Tui Hala: Ko ha Founga Lulēti ʻoku Ikuna Maʻu Pē
“ʻOku ʻi ai haʻaku sisitemi ʻoku ikuna ʻi he 80% ʻo e taimi.” Mahalo. ʻOku kei mole ai pē ʻa e paʻanga.
ʻE lava ʻe ha sisitemi ʻo ʻai ke faʻa hoko ʻa e ngaahi taimi vaʻinga ikuna. ʻOku ʻikai lava ke ne ʻai ʻa e mahuʻinga ʻamanekina ke ʻi ʻolunga ʻi he noa, koeʻuhi ko e peti kotoa pē ʻoku ne tuku ko e −1/37 ia ʻo hono lahi pea ʻoku tānaki ʻa e ngaahi mahuʻinga ʻamanekina. Ko e ngaahi sisitemi ʻoku faʻa ikuna lahi taha ʻoku mole lahi taha ʻi he taimi ʻoku nau mole ai.
Ko e taukave
Ko e tui: ʻoku ʻi ha feituʻu ha founga lulēti ʻoku ikuna maʻu pē, ko ha sisitemi ʻo e liliu ʻo e lahi ʻo e peti ʻo fakatuʻunga ʻi he ngaahi ola kuo hoko ʻa ia ʻoku ne liliu ʻa e lulēti ko ha vaʻinga ʻoku ikuna ai. Ko e fakamoʻoni ʻoku ʻomai: ko ha hokohoko ʻo e ngaahi taimi vaʻinga ikuna, ko ha vitiō ki he founga ke ikuna ʻi he lulēti ʻi he taimi kotoa pē, ko ha fakamoʻoni ʻa ha taha, ko ha lauʻi pepa fika ʻo ha uike monūʻia. ʻOku faʻa faitotonu ʻa e taukave; ʻoku tui ki ai ʻa e tokotaha koeʻuhi kuo ngāue.
Ko e hā ʻoku hala ai, ʻi ha laine ʻe taha
ʻOku tānaki ʻa e ngaahi mahuʻinga ʻamanekinamatematikaMahuʻinga ʻamanekinaKo e ola ʻavalisi ʻi he peti takitaha ʻi he taimi lōloa. −1/37 ʻo e peti ki he peti ʻIulope angamaheni kotoa pē.Lau kotoa →. Kapau ko e peti taki taha ʻoku ʻi ai hono EV = −1/37 ʻo hono lahi, ko ha hokohoko pē ʻo e ngaahi peti ʻoku ʻi ai hono EV = −1/37 ʻo e fakakātoa naʻe peti, neongo pe ko e hā ʻa e lao naʻa ne fili ʻa e lahi ʻo e ngaahi peti. Ko ha sisitemi ko ha lao ia ki hono fili ʻo e lahi ʻo e ngaahi peti. Ko ia ko e sisitemi kotoa pē ʻoku ʻi ai hono EV = −1/37 ʻo e fakakātoa ʻo e petipaʻangaFakakātoa ʻo e petiKo e fakakātoa ʻo e paʻanga naʻe peti ʻaki ʻi ha taimi vaʻinga pe vahaʻa taimi, kau ai ʻa e paʻanga naʻe ikunaʻi kuo toe peti ʻaki. ʻOku toe ui: handle, action.Lau kotoa →. Ko ha teolemi ʻeni (naʻe fakamoʻoniʻi ia ʻe Doob mo Halmos ʻi he ngaahi taʻu 1930; ʻoku fakahā ʻe Thorp 1969 ʻa e ngaahi tuʻunga), pea ʻoku ʻikai ha tuku kehe ki ha ngaahi lao poto. Ko e tuʻunga pē ʻe taha ʻoku mahuʻinga ke ʻilo ko ha peti siʻi taha: ʻoku peti ʻa e sīpinga ʻa Thorp ʻaki ʻa e $1,000 ki he kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa →, pea mo e seniti ʻe 90, pea mo e seniti ʻe 9 pea pehē atu, ʻo siʻi ange ʻo taʻengata. ʻI he faingamālie ʻo e 18/37 ʻoku ikuna ʻa e ʻuluaki peti pea ʻoku nofo ʻa e tokotaha vaʻinga ʻi he tupu ʻo taʻengata, neongo ko e ola ʻamanekina ʻoku kei −1/37 ʻo e meʻa kotoa naʻe peti. ʻOku taʻofi ia ʻe he peti siʻi taha ʻo ha tēpile moʻoni, pea fakataha mo ia ʻa e ʻamanaki kotoa pē ke nofo ʻi he tupu ʻi he taimi lōloa.
