzayo. Limnene kune-Martingale, ngakho limelana nochungechunge olude lokuhlulwa ngaphambi kokufika emkhawulweni, futhi libuyisa imali kancane. Ukulahlekelwa okulindelekile kuyafana, ku-2.70% wemali yonke ebhejiweimaliImali yonke ebhejiweInani lonke elibhejwe phakathi neseshini noma esikhathini esithile, kubalwa nemali ewiniwe ephinde yabhejwa. Kubuye kuthiwe: handle, action.Funda konke →.
Indlela uchungechunge lwezinombolo olwakhiwa ngayo
Inombolo ngayinye iyisamba sezimbili ezingaphambi kwayo.
Ngakho ngemuva kuka-8 no-13 kuza u-21.
Dweba inombolo ngayinye njengesikwele, futhi izikwele zihlangana kahle: esisha ngasinye side njengezimbili ezingaphambi kwaso uma zibekwe eceleni kwazo. Ingxenye yesine yendingilizi kusikwele ngasinye ihlangana ibe ngumugqa ozombelezayo.
Hamba nochungechunge
Ukuhlulwa kuhambisa isinyathelo esisodwa ngakwesokudla. Ukuwina kubuyisela emuva izinyathelo ezimbili.
Amanani abhejwayo nemiphumela kungamayunithi okubheja okuyisisekelo.
Lusebenza kanjani uhlelo lwe-Fibonacci ku-roulette?
Bhala phansi izinombolo ze-FibonacciisuFibonacciUkwenyuswa kwenani okulandela uchungechunge 1, 1, 2, 3, 5, 8, 13…: isinyathelo esisodwa phambili ngemuva kokuhlulwa, izinyathelo ezimbili emuva ngemuva kokuwina.Funda konke →: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. Ngayinye iyisamba sezimbili ezingaphambi kwayo. Qala kweyokuqala bese ubheja amayunithiimaliIyunithiInani elibhejwayo eliyisisekelo uhlelo noma umdlali asebenza ngalo. Ukwenyuswa kwenani kuchazwa ngamayunithi ukuze kusebenze kunoma yiliphi itafula.Funda konke → angako. Uma uhlulwa, uya isinyathelo esisodwa kwesokudla. Uma uwina, uya izinyathelo ezimbili kwesokunxele, noma ubuyele ekuqaleni uma ingekho indawo. Lolo luhlelo lonke. Ithebula likhombisa ukuthi isinyathelo ngasinye sibiza malini: uchungechunge lokuhlulwa olunqanyulwa umkhawulo wetafulaitafulaUmkhawulo wetafulaInani elincane nelikhulu kakhulu lokubheja elivunyelwe. Umkhawulo ophezulu yiwona omisa ukwenyuswa kwenani okuphindaphinda kabili.Funda konke → noma imali yakho yokubhejaimaliImali yokubhejaInani lonke lemali ebekelwe ukudlala. Ukuphatha imali yokubheja kusho ukunquma ukuthi ingakanani yayo ozoyibeka engcupheni ekubhejeni ngakunye nasesheshini ngayinye.Funda konke → lukulahlekisela isamba sakho konke okubhejiwe kuze kube manje.
Iseshini ibukeka kanjani?
Thatha isisekelo esingu-$10 nokujikeleza okuyisishiyagalombili: L L W L L L W W (L = ukuhlulwa, W = ukuwina). Amanani abhejwayo ahamba ngo-10, 10, 20 (kuwiniwe, emuva kabili, esinyathelweni 1), 10, 10, 20, 30 (kuwiniwe, emuva kabili, esinyathelweni 2), 10 (kuwiniwe, emuva ekuqaleni). Okulahlekile: 10 + 10 + 10 + 10 + 20 = 60. Okuwiniwe: 20 + 30 + 10 = 60. Ukuhlulwa okuhlanu, ukuwina okuthathu, futhi usulingana. Lokho yikho okuheha kulolu hlelo. Izindleko zisemgqeni ofanayo: kudinge u-$120 wokubheja ukuze ufike lapho, futhi lonke idola elibhejwayo liphethe inzuzo yekhasinoizibaloInzuzo yekhasinoIngxenye yenani ngalinye elibhejwayo ikhasino eyigcinayo ngokwesilinganiso: ama-2.70% ku-roulette yaseYurophu.Funda konke →.
