Vēliani
Ko e hā ʻoku ongoʻi ai ko ha peti fika ʻe taha mo ha peti kulokula ʻoku tatau honau 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 → ko ha ongo vaʻinga kehekehe.
ʻOku fua ʻe he vēliani pe ʻoku mafola fēfē ʻa e ngaahi ola ʻi he mahuʻinga ʻamanekina. Ki he iuniti naʻe peti ʻoku meimei 34 ia ki ha peti fika ʻe taha pea meimei 1 ki he kulokula.
Ko e fomula ki ha peti ʻe taha
Ki ha peti ʻoku totongi ʻa e W ki he 1 ʻaki ʻa e 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 → p, ko e ola ki he 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 → ko e +W ʻaki ʻa e ngalingali p pea ko e −1 ʻaki ʻa e ngalingali 1 − p. Ko e 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 → ko e pW − (1 − p) = −1/37. Ko e vēlianimatematikaVēlianiKo ha fua ʻo hono mafola ʻo e ngaahi ola takatakai ʻi he mahuʻinga ʻamanekina. Māʻolunga ki he peti fika ʻe taha, māʻulalo ki he ngaahi peti totongi tatau.Lau kotoa → ko e E[X²] − EV² = pW² + (1 − p) − (1/37)². Ki ha peti fika ʻe tahapetiPeti fika ʻe tahaFika pē ʻe taha, totongi ʻo e 35:1.Lau kotoa →: (1/37)(1225) + 36/37 − 0.0007 ≈ 34.08. Ki he kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa →: 18/37 + 19/37 − 0.0007 ≈ 0.999.
Ko hono ʻuhinga ki ha taimi vaʻinga
ʻOku tānaki ʻa e ngaahi vēliani ʻi he ngaahi vilo tauʻatāinamatematikaNgaahi vilo tauʻatāinaʻOku tatau pē ʻa e ngalingali ʻi he vilo takitaha neongo pe ko e hā naʻe hoko kimuʻa. Ko e tefito ia ʻo e fakatatau kotoa pē ʻi he uepisaiti ni.Lau kotoa →, ko ia ʻi ha vilo ʻe N ʻaki ha peti tatau ko e vēliani ʻo e fakakātoa ko e N × peti² × σ², pea ko e mavahe fakasitanatematematikaMavahe fakasitanateAka ua ʻo e vēliani; ko e mamaʻo angamaheni ʻo ha ola mei he mahuʻinga ʻamanekina.Lau kotoa → ko e σ × peti × √N. Vilo ʻe 100 ʻi he $10: ko e mavahe fakasitanate ʻoku meimei $584 ki he ngaahi peti fika ʻe taha pea $100 ki he kulokula, ʻo takatakai ʻi he ʻamanekina tatau ʻo e −$27. ʻOku sio ha tokotaha vaʻinga ʻe taha ki he ngaahi ola ʻoku kalakala ʻi he ngaahi teau; ʻoku sio ʻa e tokotaha kehe ki ha kiʻi ʻalu māmālie. ʻOku na totongi fakatouʻosi ʻa e mahuʻinga tatau.
Vēliani mo e ngaahi sisitemi
ʻOku ʻikai liliu ʻe ha 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 → ʻa e EV ki he iuniti naʻe peti ka ʻoku ne liliu ʻa e lahi naʻe peti mo e fōtunga ʻo e tufaki. ʻOku fakasiʻisiʻi ʻe he 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 → ʻa e vēliani ʻo e lahi taha ʻo e ngaahi taimi vaʻinga (ngaahi kiʻi ikuna lahi) pea tānaki ha iku matolu (ko e mole lahi ʻoku tātātaha); ko e vēliani fakakātoa ʻi he ngaahi taimi vaʻinga kotoa ʻoku māʻolunga ange ia 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 → koeʻuhi ko e iku ko ia. ʻOku fai ʻe he ParolifoungaParoliFakalakalaka fakapapau: fakaua hili ha ikuna, kamata foʻou hili ha mole pe hili ha ikuna ʻe tolu hokohoko. ʻOku toe ui: Martingale fakafoki.Lau kotoa → ʻa e fakafepaki. Ko hono fili ha sisitemi ko hono fili ha fōtunga ʻo e vēliani; ʻoku ʻikai ke lava ke fili ʻa e ʻavalisi.
- p10 −$500
- p25 −$500
- fika lotoloto (median) −$500
- p75 +$40
- p90 +$1,120
Founga Lulēti Peti TatauFounga Lulēti Paroli (Martingale Fakafoki)
Ko e hā ʻoku mahuʻinga ai ki ha tokotaha vaʻinga
Ko e vēliani ʻa e meʻa ʻoku ʻikai lava ai ke tomuʻa ʻiloʻi ʻa e ngaahi taimi vaʻinga nounou kae lava ʻa e ngaahi taimi lōloa. ʻAki ʻa e σ = $100 mo e EV = −$27 ʻi ha vilo ʻe 100, ko e tuʻunga lelei ko e kuata ia ʻo e longoaʻa pea ko ha taimi vaʻinga tupu ko ha meʻa angamaheni. ʻI ha vilo ʻe 10,000 ko e EV ko e −$2,700 pea ko e σ ko e $1,000; ko e tuʻunga lelei he taimí ni ʻoku meimei liunga tolu ʻi he longoaʻa pea ko ha hokohoko tupu ko ha meʻa ʻo e sikima ʻe tolu (three-sigma). Ko e vēliani ko e kaungāmeʻa ia ʻo e tokotaha vaʻinga ʻi he taimi nounou pea ʻo e kasino ʻi he taimi lōloa.
