Fehalaaki ʻa e Tokotaha Peti
Ko e tui ʻoku “taimi” ke hoko ha ola koeʻuhi kuo fuoloa ʻene ʻikai hā mai.
Hili ha kulokula ʻe hongofulu ko e ngalingali ʻo e ʻuliʻuli ʻoku kei 18/37 pē. ʻOku ʻikai tauhi ʻe he veʻeteka ha lekooti pea ʻoku ʻikai ha meʻa ʻoku ne moʻua ai.
Ko e fehalaaki
Kapau kuo hū ʻa e kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa → tuʻo hongofulu, ʻoku ongoʻi ʻe he kau vaʻinga tokolahi kuo “taimi” ke hū ʻa e ʻuliʻulipetiʻUliʻuliPeti totongi tatau ki he fika ʻuliʻuli ʻe 18. Faka-Falanisē: noir.Lau kotoa → pea nau peti ki ai. ʻOku ongoʻi ʻe he niʻihi kehe ʻoku “vela” ʻa e kulokula pea nau peti ki ai. ʻOku na fakakaukau fakatouʻosi mei ha hokohoko kuo ʻosi ki ha vilo ʻoku teʻeki hoko. ʻOku ʻikai ʻiloʻi ʻe he 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 → ʻa e vilo ʻe hongofulu kuo ʻosi; ʻoku tatau pē hono lahi ʻo e ngaahi luomeʻangāueLuoKo e taha ʻo e ngaahi luo ʻe 37 ʻoku fakafika ʻi he konga vilo. ʻOku toe ui: slot, cup.Lau kotoa → mo ia ʻi ha houa kuo ʻosi; 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 → ʻo e ʻuliʻuli ko e 18/37 ʻo hangē ko ia maʻu pē.
Ko e hā ʻoku ongoʻi moʻoni ai
ʻI he taimi lōloa ʻoku fakaofi moʻoni ʻa e ngaahi vahe ʻo e kulokula mo e ʻuliʻuli ki he 18/37 takitaha. ʻOku fakapapauʻi ia ʻe he lao ʻo e ngaahi fika lalahimatematikaLao ʻo e ngaahi fika lalahiʻOku ofi ange ʻa e ʻavalisi ʻo e ngaahi ola tauʻatāina ki he mahuʻinga ʻamanekina ʻi he tupu ʻa e lahi ʻo e ngaahi ʻahiʻahi.Lau kotoa →. Ka ʻoku hoko ʻa e fakaofi ʻi he fakavaivaiʻi, ʻo ʻikai ʻi he fakatonutonu: hili ha toe vilo ʻe 1,000 ko e kulokula lahi ange ʻe hongofulu ko ha kiʻi meʻa siʻisiʻi pē ia ʻi he vahe, ʻo ʻikai koeʻuhi naʻe maʻu ʻe he ʻuliʻuli ʻa e kulokula ka koeʻuhi naʻe tupu ʻa e sīpinga. ʻOku ʻikai ha meʻa ʻoku ne fakalahi ʻa e ngalingali ʻo e ʻuliʻuli, pea ʻoku ʻikai fiemaʻu ʻe he lao ʻo e ngaahi fika lalahi ha meʻa pehē.
Monte Carlo, 18 ʻAokosi 1913
Naʻe hū ʻa e ʻuliʻuli tuʻo 26 hoko ʻi ha tēpile ʻi he Casino de Monte-Carlo. Mei he meimei ʻuliʻuli hono hongofulu mā nima, naʻe fāʻofua ʻa e kau vaʻinga ki he kulokula, ʻo fakaua mo toe fakaua, ʻo “papau ange” ʻa e vilo takitaha ʻi he vilo kimuʻa. Naʻe ikuna ʻe he kasino ʻa e ngaahi miliona ʻo e falanika. Ko e ngalingali ʻo e hokohoko ko e 1 ʻi he miliona ʻe 137 mei he ʻuluaki ʻuliʻuli, pea ko e ngalingali ke ne hoko ʻi ha ʻaho ʻi ha feituʻu ʻi he ngaahi kasino ʻo e māmaní naʻe meimei taha. Ko e ʻuhinga ia ʻoku ui foki ai ʻa e fehalaaki ʻa e tokotaha peti ko e fehalaaki Monte Carlo.
ʻOku ʻikai makehe. ʻOku hoko tuʻo taha ʻi he 44.
ʻOku kamata ke sio ki ai ʻa e kau vaʻinga. Kuo “taimi” ʻa e kulokula.
ʻOku fonu ʻa e tēpile. ʻOku fakaua ʻa e ngaahi peti ki he kulokula hili ʻa e mole takitaha.
