Fua ʻa Kelly mo e Lulēti
ʻOku fakahā ʻe he fua ʻa Kelly ki ha tokotaha peti ʻoku ʻi ai hono tuʻunga lelei pe ʻe fiha ʻa e lahi ʻo e peti. Ki he lulēti, ʻoku ne ʻomi ha tali mahino: ʻikai ha meʻa.
Peti Kelly = tuʻunga lelei / faingamālie. ʻI ha tuʻunga lelei nēkativi, ʻoku ʻomi ʻe he fomula ha konga nēkativi, ʻa ia ʻoku ʻuhinga ke ʻoua ʻe peti. ʻOku kei ʻaonga pē ʻa e fua ke mahino ai ʻa e ʻuhinga naʻe fakafuofua ai ʻe he kau vaʻinga hehema ʻenau ngaahi peti ʻi he founga naʻa nau fai, mo e ʻuhinga ʻoku totonu ai ki he kakai kehe kotoa ke fakafuofua ʻaki ʻa e patiseti.
Ko e fua
Naʻe fehuʻi ʻe John Kelly (1956) pe ʻe fēfē hano fakafuofua ʻe ha tokotaha peti ʻoku ʻiloʻi hono tuʻunga lelei ʻa e lahi ʻo ʻene ngaahi peti ke lahi taha ai ʻa e tupu ʻi he taimi lōloa 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 →. Ko e tali, ki ha peti ʻoku totongi ʻa e b ki he 1 mo 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 → ikuna ko e p mo e ngalingali mole ko e q = 1 − p, ko hono peti ʻa e konga f* = (bp − q) / b ʻo e paʻanga vaʻinga. Kapau ʻoku pōsitivi ʻa e f*, peti ʻaki ʻa e konga ko iá; kapau ko e noa pe nēkativi, ʻoua ʻe peti. Naʻe ngāue ʻa Kelly ʻi Bell Labs, pea naʻe fokotuʻu ʻe heʻene pepa, “A new interpretation of information rate”, ʻa e palopalema ʻi he ako ʻa Claude Shannon ki he fakamatala: ko ha tokotaha peti ʻoku maʻu ha fakahinohino ʻi ha laine longoaʻa, ʻi ha faingamālie faitotonu, ʻe lava ke ne fakatupu ʻa e paʻanga vaʻinga ʻo aʻu pē ki he vave ʻoku fetuku ai ʻe he laine ʻa e fakamatala. ʻI he 1961, naʻe fakamoʻoniʻi ʻe Leo Breiman ko e peti Kelly, ʻi he taimi lōloa, ʻoku ne ngata ʻi muʻa ʻi ha founga kehe kotoa pē ʻoku kehe moʻoni, pea ʻoku ne aʻu ki ha taumuʻa kuo fokotuʻu ʻi he meimei taimi nounou taha.
Peti Kelly ʻi he lulēti
Ki he kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa →: b = 1, p = 18/37, q = 19/37; f* = (18/37 − 19/37)/1 = −1/37. Ki ha peti fika ʻe tahapetiPeti fika ʻe tahaFika pē ʻe taha, totongi ʻo e 35:1.Lau kotoa →: b = 35, p = 1/37, q = 36/37; f* = (35/37 − 36/37)/35 = −1/1295. ʻOku ʻomi ʻe he peti angamaheni kotoa pē ha konga Kelly nēkativi, koeʻuhí ʻoku maʻu ʻe he peti kotoa pē ha tuʻunga lelei nēkativi, pea ko e peti lelei taha ki he tupu ko e noa. Ko e peti Kelly ʻi he lulēti ko ha founga fakafomula ia ke pehē ai ʻa e meʻa ʻoku pehē ʻe he peesi ʻo e tuʻunga lelei ʻo e kasino: ʻoku ʻikai ha lahi ʻe tupu ai ha paʻanga vaʻinga mei ha peti ʻoku nēkativi hono ʻamanekina.