Vēliani ʻo ha fakatahaʻi
Ki ha ngaahi peti ʻe lahi ʻi he vilo tatau, ʻoku fekauʻaki ʻa e ngaahi ola (ko ha hū ʻa e 17 ko ha hū foki ia ʻi he ʻuliʻulipetiʻUliʻuliPeti totongi tatau ki he fika ʻuliʻuli ʻe 18. Faka-Falanisē: noir.Lau kotoa → mo e tasinipetiTasini1–12, 13–24 pe 25–36, totongi ʻo e 2:1.Lau kotoa → hono ua), ko ia ʻoku ʻikai ke tānaki noa pē ʻa e ngaahi vēliani. ʻOku fakafuofua ʻe he meʻangāue Bet Builder ʻa e tufaki totonu ki ha faʻahinga sipipaʻangaSipiKo ha fakaʻilonga ʻoku fakafofongaʻi ha paʻanga paʻu, ʻoku tuku ki he palani ʻo e tēpile ke fai ʻaki ha peti. ʻOku toe ui: check.Lau kotoa → pē ʻaki hono lau ʻa e ola kotoa ʻe 37, ʻa ia ko e founga totonu pē ʻe taha ke fai ai.
Fomula
Ngaahi fehuʻi
ʻIkai. ʻOku tatau ʻa e mahuʻinga ʻamanekina ʻo e peti kotoa pē. Ko e vēliani māʻolunga ange ʻoku ʻuhinga ia ki ha kalakala lahi ange ʻo takatakai ai.
Ko e ngaahi peti totongi tataupetiPeti totongi tatauKulokula/ʻuliʻuli, taʻehoa/hoa, māʻolunga/māʻulalo. Fika ʻe 18, totongi ʻo e 1:1.Lau kotoa →, ʻi he σ ≈ 1 ki he iuniti. ʻOku toe māʻulalo ange mo e la partagelaoLa partageLao faka-Falanisē: ʻi he hū ʻa e noa, ʻoku fakafoki ʻa e vaeua ʻo ha peti totongi tatau. ʻOku vaeua ai ʻa e tuʻunga lelei ʻo e kasino ʻi he ngaahi peti ko ia ki he 1.35%.Lau kotoa →, ʻa ia ʻoku ne toe fakaleleiʻi foki ʻa e ʻavalisi.
ʻOku tatau ʻa e tupu ʻamanekina ki he tola takitaha; ʻoku uesia pē ʻe he vēliani pe ʻoku taʻemolemole fēfē ʻa e paʻanga hū mai ʻa e kasino, pea ʻoku ʻi ai ha kau vaʻinga ʻe laui afe ʻa e kasino ke fakamolemoleʻi ia.
Vaʻinga mo e Matematika
ʻUluaki feinga ke ke fakaleleiʻi ʻe koe. Kuo pelu ʻa e tali takitaha; fakaava ia ʻi hoʻo mateuteu.
ʻOku peti ʻe ha tokotaha vaʻinga ʻe toko ua ʻa e $1 takitaha ʻi he vilo ʻi he vilo ʻe 100 ʻi ha veʻeteka ʻIulope, ko e tokotaha ki he kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa → maʻu pē, ko e tokotaha ʻe taha ki he 17 maʻu pē. Ko hai ʻoku ngalingali lahi ange ke ʻi muʻa ʻi he ngataʻanga?
Fakahā ʻa e tali
Tali Ko e tokotaha vaʻinga ʻi he 17: 50.9%, ʻi he fāitaha mo e 35.5% ki he kulokula. ʻOku mole fakatouʻosi ʻa e $2.70 ʻi he ʻavalisi.
Kulokula: ʻoku ʻi muʻa ʻa e tokotaha vaʻinga ʻi he ikuna ʻe 51 pe lahi ange ʻi he 100, ʻa ia ko e 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 → takitaha ko e 18/37. ʻOku ʻomi ʻe he tufaki binomial ʻa e 35.5%, pea ko e ikuna ʻe 50 tofu pē, ʻa ia ʻoku tatau pē, ko e 7.7% kehe.
Fika 17: ʻoku fakafoki ʻe he ikuna takitaha ʻa e $36, ko ia ʻoku ʻikai feʻunga ʻa e ikuna ʻe ua (−$28) pea ʻoku feʻunga ʻa e tolu (+$8). Ko e ngalingali ʻo e tonu ʻe tolu pe lahi ange ʻi he vilo ʻe 100 ʻi he 1/37 ko e 50.9%.
ʻOku faʻa ʻi muʻa lahi ange ʻa e tokotaha vaʻinga peti fika ʻe taha, ka ʻoku taʻemaau ange ʻa e ngaahi ola: ko ha tonu ʻe taha lahi ange pe siʻi ange ʻoku ne hiki ʻa e ola ʻaki ʻa e $36, pea ko e kau vaʻinga ʻoku ʻi mui ʻoku nau faʻa ʻi mui mamaʻo ange. ʻOku ʻomi ʻe Bollman (2024) ʻa e ngaahi fika ʻAmelika, 26.5% mo e 49.2%.
Meʻa fakaoli
Mole ʻamanekina tatau. ʻOku talaatu ʻe he taha ʻo kinaua ʻi ha leʻo lahi.
Ngaahi Maʻuʻanga
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.