Kuo mole ʻa e ngaahi koloa lahi. Ko e ʻuliʻuli foʻou takitaha ʻoku ne fakaongoʻi ʻoku papau ange ʻa e kulokula.
ʻOku ngata ʻa e hokohoko. Kuo ikuna ʻe he kasino ʻa e ngaahi miliona ʻo e falanika mei he kakai naʻa nau peti fakafepakiʻi ha hokohoko naʻe ʻikai lava ke ne “ʻiloʻi” ko ha hokohoko ia.
Ko e nima vela
Ko hono poupouʻi ha lanu koeʻuhi ʻoku ʻi ha hokohoko ko e fehalaaki tatau ia kuo fulihi: ʻoku ʻamanekina ke hoko atu ʻa e hokohoko ʻo ʻikai ke ngata. ʻOku ui ia ʻe he kau saikolosia ko e nima velatui halaNima velaKo e tui ʻoku ʻai ʻe ha hokohoko ikuna, pe ʻo ha ola ʻe taha, ke ngalingali lahi ange ha toe taha. ʻI he veʻeteka ko e fehalaaki ʻa e tokotaha peti ia kuo fulihi.Lau kotoa →, hili ha ako ʻi he 1985 ʻe Gilovich, Vallone mo Tversky naʻa nau kumi ki ha ngaahi hokohoko ʻi he fana ʻi he pasiketipolo pea naʻe ʻikai ha meʻa naʻa nau maʻu ʻo laka ange ʻi he faingamālie. ʻI he 2018 naʻe fakahā ʻe Miller mo Sanjurjo naʻe hehema ʻa e sivi tonu: ʻi ha lekooti nounou, ko e konga ʻo e ngaahi hū ʻi he hili pē ha hū ʻoku māʻulalo ange ia ʻi he tuʻunga fakakātoa ʻo e tokotaha fana ʻi he ʻavalisi, ko ia ko ha tokotaha vaʻinga ʻoku ʻikai ha nima vela ʻoku hā ʻoku kiʻi momoko. Hili hono fakatonutonu, ʻoku fakahā ʻe he ngaahi fakamatala tatau ha kiʻi nima vela. ʻE lava ke mafana ha tangata; ka ʻoku ʻikai ha tuʻunga ʻo ha veʻeteka ke ne ʻi ai. ʻOku tui ʻa e kau vaʻinga ʻe niʻihi ki he ongo meʻa ʻi he taimi tatau, ʻoku hoko atu ha hokohoko kae ʻoua kuo “lōloa fau” pea toki ngata. ʻI ha veʻeteka faitotonu ko e faʻahinga kotoa pē ʻoku tatau hono 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 → mo hono fili ha lanu ʻaki hono lī ha paʻanga: −2.70% ʻo e peti.
ʻI ha tēpile moʻoni
Naʻe mamata ʻa Croson mo Sundali (2005) ki ha vitiō malu ʻo e houa ʻe 18 mei ha tēpile 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 ʻe taha ʻi ha kasino lahi ʻi Reno: kau vaʻinga ʻe 139 naʻa nau tuku ha peti ʻe 24,131. ʻI he ngaahi peti totongi tataupetiPeti totongi tatauKulokula/ʻuliʻuli, taʻehoa/hoa, māʻolunga/māʻulalo. Fika ʻe 18, totongi ʻo e 1:1.Lau kotoa →, naʻe meimei vahe tatau ʻa e kau vaʻinga ʻi he muimui ki he ngaahi hokohoko nounou mo e fakafepakiʻi kinautolu. Hili ha meʻa tatau ʻe nima hoko naʻa nau hehema ke fakafepakiʻi ʻa e hokohoko, pea hili ha ono pe lahi ange, ko e 85% ʻo ʻenau ngaahi peti naʻe ʻi he tafaʻaki ʻe taha. Naʻe fakahā ʻe he kau vaʻinga tatau ʻa e nima vela fekauʻaki mo kinautolu pē: hili ha ikuna ʻi he ngaahi fika naʻa nau kāpui ha fika ʻe 13.6 ʻi he vilo hoko ʻi he ʻavalisi, ʻo fakahoa ki he 9.2 hili ha mole. Naʻe ʻikai ha fakaʻilonga ʻo ha hehema ʻi honau veʻeteka, ko ia naʻe ʻikai liliu ʻe ha meʻa ʻi he ngaahi meʻa ni ʻa e meʻa naʻe lava ke ʻamanekina ʻe ha taha ʻo kinautolu.
ʻI tuʻa ʻi he kasino
ʻOku hā ʻa e fusi tatau ʻi he feituʻu ʻoku fai ai ha ngaahi fili moʻoni. Naʻe muimui ʻa Clotfelter mo Cook (1993) ki he vaʻinga fika fakaʻaho ʻa Maryland: naʻe holo vave ʻa e paʻanga naʻe peti ki ha fika ʻi he taimi pē naʻe toʻo ai pea naʻe fiemaʻu ha ngaahi māhina ke toe foki, neongo ʻoku ʻikai ha manatu ʻa e toʻo. Naʻe maʻu ia ʻe Chen, Moskowitz mo Shue (2016) ʻi he kau taukei. Naʻe aʻu ki he poini peseti ʻe 3.3 ʻa e lahi ange ʻo e ngalingali ke fakafisi ʻa e kau fakamaau hūfanga ʻo ʻAmelika ki ha keisi kapau naʻa nau tali ʻa e keisi kimuʻa. Naʻe siʻi ange ʻaki ʻa e poini ʻe 1.5 ʻa e ngalingali ke ui ʻe he kau ʻampaea pesipolo ha strike hili ʻenau ui ha taha, pea laka hake ʻi he liunga ua ʻo ia ʻi he ngaahi lī ofiofi. ʻI ha sivi ʻi he malaʻe mo e kau ʻōfisa nō naʻe totongi ʻaki ha totongi tatau, naʻe aʻu ki he 9% ʻo e ngaahi fili naʻe fulihi ʻi he founga ni. Naʻe haʻu ʻa e ngaahi keisi ʻi ha hokohoko taʻefakataumuʻa, ko ia naʻe ʻikai ha meʻa naʻe tala ʻe he fili fakaʻosi ki he hoko, ʻo hangē pē ko e ʻikai ha meʻa ʻoku tala ʻe he vilo fakaʻosi ki he vilo hoko.
Ko e fehalaaki fakafoki ʻa e tokotaha peti
Naʻe fakahingoa ʻe he filōsefa ko Ian Hacking (1987) ha faʻahinga hono tolu. ʻOku hū ha taha ki ha loki, ʻo ne sio ki ha ongo taisi ʻoku tō ko e ono ua pea ne pehē kuo pau pē kuo ʻosi lī tuʻo lahi. ʻOku tatau ʻa e ngalingali ʻo e lī kotoa pē ke ono ua, ʻa e ʻuluaki ʻo e efiafi pe ko hono afe, ko ia ʻoku ʻikai ha meʻa ʻoku tala ʻe he meʻa naʻe sio ki ai ki he fuoloa ʻo e vaʻinga. ʻI he lulēti ko e tokotaha vaʻinga ia ʻoku aʻu ki ha papa ʻoku fakahā ai ha kulokula ʻe valu pea ne pehē kuo pau pē kuo vilo ʻa e tēpile ʻi ha ngaahi houa ke maʻu ai kinautolu. ʻOku lau ʻe he fehalaaki angamaheni ʻa e kuohili ki he vilo hoko; ʻoku lau ʻe he fehalaaki ni ha meʻa tātātaha ki ha kuohili naʻe ʻikai ha taha naʻe sio ki ai.
Ko ha saikolosia naʻa ne tui ki ai
Kuo ʻi ai ha kau poto naʻa nau taukapoʻi ʻa e fehalaaki. Naʻe vakaiʻi ʻe he saikolosia Siamane ko Karl Marbe ha tohi lēsisita ʻe fā ʻo e fāʻeleʻi ʻe 49,152 takitaha, ʻo ne maʻu ko e hokohoko lōloa taha ʻo e tamaiki tangata pe ʻo e tamaiki fefine naʻe 17, pea ne pehē ʻoku tātātaha ange ʻa e ngaahi hokohoko lōloa ʻi he meʻa ʻoku fakaʻatā ʻe he faingamālie, ko ia ʻoku fakalahi ʻe ha hokohoko ʻa e ngalingali ʻo e ola ʻe taha. ʻOku kehe ʻa e meʻa ʻoku tala ʻe he faingamālie: ʻi he fāʻeleʻi ʻe 196,608 ʻoku hā ha hokohoko ʻo e 17 pe lahi ange ʻi he meimei tuʻo fā ʻi he nima. Naʻe maʻu ʻe Marbe ʻa e fōtunga totonu pē ʻo ha hokohoko taʻefakataumuʻa. ʻOku toe talanoa ʻe Epstein (2013) ki he meʻa ni; ʻoku ʻoatu ʻe he Ngalingali ʻo e Ngaahi Hokohoko ʻi he Lulēti ʻa e faʻahinga ki he lulēti.