Fakaofi ʻi he Taimi Lōloa: Ko e Lao ʻo e Ngaahi Fika Lalahi ʻi he Lulēti
Ko e hā ʻoku hā ngāue ai
ʻOku ʻai ʻe he ngaahi fakalakalaka petifoungaFakalakalaka petiKo ha lao pē ʻoku ne liliu ʻa e lahi ʻo e peti ʻo fakatatau ki he ngaahi ola kimuʻa. Ko e ngaahi fakalakalaka fakafepaki ʻoku nau hiki hake ia hili ha mole, ko e ngaahi fakalakalaka fakapapau hili ha ikuna.Lau kotoa → ʻoku fakalahi ʻi he mole ke faʻa hoko ʻa e ngaahi taimi vaʻinga ikuna. Ko e MartingalefoungaMartingaleFakalakalaka peti ʻoku ne fakaua ʻa e peti hili ʻa e mole takitaha. Vakai ki he konga Ngaahi Founga ki he meʻa ʻoku ne fai mo e meʻa ʻoku ʻikai te ne fai.Lau kotoa → mei he $10 ʻi ha fakangatangata ʻo e $500 ʻoku ʻosi ai ʻa e 80% nai ʻo e ngaahi taimi vaʻinga ʻo e vilo ʻe 100 ʻi he tupu ʻaki ha iunitipaʻangaIunitiKo e peti tefito ʻoku ngāueʻaki ʻe ha sisitemi pe ha tokotaha vaʻinga. ʻOku fakamatalaʻi ʻa e ngaahi fakalakalaka peti ʻaki ʻa e iuniti koeʻuhi ke ngāue ʻi ha tēpile pē.Lau kotoa → siʻi. Ko ha tokotaha vaʻinga ʻoku ne fakalele ia ʻi ha taimi vaʻinga ʻe uofulu ʻoku ne ikuna ʻa e hongofulu-mā-ono pea manatuʻi ia. Ko e taimi vaʻinga mole ʻe fā ʻoku mole ʻe he taha kotoa ʻo lahi ange ʻi he meʻa ʻoku maʻu ʻe ha taimi vaʻinga ikuna ʻe hongofulu, pea ko e matematika ʻi he taimi vaʻinga ʻe uofulu ʻoku ʻi lalo ʻi he noa. Kuo ʻikai liliu ʻe he sisitemi ʻa e ʻavalisi; kuo ne hiki ʻa e ngaahi mole ki ha ngaahi taimi vaʻinga siʻi ange mo lalahi ange ʻa ia ʻoku faingofua ange ke ui ko e taʻemonūʻia.
Ko e sivi ʻe lava ʻo fai ʻe ha taha pē
ʻOku fakalele ʻe he Meʻa Faʻifaʻitaki ʻo e Ngaahi Founga Lulēti ʻi he uepisaiti ni ha taimi vaʻinga ʻe 10,000 ʻo ha sisitemi pē, pe ko hoʻo koloa polokalama ʻaʻau, ʻi ha sekoni ʻe taha. Fokotuʻu ia ki he sisitemi ʻoku ke tui ki ai pea lau ʻa e ʻavalisi. Kapau naʻe ʻi ʻolunga ʻi he noa ʻa e ʻavalisi ki ha fokotuʻu pē, ʻe pehē ia ʻe he peesi ni. Ko e fokotuʻu kotoa pē, ko e sisitemi kotoa pē, ko e fakangatangata ʻo e tēpiletēpileFakangatangata ʻo e tēpileKo e peti siʻi taha mo e peti lahi taha ʻoku ngofua. Ko e peti lahi taha ʻoku ne taʻofi ʻa e ngaahi fakalakalaka peti fakaua.Lau kotoa → kotoa pē ʻoku ʻomai ai ha ʻavalisi ʻo e −2.70% ʻo e fakakātoa ʻo e peti fakataha mo e longoaʻa. Ko e ngaahi fakamoʻoni ʻa e kakai ko ha sīpinga ʻo e taha pē; ko e meʻa faʻifaʻitaki ko ha sīpinga ʻo e mano ʻe taha.