Ko e feituʻu naʻe ngāue moʻoni ai ʻa Kelly
Naʻe maʻu ʻe he kau vaʻinga hehema ha tuʻunga lelei mo ha palopalema ʻi hono fakafuofua ʻo e peti. Naʻe pau ke fili ʻe Jagger, ko e kau García-Pelayo mo e kau Eudaemons pe ʻe fiha ʻa ʻenau peti ʻi he tuʻunga lelei naʻa nau fuaʻi, pea ko e peti siʻi fau ʻoku ne maumauʻi ʻa e tuʻunga lelei, lolotonga ʻoku fakatuʻutāmaki ʻa e peti lahi fau ke ʻosi ʻa e paʻanga kimuʻa pea hā ʻa e tuʻunga lelei. Ki ha luomeʻangāueLuoKo e taha ʻo e ngaahi luo ʻe 37 ʻoku fakafika ʻi he konga vilo. ʻOku toe ui: slot, cup.Lau kotoa → ʻoku tau ʻo 1 ʻi he 30, ʻoku pehē ʻe Kelly ko e 0.57% ʻo e paʻanga vaʻinga ʻi he vilo ʻe taha ki he fika ko iá: mo e $10,000, ko e meimei $57 ʻi he vilo, ki ha tupu angamaheni ʻo e meimei 0.054% ʻi he vilo, pe ×1.7 ʻi he vilo ʻe 1,000. Ko e tupu ʻavalisi ʻoku liunga ua ia, 0.11% ʻi he vilo, ka ʻoku taumuʻa ʻa Kelly ki he paʻanga vaʻinga angamaheni, ʻo ʻikai ko e ʻavalisi, ʻa ia ʻoku fakalahi ʻe ha ngaahi lele monūʻia siʻi. Ko e vaeua-Kelly ʻa e fili angamaheni ʻi he ngāue koeʻuhí ʻoku taʻepau ʻa e fakafuofua ʻo e tuʻunga lelei.
Angamaheni mo e ʻavalisi
ʻOku lahi ʻa e vahaʻa ʻo e paʻanga vaʻinga angamaheni mo e ʻavalisi. Toʻo ha luo ʻoku tau ʻo 1 ʻi he 25, ko ha tuʻunga lelei ʻo e 44%, ko e fika ia ʻoku ʻomi ʻe Thorp ki heʻene meʻangāue. ʻOku peti ʻe Kelly ʻa e 1.26% ʻo e paʻanga vaʻinga ki ai. Hili ha vilo ʻe 1,000, kuo tupu ʻa e paʻanga vaʻinga angamaheni ʻo meimei liunga 11.5, lolotonga ko e ʻavalisi, ʻa ia ʻoku hiki hake ʻe ha ngaahi lele monūʻia lahi siʻi, kuo tupu ʻo meimei liunga 249. ʻOku hiki hake ʻe he peti lahi ange ʻi he Kelly ʻa e ʻavalisi pea fakasiʻisiʻi ʻa e ola angamaheni: ʻi he liunga ua ʻo e peti Kelly, ʻoku liunga ua pē ʻa e paʻanga vaʻinga angamaheni, pea ʻi he liunga ua vaeua ʻo e peti Kelly ʻoku siʻisiʻi ange ia, neongo ʻoku kei maʻu ʻe he peti kotoa pē ha tuʻunga lelei ʻo e 44%. ʻOku siʻi pē ʻa e fakamole ʻo e peti siʻi ange: ko e vaeua ʻo e peti ʻoku ne tauhi ʻa e meimei konga ʻe tolu ʻi he fā ʻo e tupu.
ʻI he taimi ʻoku fakafuofua pē ai ʻa e tuʻunga lelei
ʻOku pehē ʻe Kelly ʻoku ʻiloʻi ʻa e tuʻunga lelei. ʻI he tēpile ʻoku fakafuofua pē ia, pea ʻoku faʻa māʻolunga fau ʻa e fakafuofua. Ko e sīpinga ʻa Epstein, ʻoku langa ʻi he 44% ʻa Thorp, ko ha fika naʻe tau ʻo tuʻo 49 ʻi ha vilo ʻe 1,225 ʻo 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 → ua: 1 ʻi he 25, ko ha tuʻunga lelei ʻo e 44%, ko ha peti Kelly ʻo e 1.26%. Ka ʻoku ʻi ai ʻa e fika ʻe 38 ʻi ha veʻeteka noa ua faitotonu, pea ko e fika ʻoku tau lahi taha ʻiate kinautolu ʻoku aʻu ki he 49 pe lahi ange ʻi ha vilo ʻe 1,225 ʻi he meimei tuʻo taha ʻi he hiva. Ko e fika ʻoku tau lahi taha ʻi ha lekooti pē ko e fika foki ia kuo tokoni lahi taha ki ai ʻa e monūʻia, ko ia neongo ha luo ʻoku hehema moʻoni, ʻoku hā lelei ange ia ʻi he lekooti ʻi hono tuʻunga moʻoni: ko e talatuki ʻo e tokotaha ikuna. Kapau ʻoku ʻikai hehema moʻoni ʻa e luo ko iá, ko e peti Kelly ko ha peti pē ia ʻoku mole ai ʻa e 5.26% ʻi he ʻavalisi. Ko e ngaahi tali angamaheni ko hono peti ʻa ha konga ʻo e Kelly pea hokohoko atu hono lau kae ʻoua kuo kei tuʻu ʻa e tuʻunga lelei ʻi ha lekooti foʻou (vakai ki he Founga ke ʻIloʻi ai ʻa e Hehema ʻo e Veʻeteka Lulēti).
