Fakahinohino Sitepu: Ko ha Taimi Vaʻinga Martingale
Ko e tola ʻe hongofulu ki he kulokula, ʻo fakaua hili ʻa e mole kotoa pē, ʻi ha tēpile ʻo e $500. Vilo ki he vilo, kau ai ʻa e vilo ʻoku ne fakaʻosi ia.
Ko ha taimi vaʻinga faʻifaʻitaki Martingale mei ha paʻanga vaʻinga ʻo e $1,000. Ikuna siʻisiʻi ʻe fāngofulu-mā-taha, pea mole ʻe ono hokohoko mo ha peti hono fitu naʻe taʻetali. ʻOku ʻosi ʻa e taimi vaʻinga ʻi he mole ʻo e $220 hili hono tupu ʻaki ʻa e $410, ʻa ia ko e meʻa ia ʻoku fai ʻe he sisitemi.
Ko e palani
Peti ʻaki ʻa e $10 ki he kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa →. Hili ha mole, fakaua. Hili ha ikuna, foki ki he $10. 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 → $500, ko ia ko e ngaahi peti ko e 10, 20, 40, 80, 160, 320 pea mo ha peti ʻo e $640 ʻe taʻetali ʻe he tēpile. ʻOku maumau ʻa e sisitemi ʻi he mole ʻe ono hokohoko; ʻoku ʻi he feinga taki taha ʻa e (19/37)⁶ ≈ 1.8% ke hoko ai ia, pea ʻoku ʻi ha taimi vaʻinga ʻo e vilo ʻe 100 ha feinga ʻe 50 nai. ʻAmanekina: ko ha faingamālie ʻo e 60% nai ke maumau ʻi loto ʻi he vilo ʻe 100, mo ha mole ʻo e $630 ʻi he taimi ʻoku hoko ai.
Vilo 1–30
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 → angamaheni: ngaahi hokohoko mole ʻe taha ki he tolu, ʻoku fakaʻosi taki taha ʻe ha ikuna ʻoku maʻu ai ʻa e +$10. ʻI he vilo 30 kuo mau maʻu ʻa e ikuna ʻe 17, ʻoku tāpuni ʻe he taha kotoa ha takai, pea ʻoku mau tupu ʻaki ʻa e $170. Ko e peti lahi taha ʻo aʻu mai ki heni ko e $80 hili ha mole ʻe tolu. ʻOku ongoʻi hangē ha misini paaki ʻo e ngaahi pepa paʻanga $10.
Vilo 31–60
Ko e meʻa tatau pē, mo ha takai ʻe taha ʻo e mole ʻe fā (ko e ngaahi peti ʻo aʻu ki he $160, pea mo ha ikuna) ʻa ia naʻe tuku nounou ai ʻa e $310 ʻi he tēpile pea naʻe ongoʻi hangē ha loto toʻa. Hili ʻa e vilo ʻe 60: takai ʻe 41 kuo kakato, tupu ʻaki ʻa e $410, pea ko e tuʻunga māʻulalo taha ʻo e paʻanga vaʻingapaʻangaPaʻanga vaʻingaKo e fakakātoa ʻo e paʻanga kuo vahe ke vaʻinga ʻaki. Ko e puleʻi ʻo e paʻanga vaʻinga ko e fili pe ko e hā hono lahi ʻoku tuku ki he fakatuʻutāmaki ʻi he peti takitaha mo e taimi vaʻinga takitaha.Lau kotoa → talu mei he vilo 30 ko e $1,040. ʻOku hā pehē ʻa e histogram ʻo e taimi vaʻinga Martingale kotoa pē ʻi he lahi taha ʻo hono lōloa.