Ko ha sisitemi ʻoku ʻikai lava ʻo mole
ʻI he 1997 naʻe pulusi ʻe he tokotaha tohi ki he poker ko Mike Caro ha sisitemi lulēti ko ha fakakata, pea naʻe toe pulusi ia ʻe Gambling Times ʻi he 2001. Ko ha lisi ia ʻo e ngaahi peti ke ʻoua ʻe fai: ʻoua ʻaupito ʻe peti ki he kulokula pe ʻuliʻulipetiʻUliʻuliPeti totongi tatau ki he fika ʻuliʻuli ʻe 18. Faka-Falanisē: noir.Lau kotoa →, taʻehoa pe hoa, pe ko e ngaahi noaveʻetekaNoaKo e luo lanu mata pē ʻe taha ʻoku ʻikai kāpui ʻe ha peti totongi tatau, peti tasini pe peti kōlomu; ko e tupuʻanga ia ʻo e tuʻunga lelei ʻo e kasino. ʻOku toe ui: noa ʻe taha, 0.Lau kotoa →; ʻikai ha fika kulokula taʻehoa pea ʻikai ha fika ʻuliʻuli hoa; pea ʻikai ha meʻa ki he 30, pe ki he hokohoko lōloa ʻo e ngaahi luomeʻangāueLuoKo e taha ʻo e ngaahi luo ʻe 37 ʻoku fakafika ʻi he konga vilo. ʻOku toe ui: slot, cup.Lau kotoa → mei he 11 ʻo takai ʻo hangē ko e ʻalu ʻa e uasi ki he 14 ʻi he veʻeteka ʻAmelika. Fakatahaʻi ʻa e ngaahi lao pea ʻoku ʻikai toe ha fika. Ko e ngaahi luo pē ʻoku ʻi tuʻa ʻi he hokohoko ko ia ko e 0, 28, 9, 26, 30 mo e 2; ʻoku tapui ʻa e 30 ʻi hono hingoa, pea ko e toenga ko ha noa, hoa mo ʻuliʻuli, pe taʻehoa mo kulokula. Ko ha tokotaha vaʻinga ʻoku muimui ʻi he sisitemi ʻoku ʻikai ʻaupito peti pea ʻikai ʻaupito mole. Ko hono tuʻunga lelei ko e noa, pea ko e sisitemi lulēti pē ia ʻe taha ʻoku faitotonu ki he founga ʻoku aʻu ai ki ai.
Ngaahi sisitemi kuo fakahingoa, laine ʻe taha taki taha
Ko e ngaahi sisitemi ʻoku fakatau ʻi ha hingoa, pe ko ha fomula ikuna lulēti, ʻoku ʻikai kehe. Ko e taha kotoa ko ha kulupu ʻo e ngaahi peti, pea ʻoku totongi ʻe he peti taki taha ki he veʻeteka ʻa hono 2.70%. ʻOku ngāueʻi ʻe Bollman (2024) ha niʻihi ki ha veʻeteka ʻAmelika, ʻa ia ʻoku fakamole ai ʻa e taha kotoa ʻa e 5.26%; ko ʻeni ʻa kinautolu ʻi ha veʻeteka ʻIulope.
Ko e fakamatala faitotonu
ʻOku liliu ʻe he ngaahi sisitemi ʻa e fōtunga ʻo ha taimi vaʻinga: ʻa e faʻa ikuna, ʻa e lahi ʻo e ngaahi ikuna, ʻa e kovi ʻo e meʻa kovi taha. Ko ha ngaahi fili moʻoni ia pea ʻe lava ke saiʻia ha tokotaha vaʻinga ʻi ha fōtunga ʻe taha ʻi ha fōtunga kehe. Ko e meʻa ʻoku ʻikai liliu ʻe he ngaahi sisitemi ko e fakamole, ʻa ia ko e 2.70% ʻo e meʻa kotoa naʻe peti, pea koeʻuhi ʻoku peti lahi ange ʻa e ngaahi fakalakalaka peti ʻi he peti tataufoungaPeti tatauPeti ʻaki ʻa e paʻanga tatau ʻi he vilo kotoa pē. Ko e tefito ia ʻoku fakahoa ki ai ʻa e fakalakalaka peti kotoa pē.Lau kotoa →, ʻoku nau totongi lahi ange ia.
Ngaahi fehuʻi
Ko e māhina ʻe ono ʻo e ngaahi taimi vaʻinga fakauike ko e taimi vaʻinga ʻe 25 nai. ʻOku ikuna ʻa e Martingale ʻi he 80% ʻo kinautolu. ʻOku haʻu ʻa e ngaahi taimi vaʻinga mole, pea ʻoku nau lalahi ange.