Kungani ubuyela emuva kabili, hhayi kanye?
Ngoba ukuwina okukodwa kukhokhela ukulahlekelwa okubili ncamashi. Inombolo ngayinye iyisamba sezimbili ezingaphambi kwayo, ngakho ukuwina emayunithini angu-5 kubuyisa u-2 no-3 alahleke ngaphambi nje kwalokho. Cabanga ngezitebhisi: isinyathelo esisodwa phezulu ngakho konke ukuhlulwa, izinyathelo ezimbili phansi ngakho konke ukuwina. Isinyathelo omi kuso yisikweletu sakho. Esinyathelweni 5 usuhlehle ngamayunithi angu-7, esinyathelweni 8 usuhlehle ngangu-33, futhi uma ubuyele esinyathelweni sokuqala ulingana ncamashi. Inzuzo ivela kuphela ekuwineni esinyathelweni sokuqala, iyunithi elilodwa ngesikhathi.
Njengoba ukuwina cishe kulingana nokuhlulwa, izinyathelo ezimbili ngesisodwa zizwakala njengentengo enhle, futhi isikhathi esiningi izitebhisi ziyakwehlisela phansi ngempela. Inkinga ukuthi izinyathelo ziba zinde njengoba ukhuphuka. Ukuwina okuyishumi esinyathelweni sokuqala kuzuza amayunithi angu-10. Ukuhlulwa okuthathu ezinyathelweni 6, 7 no-8 kubiza 8 + 13 + 21 = 42.
- p10 −$500
- p25 −$500
- phakathi −$500
- p75 +$250
- p90 +$920
Ingabe uhlelo lwe-Fibonacci luyasebenza?
Cha. Hhayi njengendlela yokuphuma usaphambili. Ukubala kuyafana nakulo lonke uhlelo: ukubheja ngakunye kulahlekelwa ngu-1/37 wenani elibhejwayo ngokwesilinganiso, ngakho lonke uchungechunge lulahlekelwa ngu-1/37 wakho konke okubhejiwe. Ukusebenzisa uchungechunge lwe-Fibonacci ku-roulette akukushintshi lokho, ngoba isondo likhokha amathuba afanayo noma ngabe ithokheniimaliIthokheniUphawu olumele inani elinqunyiwe, olubekwa ethebuleni lokubheja ukuze ubheje. Kubuye kuthiwe: check.Funda konke → likhulu kangakanani. Amanani abhejwayo e-Fibonacci akhuphuka kancane, ngakho libheja imali eningi ngokujikeleza ngakunye kunalokho ukubheja inani elingaguqukiisuUkubheja ngenani elilodwaUkubheja inani elifanayo kukho konke ukujikeleza. Isisekelo okuqhathaniswa naso konke ukwenyuswa kwenani.Funda konke → okwenzayo, futhi ukulahlekelwa kwalo okulindelekileizibaloUkulahlekelwa okulindelekileInani elilindelekile liphindaphindwe ngemali yonke ebhejiwe; inani elilahlekayo ngokwesilinganiso phakathi neseshini noma esikhathini esithile.Funda konke → ngeseshini ngayinye kuphezulu. 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 → ibheja imali eningi nakakhulu, futhi ilahlekelwa kakhulu.
Ingabe liphephile kune-Martingale?
