Ngaahi Bonasi, Fakatau Fakalahi mo e Paʻanga Fakafoki ʻi he Lulēti
Ko e ngaahi bonasi lulēti hangē ko e ngaahi kupone fakaliunga (matchplay), ngaahi sipi ʻoku ʻikai lava ʻo fetongi ki he paʻanga mo e ngaahi paʻanga fakafoki ʻi he mole ʻoku nau fetuku ha kiʻi paʻanga siʻi mei he kasino ki he tokotaha vaʻinga. ʻI hono fakafuofua totonu ʻo honau mahuʻinga, ko e niʻihi ʻoku lahi ange honau mahuʻinga ʻi he meʻa ʻoku toʻo ʻe he veʻeteka.
Ko ha kupone ʻoku ne fakaliunga ua ʻa e totongi ʻo ha peti totongi tatau ʻoku mahuʻinga ʻaki ʻa e meimei 46% ʻo e peti ʻi ha veʻeteka ʻIulope. Ko ha sipi fakatau fakalahi ʻoku ngāue tuʻo taha pē ʻoku mahuʻinga ʻaki ʻa e (36 − n)/37 ʻo hono mahuʻinga ʻi ha peti ʻoku ʻufiʻufi ha fika ʻe n: 95% ʻi ha peti fika ʻe taha, 49% ʻi he kulokula. Ko ha fakafoki ʻo e vaeua ʻo hoʻo mole kakato ʻoku ne ʻai ke ʻaonga ke vaʻingaʻi ha taimi vaʻinga nounou ʻi he kulokula. ʻOku ʻikai liliu ʻe ha meʻa ʻi heni ʻa e veʻeteka; ʻoku ne liliu pē pe ko hai ʻoku totongi.
Ko e ʻuhinga ʻe lava ai ha fakatau fakalahi ʻo ikunaʻi ʻa e tuʻunga lelei
Ko e tuʻunga lelei ʻo e kasinomatematikaTuʻunga lelei ʻo e kasinoKo e konga ʻo e peti takitaha ʻoku tauhi ʻe he kasino ʻi he ʻavalisi: 2.70% ʻi he lulēti ʻIulope.Lau kotoa → ko ha totongi ia ʻi 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 → ʻe taha naʻe peti: 2.70% ʻi ha veʻeteka ʻIulope. ʻOku tānaki ʻe ha bonasi lulēti ha paʻanga ki ha tafaʻaki ʻe taha ʻo ha peti, pea kapau ʻoku lahi ange ʻa e meʻa ʻoku ne tānaki ʻi he 2.70% ʻo e peti, ʻoku pōsitivi ʻa e peti ko iá ʻi he lolotonga ʻo e fakatau fakalahi. ʻOku kei ʻoatu pē ia ʻe he ngaahi kasino koeʻuhí ʻoku fakangatangata ia: kupone ʻe taha ʻi he ʻaʻahi, ngaahi 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 lava ʻo peti kae ʻikai fetongi ki he paʻanga, ngaahi fakafoki ki he kau vaʻinga pē ʻoku mole ha paʻanga lahi. ʻOku tatau ʻa e fika mo e feituʻu kotoa pē ʻi he uepisaiti ni: faingamālie liunga ʻaki ʻa 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 →, ʻo tānaki fakataha ʻi he ngaahi ola kotoa.
Ngaahi kupone fakaliunga
ʻOku tuku ha kupone fakaliunga (matchplay) ʻi he tafaʻaki ʻo ha peti paʻanga pea ʻoku ne fakaliunga ua ʻa e meʻa ʻoku totongi ʻe he peti kapau ʻe ikuna; ikuna pe mole, ʻoku tauhi ʻe he kasino ʻa e kupone. ʻOku fakafuofua ʻe Bollman (2024) ʻa e mahuʻinga ʻo ha kupone Las Vegas mei he 2022 naʻe fakatatau ʻo aʻu ki he $50 ʻi ha peti totongi tataupetiPeti totongi tatauKulokula/ʻuliʻuli, taʻehoa/hoa, māʻolunga/māʻulalo. Fika ʻe 18, totongi ʻo e 1:1.Lau kotoa →. ʻI ha veʻeteka ʻIulope, ko e $50 ki he kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa → mo e kupone ʻoku ikuna ʻa e $100 ʻi he ngalingali ʻo e 18/37 pea mole ʻa e $50 ʻi he ngalingali ʻo e 19/37: ko ha ʻamanekina ʻo e +$22.97, pe 45.9% ʻo e peti. ʻI ha veʻeteka ʻAmelika ko e +$21.05, 42.1%. ʻI ha peti fika ʻe tahapetiPeti fika ʻe tahaFika pē ʻe taha, totongi ʻo e 35:1.Lau kotoa →, ʻe liunga ua hono mahuʻinga ʻo e kupone tatau, ko e ʻuhinga ia ʻoku fakangatangata ai ʻa e ngaahi kupone ki he ngaahi peti totongi tatau.