Kakai ʻoku ʻi ai honau tuʻunga lelei
ʻOku ʻikai tatau ʻa e ʻiloʻi ʻo e tuʻunga lelei mo hono fakaʻaongaʻi lelei. Naʻe ʻoatu ʻe Haghani mo Dewey (2016) ki ha kakai ʻe toko 61 ʻa e $25 taki taha ke nau peti ʻi ha houa vaeua ki ha sēniti naʻe tala ange ʻoku hā hake ʻa e ʻulu ʻi he 60% ʻo e taimi, pea naʻe fakangatangata ʻa e paʻanga naʻe ikunaʻi ki he $250 (naʻe toki ʻilo pē ʻe he kau vaʻinga ʻa e fakangatangata ʻi heʻenau aʻu ki ai). ʻOku pehē ʻe Kelly ke peti ʻa e 20% ʻo e paʻanga vaʻinga ki he ʻulu ʻi he taimi kotoa pē, pea ʻoku fakafuofua ʻe he kau faʻu ʻe aʻu ʻa e ngaahi peti maau ʻo e 10–20% ki he fakangatangata ʻi he meimei 95% ʻo e taimi. Ko e 21% pē ʻo e kau vaʻinga naʻa nau aʻu ki ai. Naʻe ʻosi ʻa e paʻanga ʻa e 28%, naʻe peti ʻe he toko 18 ʻi he 61 ʻa e meʻa kotoa ʻi ha tolo pē ʻe taha, ko e meimei vahe tolu naʻa nau ngata ʻi lalo ʻi he $25 naʻa nau kamata ʻaki, pea ko e totongipaʻangaTotongiKo e meʻa ʻoku fakafoki ʻe ha peti ikuna, ʻoku fakahā ko e “X ki he 1” ʻi ʻolunga ʻi he peti ʻoku fakafoki.Lau kotoa → ʻavalisi ko e $91. Ko e toko nima pē ʻi he 61 naʻa nau fanongo ki he fua ʻa Kelly. ʻI ha tuʻunga lelei, ko e lahi ʻo e ngaahi peti ʻoku ne fakapapauʻi pe te ke tauhi ia; ʻi he ʻikai ha tuʻunga lelei, ʻo hangē ko ha veʻeteka faitotonu, ʻoku ʻikai tokoni ha lahi.
Ko e hā ke fakaʻaongaʻi ʻo fetongi ai
ʻI he ʻikai ha tuʻunga lelei, ko e fakafuofua ʻo e peti ko ha fehuʻi ia ʻo e patiseti, ʻo ʻikai ko ha fehuʻi ʻo e tupu: peti = ko e meʻa ʻoku ke loto ke fakamoleʻi ʻi he vilo ʻe taha, ʻo maʻu mei he patiseti ʻi he houa mo e vave ʻo e tēpile (peesi Puleʻi ʻo e Paʻanga Vaʻinga Lulēti). Ko e tokoni ʻa Kelly ki he tokotaha vaʻinga angamaheni ko e mahino ʻo ʻene tali: noa. Ko e meʻa kotoa pē ʻoku ke peti ʻi ʻolunga ʻi he noa ko e totongi ia ʻo e vaʻinga, ʻoku ke fili ʻe koe, ʻo ʻikai fakalelei ʻe ha fomula.
Fakamatala ki he konga ʻo e Kelly mo e “puleʻi paʻanga”
Ko e ngaahi sisitemi ʻoku fakatau atu ko e “Kelly ki he lulēti” ʻoku nau fokotuʻu ha peseti paʻu ʻo e paʻanga vaʻinga ki he peti taki taha, ko e 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 → pē ia mo ha peti ʻoku siʻisiʻi ange. ʻOku nau mole ʻa e 2.70% 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 → pea, koeʻuhí ʻoku siʻisiʻi ange ʻa e peti ʻi hoʻo mole, ʻoku nau fakatuai ʻa e ʻosi ʻa e paʻanga kae ʻikai ke fakasiʻisiʻi hono ngalingali. Ko ha founga lelei ia ke tolonga ai ha patiseti; ka ʻoku ʻikai ko e Kelly ia, ʻa ia te ne pehē ke taʻofi.
