Umlando wezinhlelo zokubheja ku-roulette
Amakhulu amabili eminyaka abantu bebhala phansi imithetho yokushintsha inani abalibhejayo.

I-Martingale ingeyekhulu le-18; i-D’Alembert iqanjwe ngesazi sezibalo esasingayithandi; i-Labouchère yayiwumdlalo wokuzilibazisa kasopolitiki wenkathi kaVictoria. Akukho neyodwa kuzo eyasebenza nangaleso sikhathi.
Martingale
Igama livela olimini lwesitsotsi sabagembuli sesi-Provençal (à la martegalo, “ngendlela yabantu base-Martigues”, ababaziwa ngokunganaki) okusho ukubheja okuphindwa kabili, futhi libhalwe ezichazamazwini zesiFulentshi kusukela ngama-1760. UThorp (1984), elandela i-American Heritage Dictionary, unikeza enye incazelo yesintu: abantu base-Martigues babehlekwa ngemikhuba exakile, phakathi kwayo ukubopha amabhulukwe abo ngemuva, ngakho leli binzana laqala ukusho “ngendlela ehlekisayo”. Kwase kuyindaba yesixwayiso eParis ngekhulu le-18: uCasanova uchaza ukulahlekelwa yingcebo ngokuphinda kabili e-faro eVenice ngama-1750. Izibalo zokuthi kungani yehluleka, umkhawulo wetafulaitafulaUmkhawulo wetafulaInani elincane nelikhulu kakhulu lokubheja elivunyelwe. Umkhawulo ophezulu yiwona omisa ukwenyuswa kwenani okuphindaphinda kabili.Funda konke → kanye nemali yokubhejaimaliImali yokubhejaInani lonke lemali ebekelwe ukudlala. Ukuphatha imali yokubheja kusho ukunquma ukuthi ingakanani yayo ozoyibeka engcupheni ekubhejeni ngakunye nasesheshini ngayinye.Funda konke → enomkhawulo, zase ziqondakala ngama-1770. Kuthiyori yamathubaizibaloAmathubaIthuba lomphumela, kusukela ku-0 kuya ku-1 noma ku-0% kuya ku-100%. Inombolo eyodwa: 1/37 = 2.70%.Funda konke → igama elithi “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 →” laba igama lobuchwepheshe ngama-1930 elisho umdlalo olinganayoizibaloUmdlalo olinganayoUmdlalo lapho kungekho hlangothi olunenzuzo: konke ukubheja kunenani elilindelekile eliyiqanda.Funda konke →, okuyiyona nto eyodwa i-Martingale ye-roulette engeyona.

D’Alembert
UJean le Rond d’Alembert waphikisa ku-Encyclopédie (1754) ukuthi ngemuva kochungechunge lwamakhanda, imisila iba namathuba amakhulu, okungukuchazwa kwakuqala kwephutha lomgembuli yisazi sezibalo esihamba phambili. Uhlelo lokubheja olwengeza iyunithiimaliIyunithiInani elibhejwayo eliyisisekelo uhlelo noma umdlali asebenza ngalo. Ukwenyuswa kwenani kuchazwa ngamayunithi ukuze kusebenze kunoma yiliphi itafula.Funda konke → elilodwa ngemuva kokuhlulwa futhi lukhiphe eyodwa ngemuva kokuwina laqanjwa ngaye ngabagembuli bakamuva ababenenkolelo efanayo. Akaluphakamisanga futhi, ngezinsuku lapho ayecabanga kahle, wayengalwenqaba.
Labouchère
UHenry LabouchèreisuLabouchèreUhlelo lokucisha: bhala umugqa wezinombolo, bheja isamba sezinombolo ezimbili ezisemaphethelweni, uzicishe ngemuva kokuwina, wengeze inani elibhejwe walahleka ngemuva kokuhlulwa.Funda konke → (1831–1912), intatheli, umnikazi wetiyetha neLungu lePhalamende le-Liberal, wenza uhlelo lokucisha lwaziwe kakhulu emphakathini waseLondon ngama-1870 futhi kubikwa ukuthi walusebenzisa e-Monte Carlo. Le ndlela, yokubhala umugqa wezinombolo bese ubheja isamba sezinombolo ezisemaphethelweni, yandulela yena. Igama lakhe lanamathela ngoba wayedume ngezinye izinto futhi ngoba uhlelo lunesici esingavamile sokuthi luvame ukusebenza, okwalwenza lube yindaba yokuxoxwa etafuleni lesidlo sakusihlwa.
UCasanova uyalahlekelwa ngokuphinda kabili e-faro. I-Martingale isindala kakade.
U-d’Alembert ushicilela iphutha elathi kamuva laqanjwa ngegama lakhe njengohlelo.
Igama elithi “Martingale” lingena ezichazamazwini zesiFulentshi njengesitsotsi sabagembuli.
U-Labouchère wenza ukucisha kwaziwe kakhulu eLondon.
Ukwenyuswa kwenani kwe-Fibonacci nokwe-Paroli kuvela ezincwadini zeziqondiso zokugembula.
Izinhlelo “zezigaba” ezisekelwe ekuhlelekeni kwesondo zithengiswa ngeposi.
UHalmos, umfundi kaDoob, ufakazela ukuthi alukho uhlelo lokubheja olungaguqula umdlalo ongamzuzisi umdlali ube umdlalo omzuzisayo.
Amakhompyutha alingisa lonke uhlelo. Zonke izinhlelo zibonisa u-−1/37 wemali ebhejwe yonke.
Izinhlelo ezifanayo zithengiswa ku-inthanethi zinemiphumela efanayo, zilingiswa kusiphequluli kule sayithi.
Ikhulu le-20
I-FibonacciisuFibonacciUkwenyuswa kwenani okulandela uchungechunge 1, 1, 2, 3, 5, 8, 13…: isinyathelo esisodwa phambili ngemuva kokuhlulwa, izinyathelo ezimbili emuva ngemuva kokuwina.Funda konke → ne-ParoliisuParoliUkwenyuswa kwenani ngemuva kokuwina: phinda kabili ngemuva kokuwina, buyela ekuqaleni ngemuva kokuhlulwa noma ngemuva kokuwina kathathu kulandelana. Kubuye kuthiwe: i-Martingale ephambene.Funda konke → zangena ezincwadini zeziqondiso zokugembula cishe ngo-1900. Maphakathi nekhulu leminyaka kwafika izinhlelo ezithengiswa ngeposi, ngalunye lunobufakazi bomuntu othile nesiqinisekiso sokubuyiselwa imali, kanye nokulingisa kokuqala ngekhompyutha, okwabonisa lokho izibalo ezase zikushilo. Ubufakazi bokuthi alukho uhlelo olungasebenza base bukhona: uJoseph Doob (1936) noPaul Halmos (1939) babonisa ukuthi awukho umthetho wokukhetha ukuthi uzobheja nini futhi malini oshintsha umphumela olindelekile womdlalo olinganayo noma ongamzuzisi umdlali, kwathi ucwaningo lukaThorp lwango-1969 lwachaza izimo ngendlela abagembuli abahlangabezana nazo ngayo. Kusukela lapho izinhlelo azishintshanga; ukumaketha sekusuke emapheshaneni kwaya kumavidiyo.

