Ngalingali ʻo e Ngaahi Hokohoko ʻi he Lulēti
ʻOku angamaheni ʻa e ngaahi hokohoko lōloa ʻo ha lanu ʻe taha. ʻOku ʻikai foki ha ʻuhinga ʻo kinautolu ki he vilo hoko.
Kulokula ʻe nima hoko: 2.7%. Hongofulu: 0.074%. ʻI ha taimi vaʻinga ʻo e vilo ʻe 200, ko ha hokohoko ʻe ono ʻo ha lanu ʻe taha ʻoku hā lahi ange ia ʻi he ʻikai.
Ko e hā hono tuʻo lahi ʻo ha hokohoko mole
ʻOku mole ha peti totongi tatau ʻi ha veʻeteka noa ʻe taha ʻi he vilo ʻe 19 ʻi he 37. Ko e laine takitaha ko e ngalingali ke mole kotoa ha hokohoko vilo, mo e lahi kuo mole ai ʻe ha tokotaha vaʻinga Martingale, ʻa ia ʻoku ne fakaliunga ua ʻa e peti hili ʻa e mole kotoa pē.
| mole hokohoko | faingamālie | meimei 1 ʻi he | mole ki he taimi ni | peti hoko |
|---|---|---|---|---|
| 1 | 51.4% | 2 | $1 | $2 |
| 2 | 26.4% | 4 | $3 | $4 |
| 3 | 13.5% | 7 | $7 | $8 |
| 4 | 7.0% | 14 | $15 | $16 |
| 5 | 3.6% | 28 | $31 | $32 |
| 6 | 1.8% | 55 | $63 | $64 |
| 7 | 0.94% | 106 | $127 | $128 |
| 8 | 0.48% | 207 | $255 | $256 |
| 9 | 0.25% | 403 | $511 | $512 |
| 10 | 0.13% | 784 | $1,023 | $1,024 |
| 11 | 0.065% | 1527 | $2,047 | $2,048 |
| 12 | 0.034% | 2974 | $4,095 | $4,096 |
| 13 | 0.017% | 5792 | $8,191 | $8,192 |
| 14 | 0.0089% | 11279 | $16,383 | $16,384 |
| 15 | 0.0046% | 21965 | $32,767 | $32,768 |
Ko e ngalingali ko e 19/37 kuo liunga ʻaki ia ʻe ia tuʻo taha ki he mole takitaha, lau mei ha vilo pau ʻe taha. ʻOku lahi ʻa e ngaahi vilo ʻi ha taimi vaʻinga lōloa ʻe lava ke kamata ai ha hokohoko pehē, ko ia ʻi ha efiafi ʻoku mahulu ange hono ngalingali ʻi he meʻa ʻoku fakahā ʻe ha laine ʻe taha.
Hokohoko ʻe taha
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 → ke kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa → kotoa ʻa e vilo hoko ʻe k ko e (18/37)ᵏ. Ua: 23.7%. Nima: 2.7%. Hongofulu: 0.074%, ʻo meimei 1 ʻi he 1,350. Uofulu: 1 ʻi he miliona ʻe 1.8. Uofulu mā ono, ko e lekooti ʻi Monte Carlo: 1 ʻi he miliona ʻe 137. Ko e ngaahi ngalingali eni ʻo ha hokohoko pau ʻoku kamata ʻi ha vilo pau, ʻa ia ko e fehuʻi ʻoku meimei ʻikai ha taha ʻe fehuʻi moʻoni.