Fomula
Ngaahi fehuʻi
ʻI ha tuʻunga lelei pē kuo fuaʻi mei 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 → pe ha meʻangāue fua taimi. ʻIkai ʻi ha veʻeteka faitotonu.
Koeʻuhí ʻoku ʻi ai ha fehalaaki ʻi he fakafuofua ʻo e tuʻunga lelei, pea ʻoku mamafa ange ʻa e peti lahi fau ʻi he peti siʻi fau. ʻOku ʻomi ʻe he vaeua-Kelly ʻa e konga ʻe tolu ʻi he fā ʻo e tupu ʻi he konga ʻe taha ʻi he fā ʻo 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 →.
ʻIkai. ʻOku fakalelei ʻe Kelly ʻa e tupu ʻi he ʻi ai ha tuʻunga lelei. ʻOku puleʻi ʻe he puleʻi ʻo e paʻanga vaʻinga ʻa e fakamole ʻi he ʻikai ha tuʻunga lelei.
Vaʻinga mo e Matematika
ʻUluaki feinga ke ke fakaleleiʻi ʻe koe. Kuo pelu ʻa e tali takitaha; fakaava ia ʻi hoʻo mateuteu.
Naʻe ʻomi ʻe he meʻangāue tomuʻa tala ʻa Thorp mo Shannon ha tuʻunga lelei ʻo e 44% nai. ʻI ha fika ʻe taha kuo tomuʻa tala, ʻoku pehē ʻe Kelly ke peti ʻa e 1.26% 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 →. Fēfē kapau naʻe maʻu ʻa e tuʻunga lelei tatau ʻo e 44% ʻi ha peti ʻe taha kuo vahevahe ki ha fika kaungāʻapi ʻe nima?
Fakahā ʻa e tali
Tali ʻOku pehē leva ʻe Kelly ko e 7.1% ʻo e paʻanga vaʻinga, pea ʻoku tupu ʻa e paʻanga vaʻinga ʻo ofi ki he vave ʻe ono: ʻo liunga 1.25 miliona nai ʻi he peti ʻe 1,000, ʻi he fāitaha mo e liunga 11.5 nai.
ʻOku ikuna ha peti fika ʻe tahapetiPeti fika ʻe tahaFika pē ʻe taha, totongi ʻo e 35:1.Lau kotoa → mo ha tuʻunga lelei ʻo e 44% ʻi he ngalingali ʻo e 0.04, koeʻuhi ko e 36 × 0.04 = 1.44. Ko e lahi ʻo e peti ʻa Kelly ko e tuʻunga lelei ʻoku vahe ʻaki ʻa e faingamālie: 0.44/35 = 1.26%. Ko e tupu angamaheni ʻi he peti takitaha ko e 0.04 × ln(1 + 35 × 0.0126) + 0.96 × ln(1 − 0.0126) ≈ 0.00244, ko ia ʻoku fakaliunga ʻe he peti ʻe 1,000 ʻa e paʻanga vaʻinga ʻaki ʻa e e^2.44 ≈ 11.5 nai.
Vahevahe ha peti ʻe taha ki ha fika ʻe nima pea ʻoku ikuna ʻa e peti ʻi he ngalingali ʻo e 0.20 pea totongi ʻa e 36/5 maʻa e 1, ʻa ia ko e 6.2 ki he 1: ko ha tuʻunga lelei ʻo e 44% pē, koeʻuhi ko e 0.2 × 7.2 = 1.44. ʻOku hoko ʻa e lahi ʻo e peti ʻa Kelly ko e 0.44/6.2 = 7.10%, pea ko e tupu ʻi he peti takitaha ko e 0.01404, ʻo liunga 5.75 nai. ʻI he peti ʻe 1,000 ko e e^14.04 ia, ʻo ofi ki he 1.25 miliona.
ʻOku tatau pē ʻa e tuʻunga lelei; ʻoku siʻi ange ʻa e ngaahi hiki mo e holo. ʻE lava ʻe ha peti ʻoku ikuna tuʻo taha ʻi he tuʻo nima ʻo fua ha konga lahi ange ʻo e paʻanga vaʻinga ʻo ʻikai fakatuʻutāmakiʻi ke ʻosi ʻa e paʻanga, pea ʻoku fakapaleʻi ia ʻe he tupu ʻa Kelly. ʻOku ngāueʻaki ʻe Thorp (1984) ʻa e fakatātā ke fakahā ʻa e ʻuhinga ʻoku peti ai ʻa e kau vaʻinga tomuʻa tala ki he ngaahi kongaveʻetekaKongaKo ha konga fakavilo hokohoko ʻo e ngaahi luo ʻi he veʻeteka, ʻoku kehe ia mei ha kulupu ʻi he palani ʻo e tēpile.Lau kotoa →. ʻI he moʻui moʻoni ʻoku siʻi siʻi hifo ʻa e tuʻunga lelei ʻo e kaungāʻapipetiKaungāʻapiKo ha fika mo e luo ʻe ua ʻi he tafaʻaki takitaha ʻo ia ʻi he veʻeteka, sipi fika ʻe taha ʻe nima.Lau kotoa → ʻe nima ʻi he fika ʻe taha lelei taha (vakai ki he Vaʻinga Kumi Tuʻunga Lelei ʻi he Lulēti).