ʻOku fakasiʻisiʻi ʻe he lao taʻofi ʻa e fakakātoa ʻo e peti pea ko ia ʻoku fakasiʻisiʻi ai ʻa e mole ʻamanekinamatematikaMole ʻamanekinaKo e mahuʻinga ʻamanekina liunga ʻaki ʻa e fakakātoa ʻo e paʻanga naʻe peti ʻaki; ko e ʻavalisi ʻo e paʻanga ʻoku mole ʻi ha taimi vaʻinga pe ha vahaʻa taimi.Lau kotoa →. ʻOku ʻikai ke ne ʻai ia ke ʻi ʻolunga ʻi he noa.
ʻIkai ʻi ha veʻeteka faitotonu. ʻI ha veʻeteka hehemalēpiVeʻeteka hehemaKo ha veʻeteka ʻoku ʻi ai hano ngaahi maumau fakatuʻasino ʻoku ne ʻai ke ngalingali lahi ange ʻa e ngaahi luo ʻe niʻihi ʻi he 1/37. ʻOku tātāitaha, pea ʻoku ʻiloʻi pē ʻaki ha ngaahi afe ʻo e ngaahi vilo kuo hiki.Lau kotoa →, ʻa ia ko ha palopalema fakafisiki ia, ʻikai ko ha sisitemi.
Vaʻinga mo e Matematika
ʻUluaki feinga ke ke fakaleleiʻi ʻe koe. Kuo pelu ʻa e tali takitaha; fakaava ia ʻi hoʻo mateuteu.
Ko e sisitemi fakaoli ʻa Mike Caro ʻo e 1997 ki he veʻeteka ʻAmelika ʻoku ne tapui ʻa e kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa → mo e ʻuliʻulipetiʻUliʻuliPeti totongi tatau ki he fika ʻuliʻuli ʻe 18. Faka-Falanisē: noir.Lau kotoa →, taʻehoa mo hoa, pea mo e ongo noaveʻetekaNoaKo e luo lanu mata pē ʻe taha ʻoku ʻikai kāpui ʻe ha peti totongi tatau, peti tasini pe peti kōlomu; ko e tupuʻanga ia ʻo e tuʻunga lelei ʻo e kasino. ʻOku toe ui: noa ʻe taha, 0.Lau kotoa →; ko e ngaahi fika taʻehoa kulokula mo e ngaahi fika hoa ʻuliʻuli; ko e fika 30; pea mo e luomeʻangāueLuoKo e taha ʻo e ngaahi luo ʻe 37 ʻoku fakafika ʻi he konga vilo. ʻOku toe ui: slot, cup.Lau kotoa → kotoa pē ʻi he hokohoko mei he 11 ʻo takai fakatatau ki he vaʻe uasi ki he 14. Ngāueʻaki ʻa e ngaahi lao ʻo taki taha. Ko e fē ngaahi fika ʻoku toe ke peti ki ai?
Fakahā ʻa e tali
Tali ʻIkai ha taha. ʻOku ʻikai ʻaupito peti ʻa e sisitemi, ko ia ko hono tuʻunga lelei ko e noa tofu pē.
Ko hono tapui ʻo e kulokula, ʻuliʻuli, taʻehoa, hoa mo e ongo noa ʻoku toe ai ʻa e ngaahi fika taha mo e ngaahi kulupu siʻisiʻi ʻi he 1 ki he 36.
ʻIkai ha kulokula taʻehoa pea ʻikai ha ʻuliʻuli hoa ʻoku toe ai ʻa e ngaahi kulokula hoa (12, 14, 16, 18, 30, 32, 34, 36) mo e ngaahi ʻuliʻuli taʻehoa (11, 13, 15, 17, 29, 31, 33, 35): fika ʻe hongofulu mā ono. Ko hono tapui ʻo e 30 ʻoku toe ai ʻa e hongofulu mā nima.
ʻI he veʻeteka ʻAmelika, ʻoku kapui ʻe he hokohoko mei he 11 fakatatau ki he vaʻe uasi ki he 14 ʻa e 32 ʻo e luo ʻe 38. Ko e ono ʻoku ʻi tuʻa ai ko e 0, 28, 9, 26, 30 mo e 2. ʻOku ʻi loto ʻi he hokohoko ʻa e fika kotoa ʻe hongofulu mā nima naʻe toe, ko ia ʻoku toʻo foki kinautolu ʻe he lao fakaʻosi. Ko ha sisitemi ʻoku ʻikai ʻaupito peti ko e taha pē ia ʻoku ʻikai ʻaupito mole, pea ko e meʻa ia naʻe fie fakahā ʻe Caro.