ʻI ha taimi vaʻinga
Ko e fehuʻi ʻoku ʻuhinga ki ai ʻa e kakai ko e “ʻe hā ha hokohoko ʻo e k ʻi ha feituʻu ʻi hoku taimi vaʻinga?”, pea ko e tali ʻoku lahi ange ʻaupito ʻi he (18/37)ᵏ he ʻoku ʻi ai ha meimei feituʻu ʻe 200 ʻi ha taimi vaʻinga ʻo e vilo ʻe 200 ke kamata ai ha hokohoko. Ko ha hokohoko ʻe ono pe lahi ange ʻo e lanu tatau, kulokula pe ʻuliʻulipetiʻUliʻuliPeti totongi tatau ki he fika ʻuliʻuli ʻe 18. Faka-Falanisē: noir.Lau kotoa →, ʻoku hā ʻi ha taimi vaʻinga ʻo e vilo ʻe 200 ʻi he meimei 94% ʻo e taimi; valu pe lahi ange ʻi he meimei 47%; hongofulu pe lahi ange ʻi he meimei 14%. Fakahingoa ʻa e lanu ʻi muʻa pea ʻoku holo ʻa e ngaahi faingamālie, ki he meimei 75%, 27% mo e 7%. Ko ha tokotaha vaʻinga ʻoku nofo ʻi ha efiafi ʻe taha te ne sio ki ha ngaahi hokohoko lōloa ʻi he efiafi kotoa pē.
Ko e hā ʻoku tokanga ai ʻa e Martingale
Ko e 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 → fakafiemoʻua kotoa pē ʻoku ʻi ai hano lōloa ʻo e hokohoko ʻoku ne maumauʻi ia: mole ʻe ono mei ha peti kamata ʻo e $10 ʻi ha fakangatangata ʻo e $500, hongofulu ki he FibonaccifoungaFibonacciFakalakalaka peti ʻoku muimui ki he hokohoko 1, 1, 2, 3, 5, 8, 13…: sitepu ʻe taha ki muʻa hili ha mole, sitepu ʻe ua ki mui hili ha ikuna.Lau kotoa →, nima ki hono fakatolu ʻi he ngaahi tasinipetiTasini1–12, 13–24 pe 25–36, totongi ʻo e 2:1.Lau kotoa →. Ko e ngalingali ʻo ha hokohoko mole ʻe ono ʻi he peti totongi tatau ko e (19/37)⁶ ≈ 1.8% ʻi he feinga takitaha, pea ko ha taimi vaʻinga ʻo e vilo ʻe 200 ʻoku ʻi ai nai ha feinga ʻe 100, ko ia ʻoku aʻu mai ʻa e maumau ʻi he meimei taimi vaʻinga ʻe fā ʻi he nima ʻo e lōloa ko ia. Ko e ngalingali ʻo e ngaahi hokohoko ʻi he lulēti ʻa e ʻuhinga ʻoku ʻikai tātātaha ai ʻa e tō ki lalo.
Ngaahi fika vela mo e momoko
ʻOku ngāue tatau pē ʻa e fika ki he ngaahi peti fika ʻe tahapetiPeti fika ʻe tahaFika pē ʻe taha, totongi ʻo e 35:1.Lau kotoa →. ʻI ha vilo ʻe 300 ko e lau ʻamanekina ki he fika takitaha ko e 8.1; ko e mavahe fakasitanatematematikaMavahe fakasitanateAka ua ʻo e vēliani; ko e mamaʻo angamaheni ʻo ha ola mei he mahuʻinga ʻamanekina.Lau kotoa → ʻoku meimei 2.8. ʻE hū ha fika ʻe taha tuʻo 15 pea ha fika ʻe taha tuʻo 2 koeʻuhi pē ko e faingamālie, ʻi he taimi kotoa pē. Ko ha papa ola ʻoku ne fakamamafaʻi ʻa e ngaahi fika “vela” ʻoku ne fakamamafaʻi ʻa e tumutumu ʻo ha tufaki angamaheni (normal). ʻOku fakamatalaʻi ʻe he Lēpi pe ko e vilo ʻe fiha ʻoku fiemaʻu kae toki ʻuhinga ha meʻa ʻa ha fika velatui halaFika velaKo ha fika kuo hū lahi ange ʻi he meʻa naʻe ʻamanekina ʻi he taimi siʻi kuo ʻosi. ʻI ha veʻeteka faitotonu ʻoku ʻikai te ne tala ki muʻa ha meʻa.Lau kotoa → (ngaahi afe, mei ha veʻeteka pau ʻe taha).