Lihamba kancane, okungeyona into efanayo. Amanani abhejwayo e-Fibonacci akhula cishe ngo-1.6× ngesinyathelo esikhundleni sika-2×, ngakho umkhawulo ongu-$500 ufinyelelwa ngemuva kokuhlulwa okulandelanayo okungaba yishumi kusuka esisekelweni esingu-$10 esikhundleni sokuyisithupha. Lokho kwenza iwa lingavami: ukuhlulwa okuyishumi kulandelana ekubhejeni okulingana nemali kungu-(19/37)¹⁰ ≈ 0.13%, uma kuqhathaniswa no-(19/37)⁶ ≈ 1.8% kokuyisithupha. Kodwa iwa liphinde libe phezulu, ngoba kubhejwe imali eningi endleleni eya khona, futhi ukuwina okukodwa akulilungisi.
Izinombolo zivelaphi?
Ziqhamuka endumbazaneni ngonogwaja. U-Leonardo wase-Pisa, kamuva owaqanjwa igama elithi Fibonacci, wayibeka encwadini yakhe ethi Liber Abaci ngo-1202: qala ngepheya elilodwa, vumela lonke ipheya likhiqize ipheya elisha nyanga zonke kusukela enyangeni yalo yesibili, bese ubala amapheya. Impendulo ihamba ngo-1, 2, 3, 5, 8, 13. Wayengesuye owokuqala ukuthola lo mthetho. Izazi zaseNdiya zesigqi senkondlo zazike zawubhala ngaphambili: u-Singh (1985) uwulandela emuva ku-Virahanka, phakathi kuka-600 no-800, bese kuya ku-Gopala naku-Hemachandra.
Akekho kubo owayecabanga ngesondo. Imithombo esetshenziswe lapha ayisho ukuthi ngubani owaqala ukubheja imali ngalolu chungechunge. Ekukhombisayo ukuthi izibalo zalo nezibalo ze-roulette azihlangani neze: ezokuqala zisho ukuthi amanani abhejwayo akhula kanjani, ezesibili zisho ukuthi inani ngalinye elibhejwayo libuyisa malini.
Kulahleka malini ngemuva kochungechunge lokuhlulwa?
Izibalo ezimbili zokulingana (identities) zenza ithebula elingenhla kube lula ukulihlola. Ngemuva kokuhlulwa okungu-n kulandelana isamba esilahlekile siyinombolo ye-Fibonacci ye-(n + 2) kususwe u-1, okunikeza u-1, 2, 4, 7, 12, 20 njalonjalo, futhi inani elibhejwayo elilandelayo liyinombolo ye-Fibonacci ye-(n + 1). U-Bollman (2021) ufakazela umphumela ofanayo nge-induction ochungechungeni oluqala ngo-1, 2, 3, olususa inombolo ngayinye indawo eyodwa. Emkhawulweni wamayunithi angu-500 kusuka ekuqaleni kweyunithi elingu-1, i-Martingale ayikwazi ukwenza ukubheja kwayo kwe-10, okungamayunithi angu-512. I-Fibonacci ingakwenza okwe-14, okungamayunithi angu-377, kodwa hhayi okwe-15, okungu-610.
Yini eshintshayo edazinini noma ekholamuni?
EdazininiukubhejaIdazini1–12, 13–24 noma 25–36, kukhokha u-2:1.Funda konke → noma ekholamuniukubhejaIkholamuIzinombolo eziyishumi nambili ekholamu eyodwa eqondile yethebula lokubheja, kukhokha u-2:1.Funda konke →, ekhokha u-2 ku-1, ukubuyela emuva akudingeki. Ukuwina ngenani elibhejwayo elingu-F kukhokha u-2F, okuhlala kungaphezu kwakho konke okulahlekile ngaphambi kwalokho, ngakho konke ukuwina kuqeda uchungechunge usaphambili. Intengo yalokho ukuthi idazini liwina izikhathi ezingu-12 kuphela kwezingu-37, ngakho uchungechunge olude lokuhlulwa luvame kakhulu: ukuhlulwa okuyishumi nane kulandelana edazinini kwenzeka cishe kanye emizamweni engu-242, uma kuqhathaniswa nokuba kanye emizamweni engu-11,000 kokubomvuukubhejaBomvuUkubheja okulingana nemali ezinombolweni eziyi-18 ezibomvu. NgesiFulentshi: rouge.Funda konke →.