ʻOku fakalele fakataha ʻe he Kryptos ha MartingalefoungaMartingaleFakalakalaka peti ʻoku ne fakaua ʻa e peti hili ʻa e mole takitaha. Vakai ki he konga Ngaahi Founga ki he meʻa ʻoku ne fai mo e meʻa ʻoku ʻikai te ne fai.Lau kotoa → ʻe tolu, taha ki he ongo peti totongi tataupetiPeti totongi tatauKulokula/ʻuliʻuli, taʻehoa/hoa, māʻolunga/māʻulalo. Fika ʻe 18, totongi ʻo e 1:1.Lau kotoa → taki taha (māʻolunga pe māʻulalo, taʻehoa pe hoa, kulokula pe ʻuliʻuli), mo e ngaahi peti 1, 2, 4, 8, 16, 32 pea taʻofi hili ha mole ʻe ono. Toʻo ha taha ʻo e tolu ʻi ha veʻeteka ʻIulope. ʻOku tuʻo fiha ʻene mole ʻa e peti kotoa ʻe ono, ko e hā ʻoku maʻu ʻe ha takai ʻe taha ʻi he ʻavalisi, pea ko e hā hono konga ʻo e paʻanga naʻe peti?
Fakahā ʻa e tali
Tali ʻOku ne mole ʻa e ono kotoa ʻo liunga taha ʻi he meimei takai ʻe 55, 1.83% ʻo e taimi, pea ʻoku mole ai ʻa e iunitipaʻangaIunitiKo e peti tefito ʻoku ngāueʻaki ʻe ha sisitemi pe ha tokotaha vaʻinga. ʻOku fakamatalaʻi ʻa e ngaahi fakalakalaka peti ʻaki ʻa e iuniti koeʻuhi ke ngāue ʻi ha tēpile pē.Lau kotoa → ʻe 63. ʻI he ʻavalisi ʻoku mole ʻe ha takai ʻa e meimei iuniti ʻe 0.17 ʻi he iuniti ʻe 6.42 naʻe peti: 2.70%, ko e totongi ia ʻo e peti kotoa pē ʻi he veʻeteka.
ʻOku mole ʻa e peti ʻi he ngalingali ʻo e 19/37, kau ai ʻa e noa. Ono hokohoko: (19/37)⁶ = 0.0183, meimei 1 ʻi he 55, pea ʻoku ʻosi ai ʻa e ngaahi peti 1 + 2 + 4 + 8 + 16 + 32 = 63. Kapau ʻoku ʻikai, ʻoku ngata ʻa e takai ʻaki ha ikuna mo e +1 iuniti.
ʻAvalisi: 1 × (1 − 0.0183) − 63 × 0.0183 = 1 − 64 × 0.0183 = −0.17 iuniti.
Paʻanga naʻe peti: ʻoku tuku maʻu pē ʻa e ʻuluaki peti, ko hono ua hili pē ha mole, pea pehē atu: 1 + 2 × (19/37) + 4 × (19/37)² + … + 32 × (19/37)⁵ = 6.42 iuniti. Pea ko e −0.17/6.42 = −2.70%.
Ko e vilo ʻe ono naʻe tohi ʻoku fakapapauʻi pē ʻe kinautolu pe ko e fē tafaʻaki ʻoku ʻi ai ʻa e peti taki taha, pea ʻoku ʻikai lava ke ʻilo kinautolu ʻe he veʻeteka. Ko hono fakalele ʻo e tolu kotoa ʻoku liunga tolu ai ʻa e paʻanga naʻe peti pea mo e mole ʻi he ʻavalisi. ʻOku ngāue ʻa Bollman (2024) ʻi he sisitemi ʻi ha veʻeteka ʻAmelika, ʻa ia ʻoku mole ai ʻe he taki taha ʻo kinautolu ʻa e ono hokohoko ʻi he 2.1% ʻo e taimi.
Meʻa fakaoli
Ko e faʻa ikuna mo e ikuna paʻanga ko ha ongo fika kehe ia.
Ngaahi Maʻuʻanga
- 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.”
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed.