Matematika · Fakakaukau tefito · miniti ʻe 7

Mahuʻinga ʻAmanekina ʻi he Lulēti

Ko e mahuʻinga ʻamanekina ʻi he lulēti ko e ola ʻavalisi ia ʻo ha peti kapau ʻe lava ke ke toe fai ia ʻo taʻengata. ʻI he lulēti ʻIulope ʻoku tatau ia ki he peti angamaheni kotoa: ʻoku ke mole ʻa e 1/37 ʻo e peti taki taha, ʻi he ʻavalisi, ʻi he vilo taki taha.

ʻI he lea faingofua

Fakakaukau atu ki hoʻo tuku ʻa e peti tatau ʻo e $10 ki he kulokula ʻo tuʻo miliona. ʻOku ikuna ʻa e $10 ʻi he ngaahi vilo ʻe niʻihi, pea mole ʻa e $10 ʻi he niʻihi. Tānaki ʻa e ola kotoa pea vahe ki he miliona: ʻoku ke maʻu ai ʻa e meimei −$0.27. Ko e fika ko ia ko e mahuʻinga ʻamanekina ʻo ha peti lulēti. ʻOku ʻikai ko e meʻa ia ʻoku hoko ʻi ha vilo pē ʻe taha; ko e ʻavalisi ia ʻi he vilo taki taha ʻi he taimi lōloa.

Tali nounouEV = ngalingali ke ikuna × lahi ʻo e ikuna − ngalingali ke mole × lahi ʻo e mole. Ki he peti lulēti angamaheni kotoa ʻoku aʻu ia ki he −2.70% ʻo e lahi ʻo e peti.

Ko e fomula ʻo e EV ʻo ha peti lulēti

EV = p · W − (1 − p) · S
p = n/37 · W = S·(36/n − 1) · n = ngaahi fika ʻoku kapui · S = lahi ʻo e peti

Fetongi ʻaki ʻa e lao ʻo e totongi ʻi he lulēti, 36/n − 1, pea ʻoku tāmateʻi ʻa e n. Ko e talanoa kakato ia ʻo e tuʻunga lelei ʻo e kasino ʻi ha laine ʻe taha:

EV = (n/37)·S·(36/n − 1) − ((37−n)/37)·S
   = S·(36 − n − 37 + n)/37
   = −S/37

Feinga: ko ha meʻa fika ki he mahuʻinga ʻamanekina ʻi he lulēti

Fili pe ko e fika ʻe fiha ʻoku kapui ʻe he peti. ʻOku liliu ʻa e ngalingali mo e totongi; ʻoku ʻikai liliu ʻa e mahuʻinga ʻamanekina.

fika ʻe 1 ʻoku kāpui · totongi 35:1peti $10
p(ikuna)1/37 = 2.70%
totongi ʻo e ikuna+$350
fakamole ʻo e mole−$10
EV = p·W − (1−p)·S0.0270·$350 − 0.9730·$10
mahuʻinga ʻamanekina−$0.27 ʻi he vilo takitaha · −2.70%

Hono fōtunga ʻi he faai ʻa e taimi

Ola ʻavalisi ʻi he vilo taki taha ki ha peti kulokula ʻo e $10, ʻi he tupulaki ʻa e ngaahi vilo. ʻI he kamataʻanga, ʻoku puleʻi ʻe he monūʻia; ʻoku nofo ʻa e ʻavalisi ʻoku lele ʻo ofi ki he −$0.27 ʻi he tupu ʻa e sīpinga. Ko e fakaofi ia ʻi he taimi lōloa ʻoku falala ki ai ʻa e kasino.

EV −$0.27vilo 1vilo 2,000
Vilo ki he vilo, ʻoku taʻofi ʻa e kalokalo ʻa e ʻavalisi ʻoku lele pea nofo ʻi lalo siʻi ʻi he noa.

Ngaahi fakakaukau hala angamaheni

“Ko ha EV ʻoku ʻikai lelei ʻoku ʻuhinga ia te u mole ʻi he taimi vaʻinga kotoa.”
ʻIkai. ʻOku ʻuhinga ia ko e ʻavalisi ʻi ha ngaahi taimi vaʻinga lahi ko ha mole. ʻOku kehekehe lahi ʻa e taimi vaʻinga taki taha, pea lahi ange ʻi he ngaahi peti vēliani lahi hangē ko e peti fika ʻe taha.
“ʻOku fiemaʻu ʻe he kasino ha taimi lōloa ke ikuna.”
ʻOku ngāue ʻa e tuʻunga lelei ʻo e kasino ʻi he vilo kotoa; ko e meʻa ʻoku fai ʻe he taimi lōloa ko hono ngaohi ke lava ʻo tala ʻa e ola. ʻI ha taimi vaʻinga ʻe taha, ko e monūʻia ʻa e meʻa mālohi ange.
“ʻOku lelei ange ʻa e EV ʻo e ngaahi peti ʻe niʻihi ʻi he niʻihi.”
ʻIkai ʻi he lulēti ʻIulope, tukukehe ha meʻa ʻe taha: ʻi he la partage pe en prison, ʻoku vaheua ʻa e tuʻunga lelei ʻo e kasino angamaheni ʻi he ngaahi peti totongi tatau.

Meʻa fakaoli

ʻIkai ko e meʻa ʻoku hoko ʻi ha vilo ʻe taha. Ko e ʻavalisi ʻo kinautolu kotoa.

ʻIkai ko e meʻa ʻoku hoko ʻi ha vilo ʻe taha. Ko e ʻavalisi ʻo kinautolu kotoa.