Ngaahi sipi ʻoku ʻikai lava ʻo fetongi ki he paʻanga
Ko e ngaahi sipi fakatau fakalahi, ʻoku ui foki ko e ngaahi sipi taʻefetongi, ʻe lava ʻo peti kae ʻikai fetongi ki he paʻanga. Ko e lao angamaheni ko e ngāue tuʻo taha pē: ko ha peti ikuna ʻoku totongi ʻaki ʻa e ngaahi sipi angamaheni pea toʻo ʻa e sipi fakatau fakalahi; ko ha peti mole ʻoku toʻo foki ia. Ko ha sipi $100 ʻi ha peti ʻoku ʻufiʻufi ha fika ʻe n ʻoku ikuna ʻa e (36 − n)/n × $100 ʻi he ngalingali ʻo e n/37, ko ia ʻoku mahuʻinga ʻaki ʻa e (36 − n)/37 ʻo hono mahuʻinga. ʻOku ʻikai ʻaupito foki mai ʻa e mahuʻinga ʻo e sipi tonu, ko e paʻanga naʻe ikunaʻi pē, pea ko ha peti ʻoku tātātaha hono ikuna ka ʻoku totongi lahi ʻoku siʻi taha hono mole ʻi he founga ko iá: $94.59 ʻi ha peti fika ʻe taha, $48.65 ʻi he kulokula. ʻI he feituʻu ʻoku ngofua ke nofo ai ʻa e sipi ʻi he palani ʻo e tēpilemeʻangāuePalani ʻo e tēpileKo e palani peti kuo paaki ʻi he tēpile. ʻOku toe ui: tēpile, felt, cloth.Lau kotoa → kae ʻoua kuo mole, ʻoku mahuʻinga ʻaki ʻe ha peti totongi tatau ʻa e 18/19 ʻo hono mahuʻinga ʻi ha veʻeteka ʻIulope pea 9/10 ʻi ha veʻeteka ʻAmelika (Bollman, 2024).
Liliu ʻa e ngaahi sipi ki he paʻanga
Ko ha mahuʻinga ko ha ʻavalisi ia; ko ha tokotaha vaʻinga ʻoku fiemaʻu pau ʻa e paʻanga ʻe lava ke ne fakatau ia ʻaki ha peti malu. Ko e sīpinga ʻa Bollman mei he kasino motuʻa Vegas World: $1,000 ʻo e ngaahi sipi ngāue tuʻo taha ʻi ha veʻeteka ʻAmelika, $500 ki he kulokula mo e $500 ki he ʻuliʻulipetiʻUliʻuliPeti totongi tatau ki he fika ʻuliʻuli ʻe 18. Faka-Falanisē: noir.Lau kotoa →, mo e $20 paʻanga moʻoni ki he 0 mo e 00 taki taha. ʻOku ikuna ʻe he kulokula pe ʻuliʻuli ʻa e $500 pea mole ʻa e $40 paʻanga moʻoni: +$460. Ko ha 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 → ʻoku mole ai ʻa e ongo sipi pea totongi ʻa e $700 ʻi he paʻanga moʻoni: +$680. ʻOku maʻu ʻe he tokotaha vaʻinga ʻo siʻi taha ʻa e $460, pea ko e ʻavalisi, $471.58, ko e 99.6% ia ʻo e mahuʻinga ʻo e ngaahi sipi ʻi he kulokula pē. ʻI he feituʻu ʻoku ngofua ai ʻe he ngaahi lao ʻa e ngaahi sipi ki he fika taki taha, ʻoku ʻoatu ʻe ha veʻeteka ʻIulope ha peti malu lelei ange: ngaahi sipi $25 ki he fika kotoa ʻe 36 ($900) mo e $25 paʻanga moʻoni ki he noa. Ko ha fika pē ʻe hū ʻoku totongi ʻa e $875, pea ʻoku mole ʻa e paʻanga moʻoni ʻi he noa tuku kehe kapau ʻe hū ʻa e noa tonu, ko ia ʻoku tauhi ʻe he tokotaha vaʻinga ʻo siʻi taha ʻa e $850, 94% ʻo e mahuʻinga ʻo e ngaahi sipi, ʻo ʻikai ha fakatuʻutāmaki ʻe taha.
