Matematika ʻo e Lulēti · Palopalema matematika · miniti ʻe 7

Palopalema: Tasini ʻe Ua mo ha Sipi ʻe Taha

ʻOku ʻufiʻufi ʻe he tasini ʻe ua ʻa e fika ʻe 24. Tānaki ha sipi ki he noa pea ʻoku ke ʻufiʻufi ʻa e 25. ʻOku ʻaonga ʻa e malu ko ʻeni?

Tali nounou

ʻIkai. Ko e konga taki taha ko e −2.70% ia ʻo hono peti, ko ia ko e fakatahaʻi ko e −2.70% ia ʻo e fakakātoa. ʻOku fakaʻuhingaʻi ʻe he palopalema ʻa e ʻuhinga, fakakaukauʻi ʻa e tufaki pau, pea fakahā ʻa e meʻa ʻoku liliu (ko e fōtunga) mo e meʻa ʻoku ʻikai liliu (ko e totongi).

tasini ʻe ua
24/37 · tupu +1 pe −2
fakataha mo e noa
25/37 ʻoku ʻufiʻufi
EV ʻi he iuniti ʻe taha
−1/37 ʻi ha founga pē
lēsoni
ʻoku fakataha ʻa e ngaahi EV

Ko e palopalema

ʻOku ke peti ʻa e $10 ki he ʻuluaki tasinipetiTasini1–12, 13–24 pe 25–36, totongi ʻo e 2:1.Lau kotoa →, $10 ki hono ua ʻo e tasini mo e $1 ki he 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 →. (a) Ko e hā ʻa e ngaahi ola ʻe lava ke hoko mo honau ngalingali? (b) Ko e hā ʻa 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 →? (c) ʻOku fakalelei ʻe he 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 → ʻi he noa ʻa e peti?

Solovaʻanga (a) mo e (b)

Ngaahi ola: pulumeʻangāuePuluKo e kiʻi pulu siʻisiʻi ʻoku tolongi ʻi he hala ʻo fehangahangai mo e konga vilo. Ko e ngaahi pulu ʻo onopooni ʻoku ngaohi ʻaki ʻa e ivorine pe Teflon, 18–21 mm.Lau kotoa → ʻi he 1–24 (luomeʻangāueLuoKo e taha ʻo e ngaahi luo ʻe 37 ʻoku fakafika ʻi he konga vilo. ʻOku toe ui: slot, cup.Lau kotoa → ʻe 24): ʻoku totongi ʻe ha tasini ʻe taha ʻa e $20, ʻoku mole ʻa e $10 ʻi he tasini ʻe taha, ʻoku mole ʻa e $1 ʻi he noa: tupu +$9. Pulu ʻi he 25–36 (luo ʻe 12): ʻoku mole ʻa e ongo tasini, ʻoku mole ʻa e noa: −$21. Pulu ʻi he noa (luo ʻe 1): ʻoku mole ʻa e $20 ʻi he ongo tasini, ʻoku totongi ʻe he noa ʻa e $35: +$15. EV = (24 × 9 + 1 × 15 − 12 × 21)/37 = (216 + 15 − 252)/37 = −21/37 ≈ −$0.57 ʻi he vilo ʻi he $21 naʻe peti: 2.70%.

olangaahi luongalingaliola
1–242464.9%+$9
25–361232.4%−$21
012.7%+$15
ʻamanekina−$0.57 = 2.70% ʻo e $21

Solovaʻanga (c)

ʻI he ʻikai ha sipi ʻi he noa: (24 × 10 − 13 × 20)/37 = (240 − 260)/37 = −20/37 ≈ −$0.54 ʻi he $20 naʻe peti, ko e 2.70% foki. Kuo liliu ʻe he sipi ʻi he noa ʻa e ola noa ʻo e −$20 ki he +$15 (ko ha fakalelei ʻo e $35 ʻi he tuʻo taha ʻi he 37, ʻoku mahuʻinga ʻaki ʻa e $0.95 ʻi he vilo) pea kuo fakamole ʻa e $1 ʻi he toenga vilo ʻe 36 (ʻoku mahuʻinga ʻaki ʻa e $0.97 ʻi he vilo). Liliu kakato: −$0.03 ʻi he vilo, ʻa ia ko e 2.70% ʻo e tola lahi ange. ʻOku totongi ʻa e malu ko ʻeni ʻo tatau tofu pē mo e meʻa kotoa pē kehe.

Ko e ʻuhinga ʻoku moʻoni ai ʻeni ki he meʻa kotoa

ʻOku fakataha ʻa e ngaahi mahuʻinga ʻamanekina. Ko ha fakatahaʻi pē ʻo ha ngaahi peti ʻi he taimi tatau, ʻoku tatau hono EV mo e fakakātoa ʻo e EV ʻo hono ngaahi konga, ʻa ia ko e taki taha ko e −1/37 ʻo hono peti. Ko ia ko ha fakatahaʻi pē ko e −1/37 ia ʻo e fakakātoa ʻo e peti. ʻOku ʻikai ha fokotuʻutuʻu ʻo e ngaahi 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 →, neongo pe ʻoku fiha, ʻoku hao mei ai; ʻe fakamoʻoniʻi ia ʻe he Meʻa Langa Peti ki ha fakatahaʻi pē ʻoku ke lava ʻo tuku. Ko e meʻa ʻoku liliu ʻe he ngaahi fakatahaʻi ko e tufaki: ko e tuʻo fiha hoʻo ikuna, ʻe fiha, pea ʻe kovi fēfē ʻa e meʻa kovi taha.

Ko e $21 tatau ʻi he founga ʻe tolu: ngalingali ikuna mo e meʻa kovi taha
$21 ki he kulokula: p(ikuna)
48.6% · kovi taha −$21
tasini ʻe ua + noa: p(ikuna)
67.6% · kovi taha −$21
$21 ki he 17: p(ikuna)
2.7% · kovi taha −$21
033.8067.6% · kovi taha −$21
ʻOku EV ko e −$0.57 ʻi he vilo ʻa e tolu kotoa. ʻOku nau kehekehe pē ʻi he fōtunga.

Ko ha fehuʻi hoko faingataʻa ange

Kumi ha fakatahaʻi ʻo e ngaahi peti angamaheni ʻoku ne ʻufiʻufi ʻa e fika kotoa ʻe 37. Tasini ʻe tolu ($10 taki taha) fakataha mo e $1 ki he noa: ko ha fika pē mei he 1–36 ʻoku tupu −$1 (ʻoku totongi ʻe ha tasini ʻe taha ʻa e $20, ʻoku mole ʻa e $20 ʻi he tasini ʻe ua kehe, ʻoku mole ʻa e $1 ʻi he noa), pea ko e noa ʻoku tupu +$35 − $30 = +$5. EV = (36 × (−1) + 5)/37 = −31/37 ʻi he $31 naʻe peti: 2.70%. ʻE lava ke ke fakapapauʻi ʻe ʻikai ʻaupito ke ke ʻohovale, ka ʻoku ke kei totongi pē ʻa e totongi tatau ki he monūʻia ko iá.

Fomula

EV(fakatahaʻi) = Σ EV(ngaahi konga) = −(fakakātoa ʻo e peti)/37

Ngaahi fehuʻi

ʻOku ʻi ai ha fakatahaʻi peti ʻoku siʻi ange hono tuʻunga lelei ʻo e kasino?

ʻIkai, ʻi ha tēpile ʻIulope. ʻI ha tēpile Falanisē, ko e ngaahi peti totongi tataupetiPeti totongi tatauKulokula/ʻuliʻuli, taʻehoa/hoa, māʻolunga/māʻulalo. Fika ʻe 18, totongi ʻo e 1:1.Lau kotoa → pē ʻoku 1.35%; ko hono tānaki ha meʻa kehe ʻoku ne hiki hake ʻa e tuʻunga lelei fakatahaʻi.

Fēfē ʻa e peti ki he kulokula mo e ʻuliʻuli fakatou?

ʻOku mole ʻa e $1 ʻi he $1 ʻi he noa pē, pea ʻikai ikuna ha meʻa ʻi he taimi kehe. EV −2.70% ʻo ʻikai ha tupu: ko e fakatahaʻi pē ia ʻe taha ʻoku ʻikai ʻaonga ʻaupito.

Ko ia ko e hā ke fakatahaʻi ai ha ngaahi peti?

Ke fili ha fōtunga ʻo e taimi vaʻinga ʻoku ke fiefia ai. Ko ha ʻuhinga totonu ia pea ko e ʻuhinga pē ia ʻe taha.

Meʻa fakaoli

Ko e malu ʻi ha tēpile lulēti ʻoku totongi tatau tofu pē mo e meʻa ʻoku ne fakahaofi.

Ko e malu ʻi ha tēpile lulēti ʻoku totongi tatau tofu pē mo e meʻa ʻoku ne fakahaofi.

Ngaahi Maʻuʻanga

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Vahe 13, lulēti.
naʻe vakaiʻi 2026-09-28mōtolo: ʻIulope, noa ʻe tahafounga ngāue ↗ngaahi maʻuʻanga ↗