Kuo maʻu ʻe ha tokotaha vaʻinga ha luomeʻangāueLuoKo e taha ʻo e ngaahi luo ʻe 37 ʻoku fakafika ʻi he konga vilo. ʻOku toe ui: slot, cup.Lau kotoa → kaungāʻapi ʻe ua ʻoku hā takitaha tuʻo 1 ʻi he 25 ʻo ʻikai ko e 1 ʻi he 37. ʻOku totonu ke ne peti ʻa e peti fika ʻe uapetiPeti fika ʻe uaFika ʻe ua ʻoku fehokotaki, totongi ʻo e 17:1.Lau kotoa → ʻi hona vahaʻa ʻi he 17 ki he 1, pe ko e fika takitaha ko ha peti fika ʻe taha? ʻOku fiha ʻoku pehē ʻe Kelly, pea ʻoku tupu vave fēfē ʻa e paʻanga vaʻinga ʻo fakatatau ki ha luo pehē ʻe taha?
Fakahā ʻa e tali
Tali ʻOku ʻikai ha faikehekehe: 2.59% ʻo e paʻanga vaʻinga ki he peti fika ʻe ua, pe 1.29% ki he fika takitaha. ʻOku tupu ʻa e paʻanga vaʻinga angamaheni ʻo liunga 155 nai ʻi he vilo ʻe 1,000, ʻi he fāitaha mo e liunga 11.5 ʻaki ha luo ʻe taha.
ʻOku ikuna ʻa e peti fika ʻe ua ʻi he 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 2/25 = 0.08 pea totongi ʻa e 17 ki he 1, ko ia ʻoku ne fakafoki ʻa e 18 × 0.08 = 1.44 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 → takitaha naʻe peti: ko ha tuʻunga lelei ʻo e 44%, tatau mo ha luo hehema ʻe taha. Ko e lahi ʻo e peti ʻa Kelly ko e tuʻunga lelei ʻoku vahe ʻaki ʻa e faingamālie: 0.44/17 = 2.59%.
ʻOku ʻomi ʻe ha peti fika ʻe taha ʻe ua ʻo e 1.29% takitaha ʻa e ngaahi ola tatau tofu pē. ʻI he hā ʻa e fika ʻe taha ʻo e ongo fika, ʻoku ikuna ha 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 → ʻe taha ʻi he 35 ki he 1 pea mole ʻa e sipi ʻe taha, ko e tupu kakato ʻo e 34 × 1.29% = 44% ʻo e paʻanga vaʻinga, ʻo hangē ko e totongi ʻa e peti fika ʻe ua; ʻi he ʻikai hā ha taha ʻo kinaua, ʻoku mole fakatouʻosi.
Ko e tupu ʻi he vilo takitaha ko e 0.00505, ʻi he fāitaha mo e 0.00244 ki ha luo ʻe taha, ko ia ʻi he vilo ʻe 1,000 ʻoku tupu ʻa e paʻanga vaʻinga angamaheni ʻo liunga e^5.046 ≈ 155 ʻo ʻikai ko e liunga e^2.44 ≈ 11.5. ʻOku mahuʻinga lahi ange ʻaupito ʻa e fika lelei ʻe ua ʻi he liunga ua ʻo e taha, ko e ʻuhinga ia ʻoku peti ai ʻa e kau vaʻinga hehema ki ha ngaahi kulupu fika. ʻOku fai ʻe Thorp (1984) ʻa e fakatatau tatau.
Meʻa fakaoli
Ko e peti lulēti lelei taha ki he tupu ko ha fika ʻoku ʻosi ʻiloʻi ʻe he taha kotoa.
Ngaahi Maʻuʻanga
- Kelly, J. L. “A new interpretation of information rate.”
- Breiman, L. “Optimal gambling systems for favorable games.”
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Haghani, V. & Dewey, R. “Rational decision-making under uncertainty: observed betting patterns on a biased coin.”