Ko e tauʻatāina ʻa e meʻa kotoa
Ko ha kulokula ʻe hongofulu hoko ʻoku ʻikai ke ne fakalahi ʻa e ngalingali ʻo e ʻuliʻuli, pea ʻoku ʻikai foki ke ne fakalahi ʻa e ngalingali ʻo e kulokula. Ko e 18/37 fakatouʻosi. Ko e ngaahi hokohoko ko ha anga ia ʻo e ngaahi hokohoko taʻefakataumuʻa pea ʻe fakaʻahiʻahi kapau ʻe ʻikai ke nau ʻi ai: ko ha hokohoko ʻo e vilo ʻe 200 ʻoku ʻikai ha hokohoko lōloa ange ʻi he fā ʻe mālohi ange ʻaupito ia ko ha fakamoʻoni ki ha kākā ʻi ha hokohoko ʻoku ʻi ai ha hokohoko ʻe hongofulu mā ua.
Fomula
Ngaahi fehuʻi
Ko e ʻuliʻuli ʻe 26 ʻi Monte Carlo ʻi he ʻaho 18 ʻAokosi 1913 ʻa e taha ʻiloa. Naʻe lipooti ha kulokula ʻe 32 hoko ʻi ha kasino ʻAmelika ʻi he 1943. ʻOku na hoa fakatouʻosi mo e faingamālie ʻi he lahi ʻo e ngaahi vilo ʻoku fakalele ʻe he ngaahi kasino.
Ko e 18/37 ia ʻi he founga fē pē. Peti ki he meʻa ʻoku tala ʻe hoʻo palani, pe ʻoua ʻe peti.
ʻIkai. ʻOku hā ʻa e hehema ʻi hono hū lahi ange ha luomeʻangāueLuoKo e taha ʻo e ngaahi luo ʻe 37 ʻoku fakafika ʻi he konga vilo. ʻOku toe ui: slot, cup.Lau kotoa → ʻe niʻihi ʻi ha vilo ʻe laui afe, ʻo ʻikai ko ha ngaahi hokohoko ʻo ha lanu.
Vaʻinga mo e Matematika
ʻUluaki feinga ke ke fakaleleiʻi ʻe koe. Kuo pelu ʻa e tali takitaha; fakaava ia ʻi hoʻo mateuteu.
ʻOku fiha ha vilo ʻo ha veʻeteka ʻIulope ʻoku fiemaʻu, ʻi he ʻavalisi, kae ʻoleva ke hā ʻa e fika takitaha ʻo e fika ʻe 37 ʻo aʻu ki he tuʻo taha pe lahi ange?
Fakahā ʻa e tali
Tali Ko e vilo ʻe 155 nai ʻi he ʻavalisi; ko e fika lotoloto (median) ko e 147.
Lau ʻa e tatali ki he fika foʻou takitaha. ʻOku fakahā maʻu pē ʻe he ʻuluaki vilo ha fika foʻou. Hili hoʻo sio ki he fika ʻe 1, ʻoku foʻou ʻa e luomeʻangāueLuoKo e taha ʻo e ngaahi luo ʻe 37 ʻoku fakafika ʻi he konga vilo. ʻOku toe ui: slot, cup.Lau kotoa → ʻe 36 ʻi he 37, ko ia ʻoku fiemaʻu ʻe he fika foʻou hoko ʻa e vilo ʻe 37/36 ʻi he ʻavalisi. Hili hoʻo sio ki he fika ʻe k, ʻoku fiemaʻu ʻa e 37/(37 − k).
Tānaki ʻa e ngaahi tatali: 37/37 + 37/36 + 37/35 + … + 37/1 = 37 × (1 + 1/2 + 1/3 + … + 1/37) ≈ 37 × 4.20 = 155.5 vilo.
Ko e konga lahi taha ʻo ia ko e ngataʻanga. ʻOku fiemaʻu ʻe he fika fakamuimui pē ʻa e vilo ʻe 37 ʻi he ʻavalisi, pea ko e fika fakamuimui ʻe nima ʻa e vilo ʻe 85 nai. ʻI ha veʻeteka ʻAmelika ʻoku ʻomi ʻe he tānaki tatau ʻa e 161 nai. Ko e palopalema ʻeni ʻo e tānaki kupone (coupon collector); ʻoku maʻu ʻa e ʻavalisi tatau mei he founga fika angamaheni.
ʻI he vilo ʻe 37 ʻo ha veʻeteka ʻIulope, vilo ʻe taha maʻa e luo takitaha, ʻoku fiha ha ngaahi fika kehekehe ʻoku totonu ke ke ʻamanekina ke ke sio ai?
Fakahā ʻa e tali
Tali Ko e 23.6 nai. Ko e vahe tolu nai ʻo e ngaahi fika, ʻo ofi ki he 13, ʻoku ʻikai hā ʻaupito.
Toʻo ha fika ʻe taha, hangē ko e 17. ʻI he vilo takitaha ʻoku ʻikai ke hā ia ʻi he ngalingali ʻo e 36/37, ko ia ʻoku ʻikai hā ia ʻi he vilo kotoa ʻe 37 ʻi he ngalingali ʻo e (36/37)³⁷ ≈ 0.363.
ʻOku tatau ʻa e ngalingali ʻo e fika kotoa pē, ko ia ʻi he ʻavalisi ʻoku ʻikai hā ʻa e fika ʻe 37 × 0.363 ≈ 13.4 pea ʻoku hā ʻa e 37 − 13.4 ≈ 23.6, ko e tokolahi ʻo kinautolu tuʻo ua pe lahi ange.
ʻOku ui ʻe he kau vaʻinga lulēti ʻeni ko e lao ʻo e vahe tolu. ʻOku ʻikai ko ha lao, ko e fika pē ʻo e ngaahi toe hā: ʻi ha hokohoko ʻoku lōloa tatau mo e veʻeteka, ʻoku nofo ʻi tuʻa ʻa e vahe tolu nai ʻo e ngaahi fika, ʻi ha veʻeteka faitotonu pea ʻi ha toe veʻeteka kehe foki. ʻI he luo ʻe 38 ko e konga ko e (37/38)³⁸ ≈ 0.363 foki; ki ha veʻeteka lahi ʻoku tuʻu ofi ia ki he 1/e ≈ 0.368.
ʻOku fakahā atu ʻe ho kaungāmeʻa ha lisi ʻe ua ʻo e lanu ʻe 50, kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa → pe ʻuliʻulipetiʻUliʻuliPeti totongi tatau ki he fika ʻuliʻuli ʻe 18. Faka-Falanisē: noir.Lau kotoa →, ʻo pehē naʻe maʻu takitaha mei ha veʻeteka kuo toʻo ai ʻa e ngaahi 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 liliu ʻa e lanu ʻi he ʻuluaki tuʻo 25 pea ko hono hokohoko lōloa taha ko e ono. ʻOku liliu ʻa e lanu ʻi hono ua tuʻo 35 pea ʻoku ʻikai ʻaupito ke lōloa hake ʻi he tolu. Ko fē ʻa e lisi naʻe faʻu pē?
Fakahā ʻa e tali
Tali Ko hono ua. ʻOku liliu ha lisi moʻoni ʻo ofi ki he tuʻo 24 pe 25. ʻOku hā ha lisi ʻoku liliu tuʻo 35 tuʻo taha nai ʻi he lisi ʻe 500, pea ko ha lisi ʻoku ʻikai ha hokohoko ʻoku lōloa hake ʻi he tolu tuʻo ua nai ʻi he 100.
ʻOku toe hā ʻe he lanu foʻou takitaha ʻa e lanu kimuʻa pe liliu, vaeua mo e vaeua, ko ia ʻoku ʻomi ʻe he faingamālie ʻe 49 ke liliu ʻa e liliu ʻe 24.5 ʻi he ʻavalisi, ʻo lahi ange pe siʻi ange ʻaki ʻa e 3.5 nai. Ko e tolungofulu-mā-nima ʻoku ʻi ai ha sitepu ʻe tolu pehē ʻi ʻolunga ʻi he ʻavalisi; ʻoku ʻomi ʻe ha veʻeteka faitotonu ha liliu lahi pehē tuʻo taha nai ʻi he lisi ʻe 500.