Ngaahi fakafoki ʻi he mole
ʻOku faʻa ʻoatu ki he kau vaʻinga peti lahi ha paʻanga fakafoki: ko ha konga ʻo ʻenau mole kakato ʻoku fakafoki mai ʻi he ngataʻanga ʻo ha taimi vaʻinga kuo felotoi ki ai. ʻOku totongi pē ʻa e paʻanga fakafoki ʻi hoʻo mole, ko ia ʻoku mahuʻinga lahi taha ia ʻi he taimi ʻoku kalokalo lahi ai ʻa e ngaahi ola pea ʻoku nounou feʻunga ʻa e taimi vaʻinga ke teʻeki ai ke pule ʻa e tuʻunga lelei. ʻOku fakaʻuhingaʻi ʻe Epstein (2013) ʻa e meʻa ni ki ha veʻeteka ʻAmelika; ko ʻemau ngaahi fika ki ha veʻeteka ʻIulope ʻoku hoko mai. ʻI hono fakafoki ʻa e vaeua ʻo e mole kakato, ʻoku ʻaonga ke vaʻingaʻi ʻa e peti tatau ʻi he totongi tatau ʻo aʻu ki he vilo ʻe 103 pea ʻoku lelei taha ʻi he 25, ʻoku mahuʻinga ʻaki ʻa e peti ʻe +0.51 ʻi he ʻavalisi. ʻI ha peti fika ʻe taha, ʻoku lahi ʻaupito ʻa e ngaahi kalokalo ʻo nofo pōsitivi ai ʻa e taimi vaʻinga ʻi ha meimei vilo ʻe 3,600 pea ʻoku lelei taha ʻi he 882, ʻoku mahuʻinga ʻaki ʻa e peti ʻe +17.25. ʻI ha fakafoki angamaheni ange ʻo e 10%, ʻoku pōsitivi pē ʻa e totongi tatau ʻi ha vilo pē ʻe taha, lolotonga ʻoku lelei taha ʻa e peti fika ʻe taha ʻi he vilo ʻe 20, ʻoku mahuʻinga ʻaki ʻa e peti ʻe +0.62.
Ngaahi lao ʻo e fakatau fakalahi lulēti: ko e meʻa ʻoku falala ki ai ʻa e kasino
ʻOku ʻi ai ha fakangatangata ʻi he fakatau fakalahi kotoa pē, pea ʻoku malu ʻaki ʻe he fakangatangata ʻa e kasino: kupone ʻe taha ʻi he ʻaʻahi, ngaahi sipi ʻoku ʻoatu ʻi ha lahi paʻu, ngaahi paʻanga fakafoki ʻoku felotoi ki ai pē mo e kau vaʻinga ʻoku lahi ange ʻaupito ʻenau mole ʻamanekina ʻi ha fononga ʻi he fakafoki. Ko ha tokotaha vaʻinga ʻoku ne fakaʻaongaʻi ʻa e kupone pea nofo ai ki ha efiafi ʻo e ngaahi peti $50 ki he kulokula, ʻoku ne fakafoki ʻa e $22.97 ʻi loto ʻi he vilo ʻe 17, ʻi he $1.35 ʻi he vilo. ʻOku moʻoni ʻa e mahuʻinga ki he tokotaha vaʻinga ʻoku ne toʻo ia pea mavahe, pe naʻe ʻosi palani ke ne vaʻinga ʻo lahi pehē.
Fomula
Ngaahi fehuʻi
Ki he peti pē ʻe taha ʻoku ʻalu mo ia, ʻio. ʻOku kei fakamole pē ʻe he peti kehe kotoa ʻa e 2.70% ʻo e peti.
ʻOku siʻi ʻa e kau vaʻinga ʻoku nau fakakaukau ki ai, ʻoku fakangatangata ʻa e ngaahi sipi, pea kuo ʻosi fakafuofua ʻe he kasino ʻa e fakatau fakalahi ko ha tuʻuaki.
Tātātaha. Ko ha alea ia ki he kau peti lahi, ʻoku faʻa felotoi ki ai mo ha tokotaha talitali ʻa e kasino pea totongi ʻi he mole kakato ʻi ha fononga.