Inganekwane: Isu le-roulette elihlala liwinaIsu le-Fibonacci ku-roulette
Kungani zisaphila
Uhlelo lunikeza umdlali okuthile angakwenza nendaba angayixoxa. Iningi lamaseshini ngaphansi kwezinhlelo eziningi liphela ngokuwina okuncane, okuyindaba engcono kunezibalo. Amaseshini okulahlekelwa ayavama kancane futhi akhunjulwa njengeshwa. Ukumaketha akudingi ukuqamba amanga ngamathuba; kudinga nje ukubonisa iseshini yokuwina, futhi ziningi. Impikiswano emelene nalokho, u-2.70% wemali ebhejwe yonkeimaliImali yonke ebhejiweInani lonke elibhejwe phakathi neseshini noma esikhathini esithile, kubalwa nemali ewiniwe ephinde yabhejwa. Kubuye kuthiwe: handle, action.Funda konke →, ibikhona kusukela ngo-1796 futhi ayikaze ikholise njengobusuku benhlanhla.
Izinhlelo ezithengiswayo
Abahwebi bekhulu le-20 baletha amaqhinga abo amasha, ngalinye liwukuhlelwa okusha kokubheja okufanayo okulahlekisayo. I-Phase One yathengiswa ngo-$25 kanye no-10% wokuwina komthengi, kwathenjiswa i-Phase Two uma sekukhokhwe u-$500 kanye ne-“Inner Circle” ngo-$5,000. Alikho neqhinga elilodwa kuwo elishintsha izibalo: inani elilindelekileizibaloInani elilindelekileUmphumela ovamile ekubhejeni ngakunye esikhathini eside. U-−1/37 wenani elibhejwayo kukho konke ukubheja okujwayelekile kwaseYurophu.Funda konke → lochungechunge lokubheja liyisamba samanani alo alindelekile.
Okungelona uhlelo
Imithetho yokuyeka: ukunquma kusengaphambili ukuthi uzolahlekelwa noma uwine malini bese uyahamba. Ivame ukuthengiswa njengengxenye yohlelo futhi iyiyona kuphela ingxenye eyenza okuthile, ngoba yehlisa imali ebhejwe yonke. Ayiqanjwanga ngamuntu, okufanelekile.
Imibuzo
I-Martingale, ngekhulu leminyaka noma ngaphezulu. Ukuphinda kabili ngemuva kokuhlulwa kungumqondo wokuqala wawo wonke umuntu.
U-d’Alembert wasondela kakhulu, ngephutha. UPascal, uFermat, uHuygens, uBernoulli noLaplace bonke bachaza ukuthi kungani zehluleka.
Ngoba amaseshini amaningi ayawina, futhi ividiyo yeseshini yokuwina ishibhile ukuyenza.
Okokuhlekisa

Amakhulu amabili eminyaka yamagama. Inombolo eyodwa.
Imithombo
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Doob, J. L. “Note on probability.”
- Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.”
- d’Alembert, J. “Croix ou pile.”
- Schwartz, D. G. Roll the Bones: The History of Gambling.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.