Vilo 61–66
M M M M M M. Ngaahi peti 10, 20, 40, 80, 160, 320: naʻe mole ʻa e $630. Ko e peti hoko ko e $640; ko e fakangatangata ko e $500. Kuo maumau ʻa e sisitemi. ʻE lava ke mau peti ʻaki ʻa e $500 (pea kapau ʻe ikuna, ʻe kei mole ʻaki ʻa e $130 ʻi he takai) pe kamata foʻou ʻi he $10 pea tali ʻa e mole. Ko e ʻuliʻulipetiʻUliʻuliPeti totongi tatau ki he fika ʻuliʻuli ʻe 18. Faka-Falanisē: noir.Lau kotoa → pe 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 → ʻe ono hokohoko ʻoku ʻi ai hono ngalingalimatematikaNgalingaliKo e faingamālie ʻo ha ola, mei he 0 ki he 1 pe 0% ki he 100%. Fika ʻe taha: 1/37 = 2.70%.Lau kotoa → ʻo e 1.8% ki he takai. Naʻa mau fakalele ha takai ʻe 45 nai. Ko e faingamālie ke aʻu ki he tuʻunga ko ʻeni ʻi ha feituʻu ʻi he takai ʻe 45 naʻe meimei 55%. Naʻe ʻikai ko ha taʻemonūʻia; ko e fika lotoloto ia.
- p10 −$1,000
- p25 −$1,000
- fika lotoloto (median) −$1,000
- p75 +$790
- p90 +$1,690
Ko e ngaahi fakamatala paʻanga
Tupu ʻaki ʻa e $410 hili ʻa e vilo ʻe 60, mole ʻaki ʻa e $220 hili ʻa e 66. Fakakātoa ʻo e peti: ko e $2,100 nai ʻi he vilo ʻe 66, ʻo fehoanaki mo e $660 ki ha tokotaha peti tatau ʻaki ʻa e $10. Ko 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 → ʻi he $2,100 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 e $57; ko homau ola moʻoni −$220 ʻoku meimei ko e vahe tolu ʻe taha ʻo ha mavahe fakasitanatematematikaMavahe fakasitanateAka ua ʻo e vēliani; ko e mamaʻo angamaheni ʻo ha ola mei he mahuʻinga ʻamanekina.Lau kotoa → ʻi lalo ai, ʻa ia ʻoku ʻikai ko ha meʻa fakaofo ki ha sisitemi ʻoku ʻi ai ha iku lōloa ki toʻohema ʻo hono tufaki. Kapau naʻa mau taʻofi ʻi he vilo 60 ʻaki ha fakangatangata ikunafoungaFakangatangata ikunaKo ha taumuʻa tupu kuo fokotuʻu ki muʻa ʻa ia te ke fakaʻosi ai ʻa e taimi vaʻinga.Lau kotoa → ʻo e $400, naʻa mau mei mavahe ʻi he tupu ʻo e $410, pea naʻe mei ʻi he taimi vaʻinga hoko ʻa e 1.8% tatau pē ki he takai.
Ko e meʻa ʻoku fakahā ʻe he taimi vaʻinga
ʻOku liliu ʻe he Martingale ha peti ʻo e 48.65% ki ha hokohoko ʻoku ikuna ʻi he 98% ʻo hono ngaahi takai pea mole 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 2% kehe. ʻOku ʻikai ke ne liliu ʻa e mole ʻamanekina ki he tola; ʻoku ne fakalahi ʻa e ngaahi tola. Ko e tokotaha peti tatau ʻi homau tafaʻaki naʻa ne peti ʻaki ʻa e vahe tolu ʻe taha pea mole, ʻi he ʻavalisi, ʻa e vahe tolu ʻe taha. Ko e tokotaha vaʻinga ʻoku ne fakalele ʻa e sisitemi ko ʻeni ʻi ha taʻu ʻe taha te ne ikuna ʻi he lahi taha ʻo e ngaahi efiafi pea mole ʻa e taʻu.
Ko e hā hono tuʻo lahi ʻo ha hokohoko mole
ʻOku mole ha peti totongi tatau ʻi ha veʻeteka noa ʻe taha ʻi he vilo ʻe 19 ʻi he 37. Ko e laine takitaha ko e ngalingali ke mole kotoa ha hokohoko vilo, mo e lahi kuo mole ai ʻe ha tokotaha vaʻinga Martingale, ʻa ia ʻoku ne fakaliunga ua ʻa e peti hili ʻa e mole kotoa pē.
| mole hokohoko | faingamālie | meimei 1 ʻi he | mole ki he taimi ni | peti hoko |
|---|---|---|---|---|
| 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 |
Ko e ngalingali ko e 19/37 kuo liunga ʻaki ia ʻe ia tuʻo taha ki he mole takitaha, lau mei ha vilo pau ʻe taha. ʻOku lahi ʻa e ngaahi vilo ʻi ha taimi vaʻinga lōloa ʻe lava ke kamata ai ha hokohoko pehē, ko ia ʻi ha efiafi ʻoku mahulu ange hono ngalingali ʻi he meʻa ʻoku fakahā ʻe ha laine ʻe taha.