Vaʻinga mo e Matematika
ʻUluaki feinga ke ke fakaleleiʻi ʻe koe. Kuo pelu ʻa e tali takitaha; fakaava ia ʻi hoʻo mateuteu.
ʻOku ʻoatu kiate koe 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 → pōnasi ʻo e $25 ʻa ia ʻoku toʻo hili ha peti ʻe taha, ikuna pe mole. ʻOku totonu ke tuku ia ki fē: ki he kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa →, ki ha tasinipetiTasini1–12, 13–24 pe 25–36, totongi ʻo e 2:1.Lau kotoa → pe ki ha fika ʻe taha?
Fakahā ʻa e tali
Tali Ki ha fika ʻe taha. ʻI ai ʻoku mahuʻinga ia ʻaki ʻa e $23.65 ʻi he ʻavalisi; ʻi ha tasini ko e $16.22 pea ʻi he kulokula ko e $12.16.
ʻOku ʻikai ʻaupito foki mai ʻa e sipi tonu, ko e meʻa pē ʻoku ne ikunaʻi. ʻI he kulokula ʻoku ikuna ia ʻa e $25 ʻi he ngalingali ʻo e 18/37: $12.16. ʻI ha tasini ʻoku ikuna ia ʻa e $50 ʻi he ngalingali ʻo e 12/37: $16.22. ʻI ha fika ʻe taha ʻoku ikuna ia ʻa e $875 ʻi he ngalingali ʻo e 1/37: $23.65.
Fakalūkufua, ʻoku mahuʻinga ha peti ki ha fika ʻe n ʻaki ʻa e (36 − n)/37 ʻo e sipi, ko ia ko e siʻi ange ʻa e ngaahi fika, ko e lelei ange ia. ʻI ha sipi angamaheni ʻoku ʻikai ha faikehekehe ʻi heni, koeʻuhi ʻoku foki mai ʻa e peti mo e ikuna kotoa pē pea ʻoku mahuʻinga ʻa e peti kotoa pē ʻaki ʻa e 36/37 ʻo ia. ʻOku uesia ʻe hono toʻo ʻo e peti ʻa e ngaahi peti ʻoku faʻa ikuna pea ʻoku meimei ʻikai ala ia ki he peti ʻoku ikuna tuʻo taha ʻi he 37.
ʻE fakafoki atu ʻe ha kasino ʻa e vaeua ʻo hoʻo mole kakato hili ha vilo pē ʻe taha. ʻOku taau ke vaʻinga ʻa e $100 ki he kulokula? Pea mo e $100 ki ha fika ʻe taha?
Fakahā ʻa e tali
Tali ʻIo fakatouʻosi: +$22.97 nai ʻi he kulokula pea +$45.95 ʻi he fika.
ʻI he kulokula ʻoku ke ikuna ʻa e $100 ʻi he ngalingali ʻo e 18/37 pea, hili hono fakafoki, mole ʻa e $50 ʻi he ngalingali ʻo e 19/37: (1,800 − 950)/37 = +$22.97.
ʻI ha fika ʻe taha ʻoku ke ikuna ʻa e $3,500 ʻi he ngalingali ʻo e 1/37 pea mole ʻa e $50 ʻi he ngalingali ʻo e 36/37: (3,500 − 1,800)/37 = +$45.95.
Ko e ngaahi fika ʻeni ʻo e matchplay ʻo toe. Ko ha peti $100 ʻoku mole pē ʻa e $50 ʻoku ne ikuna ʻa e $100 pe mole ʻa e $50, tatau tofu pē mo ha peti $50 mo ha kupone ʻoku ne fakaliunga ua ʻene ikuna. ʻI ha taimi vaʻinga lōloa ange ʻoku totongi pē ʻa e fakafoki ʻi he ola kakato, ʻoku fefakaʻosiʻaki ʻa e ngaahi ikuna mo e mole ʻi muʻa pea totongi ia, pea ʻoku holo ʻa e mahuʻinga; ki he kulokula mo e vaeua ʻoku fakafoki, ko e vilo ʻe 25 ʻa e lōloa lelei taha.
ʻE fakafoki atu ʻe he kasino ʻa e vaeua ʻo hoʻo mole kakato hili ha lahi kuo fakapapauʻi ʻo e ngaahi peti $100 ki he kulokula, kuo fili kimuʻa: vilo ʻe 1, 2 pe 3. Ko fē ʻa e mahuʻinga lahi taha?