ʻOku tala ʻe he ngaahi hokohoko ʻa e talanoa tatau. ʻOku ʻi ai ʻi ha lisi moʻoni ʻo e 50 ha hokohoko ʻo e fā pe lahi ange ʻi he 98% nai ʻo e taimi, pea ko hono hokohoko lōloa taha ko e nima pe ono ʻi he taimi lahi taha.
ʻOku liliu tōtuʻa ʻa e kakai ʻoku kole ke nau faʻu ha lisi taʻefakataumuʻa, koeʻuhi ʻoku hā kiate kinautolu ha hokohoko ʻo e fā pe nima ko ha sīpinga. ʻOku fakahā ʻe Taylor (2021) ʻa e fakaʻilonga tatau ʻi he ngaahi lisi ʻo e lī paʻanga naʻe faʻu ʻe he kau tamaiki ako: ʻoku lahi ange ʻa e ngaahi hokohoko ʻi he taʻefakataumuʻa moʻoni ʻi he meʻa ʻoku ʻamanekina ʻe he kakai.
ʻOku talanoa ʻa ha tohi ʻo e ngaahi talanoa kasino ki ha tokotaha vaʻinga naʻe hā ʻene fika tuʻo nima hokohoko pea ui ia ko ha lēkooti. ʻOku tātātaha fēfē ia ʻi ha veʻeteka ʻIulope? Pea ʻoku totonu ke hoko tuʻo fiha ia ʻi ha feituʻu ʻi ha kasino ʻe taha ʻoku ʻi ai ʻa e tēpile ʻe 20, ʻoku vilo takitaha tuʻo 40 ʻi he houa, ʻaho mo e pō?
Fakahā ʻa e tali
Tali Ha fika kuo fakahingoa tuʻo nima hokohoko: 1 ʻi he 69 miliona. Ha fika pē ʻoku toe hā tuʻo fā hili ʻene ʻuluaki hā: 1 ʻi he 1.87 miliona. ʻOku vilo ʻa e kasino ko ia ʻo ofi ki he tuʻo 7 miliona ʻi he taʻu, ko ia ʻoku totonu ke ne sio ki ha hokohoko ʻo e nima tuʻo tolu pe fā ʻi he taʻu.
ʻOku hā ha fika kuo fakahingoa ʻi he ngalingali ʻo e 1/37 ʻi he vilo takitaha, ko ia ko e nima hokohoko ʻoku ʻi ai hono ngalingali ʻo e (1/37)⁵ = 1 ʻi he 69,343,957. Ka ʻoku ʻikai ha taha ʻe fakahingoa ʻa e fika kimuʻa. Ko ha fika pē ʻe ʻuluaki hā, kuo pau ke toe hā ia ʻi he vilo hoko ʻe fā: (1/37)⁴ = 1 ʻi he 1,874,161.
Tēpile ʻe 20 × vilo ʻe 40 × houa ʻe 24 × ʻaho ʻe 365 = vilo ʻe 7,008,000 ʻi he taʻu. ʻE lava ke kamata ʻe he vilo takitaha ha hokohoko, ko ia ʻoku ʻamanekina ʻe he kasino ʻa e 7,008,000/1,874,161 ≈ 3.7 hokohoko ʻo e nima ʻi he taʻu.
ʻOku ʻikai ha lēkooti fakapuleʻanga ʻo e faʻahinga ko ʻeni, pea ʻoku ʻikai fiemaʻu ha taha: ko ha meʻa tātātaha ʻi ha tēpile ʻe taha ko ha meʻa angamaheni ia ʻi ha kasino kātoa, pea ʻoku talanoa ʻa e ngaahi talanoa ki he tēpile naʻe hoko ai. ʻOku fokotuʻu ʻa e talanoa ʻi he Goldman (2007) ʻi ha veʻeteka noa ua, ʻa ia ko e ngaahi fika ai ko e 1 ʻi he 79 miliona mo e 1 ʻi he 2.09 miliona.
Meʻa fakaoli
Ko e ngaahi hokohoko lōloa ko e fōtunga ia ʻo e taʻefakataumuʻa.
Ngaahi Maʻuʻanga
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.