Kuthiwani uma uyeka kuphela ngemuva kokuwina kabili kulandelana?
Olunye uhlobo luya phambili isinyathelo esisodwa ngemuva kokujikeleza ngakunye, noma uwina noma uhlulwa, futhi luma kuphela ngemuva kokuwina kabili kulandelana. Uma kunokuhlulwa okungu-n ngaphambi kokuwina okubili, inzuzo iyinombolo ye-Fibonacci ye-(n + 1) kuhlanganiswe no-1: incane uma ukuwina kufika kusenesikhathi, inkulu uma kufika sekwephuzile, futhi iwinwa ngamanani abhejwayo asekhule ngokufanayo. Ukuwina okubili kusenesikhathi kuhlala kufika ngamanani amancane; okwephuzile kungadinga ukubheja okukhulu ngqo ngesikhathi iseshini isimbi kakhulu.
Isilingisi · Fibonacci
Amaseshini angu-2,000 okubheja okulingana nemali, kuqalwa ngemali yokubheja engu-$1,000.
Ukubheja okuyisisekelo $10 · umkhawulo wetafula $500 · ukujikeleza okungu-100 ngeseshini
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-Fibonacci, odlulela isinyathelo esisodwa ochungechungeni 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 | $1 |
| 2 | 26.4% | 4 | $2 | $2 |
| 3 | 13.5% | 7 | $4 | $3 |
| 4 | 7.0% | 14 | $7 | $5 |
| 5 | 3.6% | 28 | $12 | $8 |
| 6 | 1.8% | 55 | $20 | $13 |
| 7 | 0.94% | 106 | $33 | $21 |
| 8 | 0.48% | 207 | $54 | $34 |
| 9 | 0.25% | 403 | $88 | $55 |
| 10 | 0.13% | 784 | $143 | $89 |
| 11 | 0.065% | 1527 | $232 | $144 |
| 12 | 0.034% | 2974 | $376 | $233 |
| 13 | 0.017% | 5792 | $609 | $377 |
| 14 | 0.0089% | 11279 | $986 | $610 |
| 15 | 0.0046% | 21965 | $1,596 | $987 |
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.
Imibuzo
Yebo: phambili ngemuva kokuwina, emuva ngemuva kokuhlulwa. Iziphatha njenge-ParoliisuParoliUkwenyuswa kwenani ngemuva kokuwina: phinda kabili ngemuva kokuwina, buyela ekuqaleni ngemuva kokuhlulwa noma ngemuva kokuwina kathathu kulandelana. Kubuye kuthiwe: i-Martingale ephambene.Funda konke → ehamba kancane.
Ubumnandi bezibalo
Zama lezi ngokwakho kuqala. Isixazululo ngasinye sifihliwe; sivule uma usukulungile.
Dlala uhlobo oluhamba isinyathelo esisodwa ochungechungeni ngemuva kokujikeleza ngakunye, noma uwine noma uhlulwe, futhi lume ngemuva kokuwina kabili kulandelana: amanani abhejwayo angu-1, 1, 2, 3, 5, 8 njalo njalo. Imiphumela yokuqala eyishumi nane ithi W H W H H H W H H H W H H W (W = ukuwina, H = ukuhlulwa). Ukuphi manje, futhi ukubheja okulandelayo kungakanani?
Bonisa isixazululo
Impendulo Usalahlekelwe amayunithiimaliIyunithiInani elibhejwayo eliyisisekelo uhlelo noma umdlali asebenza ngalo. Ukwenyuswa kwenani kuchazwa ngamayunithi ukuze kusebenze kunoma yiliphi itafula.Funda konke → angu-22. Ukubheja okulandelayo kungamayunithi angu-610, futhi ukuwina bekungaqeda iseshini ungaphambili ngamayunithi angu-588.