Fakahā ʻa e tali
Tali Vilo ʻe tolu: +$31.45 nai. ʻOku mahuʻinga ʻa e vilo ʻe taha ʻaki ʻa e +$22.97, pea ko e vilo ʻe ua ko e +$20.96 pē.
Vilo ʻe taha: ikuna ʻa e $100 ʻi he ngalingali ʻo e 18/37, pe mole ʻa e $100 pea maʻu ʻa e $50 ʻi he ngalingali ʻo e 19/37: +$22.97, ʻo hangē ko e ngāue ako ʻi ʻolunga.
Vilo ʻe ua: ikuna fakatouʻosi (tuʻo 324 ʻi he 1,369), +$200. Taha takitaha (tuʻo 684), $0, ʻo ʻikai ha meʻa ke fakafoki. Mole fakatouʻosi (tuʻo 361), −$200, −$100 hili hono fakafoki. ʻAvalisi: (200 × 324 − 100 × 361)/1,369 = +$20.96. ʻOku totongi pē ʻa e fakafoki ʻi ha mole, pea ʻoku liliu ʻe he vilo ʻe ua ʻa e ngaahi mole lahi ʻo e vilo ʻe taha ko ha tatau pē.
ʻOku ʻikai ʻaupito lava ke tatau pē ʻa e vilo ʻe tolu. Ikuna ʻe tolu (tuʻo 5,832 ʻi he 50,653): +$300. Ikuna ʻe ua (18,468): +$100. Ikuna ʻe taha (19,494): −$100, fakafoki ki he −$50. ʻIkai ha ikuna (6,859): −$300, fakafoki ki he −$150. ʻAvalisi: +$31.45.
ʻOku mahuʻinga lahi ange ʻa e fakafoki ko e lōloa ange hoʻo fakapapau, lolotonga ʻoku fakamole pē ʻe he tuʻunga lelei ʻo e kasino ʻa e $2.70 ʻi he vilo, ko ia ʻoku hiki ʻa e mahuʻinga ki he +$51 nai ʻi he vilo ʻe 25 (vakai ki he tēpile ʻi ʻolunga), pea ʻoku lelei ange maʻu pē ha lahi taʻehoa ʻo e ngaahi vilo ʻi he lahi hoa ʻoku hoko ai.
Naʻe tufaki ʻe ha kasino ʻi Las Vegas ha kupone: peti ʻa e $5 ki he 00 pea, kapau ʻe ikuna, ʻe totongi atu ʻa e $250 ʻo ʻikai ko e $175 angamaheni. ʻOku mahuʻinga fēfē ʻa e peti $5 mo e kupone, ko ha konga ʻo e peti, ʻi hono 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?
Fakahā ʻa e tali
Tali +34% nai: ʻoku mahuʻinga ʻa e peti ʻaki ʻa e +$1.71 ʻi he ʻavalisi. Kapau ʻoku kau ʻi he $250 ʻa e $5 ʻoku fakafoki, ko e +31.6% ia.
ʻOku ikuna ʻa e 00 tuʻo taha ʻi he vilo ʻe 38. Mo e kupone: +$250 tuʻo taha, −$5 ʻi he tuʻo 37 kehe. ʻAvalisi: (250 − 37 × 5)/38 = 65/38 = +$1.71, ʻa ia ko e 34.2% ʻo e $5. Taʻe kupone: (175 − 185)/38 = −$0.26, ko e −5.26% angamaheni.
Kapau ko e $250 ʻa e fakakātoa ʻoku totongi fakafoki, ko e ikuna ko e $245 pea ko e ʻavalisi ko e (245 − 185)/38 = +$1.58, pe 31.6%.
ʻOku fokotuʻu ʻe Bollman (2024) ʻa e kupone ko ʻeni, mei he kasino Lady Luck (ko e Downtown Grand he taimí ni), ko ha ngāue ako; ko e tali naʻe paaki mo ia, 7.89%, ʻoku ʻikai tatau mo ha ʻuhinga ʻe taha. Hangē ko ha kupone matchplay, ʻoku mahuʻinga ia tuʻo taha pē: vaʻingaʻaki pea taʻofi.
Meʻa fakaoli
Ko ha fakatau fakalahi ʻoku mahuʻinga lahi taha ki he tokotaha vaʻinga ʻoku ne toʻo ia pea ʻalu ki ʻapi.
Ngaahi Maʻuʻanga
- Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.