Ngaahi fehuʻi
ʻOku maumau ia ʻi he mole ʻe hiva kae ʻikai ko e ono: 0.25% ki he takai, pea mole ʻa e $5,110 ʻi he taimi ʻoku hoko ai. Tō taʻefaʻahoko ange, tō māʻolunga ange, −2.70% tatau pē.
Naʻe mei ikuna ia ʻi he 48.65% ʻo e taimi pea tuku ʻa e takai ʻi he −$130 pē. ʻOku ʻikai ha sitepu lelei hili ha Martingale kuo maumau; ʻoku ʻi ai pē ʻa e lahi ʻo e peti te ke fili hoko.
ʻIo, ki he taimi vaʻinga ko ia. ʻIkai ki he ʻavalisi ʻo e ngaahi taimi vaʻinga kotoa.
Vaʻinga mo e Matematika
ʻUluaki feinga ke ke fakaleleiʻi ʻe koe. Kuo pelu ʻa e tali takitaha; fakaava ia ʻi hoʻo mateuteu.
ʻI ha tēpile $1 ki he $500, ʻoku kamata ʻe ha tokotaha vaʻinga 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 → ʻaki ʻa e $1 ki he kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa → ʻi ha veʻeteka 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 → ʻe taha. Ko e mole hokohoko ʻe fiha ʻoku ne taʻofi ʻa e fakaliunga ua, ko e hā hono lahi kuo mole ʻi he taimi ko ia, pea ʻoku tuʻo fiha ʻene hoko?
Fakahā ʻa e tali
Tali Mole ʻe hiva: kuo mole ʻa e $511, pea ko e peti hoko ʻe $512. ʻOku hoko ia ʻo liunga taha ʻi he meimei hokohoko ʻe 403.
Ko e ngaahi peti ko e 1, 2, 4, 8, 16, 32, 64, 128 mo e 256: fakataha ko e $511. Ko hono hongofulu ʻe $512, ʻoku laka ia ʻi he fakangatangata. Ko ha peti ʻe $500 ʻoku ikuna ʻoku kei mole ai pē ʻa e tokotaha vaʻinga ʻa e $11; ko ha peti ʻoku mole ʻoku mole ai ʻa e $1,011.
ʻOku mole ʻa e kulokula ʻi he ngalingali ʻo e 19/37, ko ia ko e mole ʻe hiva hokohoko ʻoku ʻi ai hono ngalingali ʻo e (19/37)⁹ ≈ 0.25%, liunga taha ʻi he meimei hokohoko ʻe 403. ʻOku ikuna ʻe he hokohoko kakato taki taha ʻa e $1, ko ia ʻoku ʻamanekina ʻe he tokotaha vaʻinga ha meimei $402 ʻo e ngaahi ikuna siʻisiʻi kimuʻa pea hoko ʻa e mole pē ʻe taha ʻo e $511, pea ʻoku kei mole pē ʻa e 2.70% ʻo e meʻa kotoa naʻe peti ʻi he ʻavalisi.
ʻI ha veʻeteka noa ua ko e ngalingali ko e (20/38)⁹, liunga taha ʻi he meimei 323. ʻOku paaki ʻe Bollman (2021) ʻa e “meimei 1 ʻi he 833”, ʻa ia ko e (18/38)⁹, ko e ngalingali ia ʻo ha ikuna ʻe hiva hokohoko.
Meʻa fakaoli
Ikuna siʻisiʻi ʻe fāngofulu-mā-taha mo e mole lahi ʻe taha. Ko e sisitemi kotoa ia.
Ngaahi Maʻuʻanga
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”