Amanani abhejwayo yizinombolo zokuqala eziyishumi nane ze-FibonacciisuFibonacciUkwenyuswa kwenani okulandela uchungechunge 1, 1, 2, 3, 5, 8, 13…: isinyathelo esisodwa phambili ngemuva kokuhlulwa, izinyathelo ezimbili emuva ngemuva kokuwina.Funda konke →: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 no-377. Hlanganisa ukuwina bese ususa ukuhlulwa: +1 −1 +2 −3 −5 −8 +13 −21 −34 −55 +89 −144 −233 +377 = −22.
Umphumela wokugcina kwaba ukuwina, ngakho ukuwina okukodwa okwengeziwe kuyakuqeda. Inani elilandelayo elibhejwayo lingu-610: ukuwina kushiya +588, ukuhlulwa kushiya −632 kanye nenani elilandelayo elibhejwayo elingu-987.
Lolu hlobo luhlale luphela uphambili, kodwa lapha ludinga ukubheja kwamayunithi angu-610 ukuze kwenzeke lokho. Ngemithetho ejwayelekile, izinyathelo ezimbili emuva ngemuva kokuwina, imiphumela efanayo eyishumi nane ikushiya usalahlekelwe yiyunithi elingu-1 kuphela, nokubheja okulandelayo okungu-2. U-Bollman (2021), oqala uchungechunge ku-1, 2, 3, uthola ukulahlekelwa ngu-1 nokubheja okulandelayo okungu-3. Imithetho ejwayelekile ilahlekelwa kancane lapha ngoba ukuwina ngakunye kwehlisa amanani abhejwayo.
ukujikelezainani elibhejwayoumphumelaisamba esiqhubekayo11W+121H032W+243H−155H−668H−14713W−1821H−22934H−561055H−1111189W−2212144H−16613233H−39914377W−22Kulolu hlobo olufanayo, kungani ukuhlulwa okungu-n okulandelwa ukuwina okubili kuhlale kushiya inzuzo elingana nenombolo ye-Fibonacci yesi-(n + 1) kuhlanganise no-1?
Bonisa isixazululo
Impendulo Ukuhlulwa okungu-n kuhlangana kube yinombolo ye-Fibonacci yesi-(n + 2) kususwe u-1, futhi ukuwina okubili yizinombolo ezimbili ezilandelayo, ezithi ndawonye zidlule lokho ngenombolo yesi-(n + 1) kuhlanganise no-1.
Bhala u-F₁, F₂, F₃ … esikhundleni sika-1, 1, 2, 3, 5 … Inombolo ngayinye iyisamba sezimbili ezingaphambi kwayo.
Ukuhlulwa: F₁ + F₂ + … + Fₙ. Engeza u-1 kuleso samba, ubhalwe njengo-F₂, bese siyagoqeka: F₂ + F₁ = F₃, bese F₃ + F₂ = F₄, njalo njalo, kuze kube yilapho sonke isamba singu-Fₙ₊₂. Ngakho ukuhlulwa kuhlangana kube ngu-Fₙ₊₂ − 1.
Ukuwina kungamanani amabili alandelayo abhejwayo, u-Fₙ₊₁ no-Fₙ₊₂. Inzuzo: Fₙ₊₁ + Fₙ₊₂ − (Fₙ₊₂ − 1) = Fₙ₊₁ + 1. Ngokuhlulwa okune, lokho kungu-F₅ + 1 = 6 wamayunithi.
Okokuhlekisa
Isilinganiso segolide sihlangana nophawu lokubheja okukhulu kakhulu.
Imithombo
- RouletteDoc. Incazelo yesu nezibonelo.
- Roulette77. Incazelo yesu nezibonelo.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Sigler, L. E. Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation.
- Singh, P. The so-called Fibonacci numbers in ancient and medieval India.