ʻI he feituʻu ʻoku ʻikai ngāue ai ʻa e fehalaaki
Kapau naʻe hehema fakaesino ʻa e veʻeteka, ʻe ʻaonga ʻa e ngaahi vilo kuo ʻosi, he ʻe hoko ia ko ha fakamoʻoni fekauʻaki mo e ngaahi luo kae ʻikai ko e monūʻia. Ko e kaveinga ia ʻo e Lēpi, pea ʻoku fiemaʻu ai ha vilo ʻe laui afe mei ha veʻeteka pau ʻe taha kae toki lava ke tala ha meʻa. Ki ha kulokula ʻe hongofulu hoko ʻi ha veʻeteka ʻoku ʻikai ʻiloʻi, ko e ʻuhinga ʻo e hehema ʻoku siʻi ange ʻaupito hono ngalingali ʻi he ʻuhinga ʻo e faingamālie.
Ngaahi fehuʻi
ʻIkai. ʻOku ngāue ia ki ha meʻa tauʻatāina pē ʻoku toutou hoko: taisi, paʻanga, ngaahi fika lotolī.
ʻE ofi ʻa e ngaahi vahe. ʻE kei meimei −2.70% pē hoʻo ola ʻo e meʻa naʻa ke peti.
ʻOku ʻikai ha lao ʻo e ngaahi ʻavalisi. ʻOku ʻi ai ʻa e lao ʻo e ngaahi fika lalahi, pea ʻoku ngāue ia ʻi he fakavaivaiʻi.
Vaʻinga mo e Matematika
ʻUluaki feinga ke ke fakaleleiʻi ʻe koe. Kuo pelu ʻa e tali takitaha; fakaava ia ʻi hoʻo mateuteu.
Hili ha lī ʻe 10, ʻoku fakahā ʻe ha foʻi paʻanga ʻa e ʻulu ʻe 7 mo e hiku ʻe 3. Hili ha lī ʻe 1,000, ʻoku ne fakahā ʻa e ʻulu ʻe 517 mo e hiku ʻe 483. Naʻe aʻu atu ʻa e ngaahi hiku?
Fakahā ʻa e tali
Tali ʻIkai. Naʻe tupu ʻa e vaha mei he 4 ki he 34. Ko e vahevahe pē naʻe ofi ange ki he tatau.
Naʻe holo ʻa e vahevahe ʻo e ʻulu ki he hiku mei he 7/3, meimei 2.33, ki he 517/483, meimei 1.07. Ko e lao ʻo e ngaahi fika lalahimatematikaLao ʻo e ngaahi fika lalahiʻOku ofi ange ʻa e ʻavalisi ʻo e ngaahi ola tauʻatāina ki he mahuʻinga ʻamanekina ʻi he tupu ʻa e lahi ʻo e ngaahi ʻahiʻahi.Lau kotoa → ia ʻoku ngāue.
Naʻe tupu ʻa e vaha ʻi hona vahaʻa, mei he 4 ki he 34. ʻI ha foʻi paʻanga faitotonu, ko ha vaha ʻo e meimei 30 hili ha lī ʻe 1,000 ko e meʻa angamaheni: ʻoku tupu ʻa e vaha angamaheni ʻo meimei hangē ko e aka fakaua ʻo e lahi ʻo e ngaahi lī, lolotonga ʻoku nofo ʻa e vahevahe ki he 1.
Naʻe ʻikai ha meʻa naʻe toho ki mui ʻa e ngaahi hiku. Ko e lahi ange ʻo e ʻulu ʻi he kamataʻanga naʻe fakavaivaiʻi ʻe he lī ʻe 990 hoko, ʻikai fakatonutonuʻi.
Lī ha foʻi paʻanga ʻo liunga fā pea sio pē ki he ngaahi lī ʻoku hoko hili ha ʻulu. Ko e hā hono konga ʻo kinautolu ko e ʻulu? Fakakaukauʻi ia ki he taki taha ʻo e hokohoko ʻe 16 ʻe ala hoko pea toʻo ʻa e ʻavalisi ʻo e ngaahi konga. ʻOku 50%?
Fakahā ʻa e tali
Tali ʻIkai. Ko e 17/42 ia, meimei 40.5%. ʻI he sio ʻi he founga ni, ʻoku hā ʻoku momoko ha foʻi paʻanga faitotonu hili ha ʻulu.
Lisi ʻa e hokohoko ʻe 16 (H = ʻulu, T = hiku). Ko e ua ʻo kinautolu, TTTT mo e TTTH, ʻoku ʻikai ha ʻulu ʻi he ʻuluaki lī ʻe tolu, ko ia ʻoku ʻikai ha meʻa ʻoku hoko hili ha ʻulu; ʻoku toe ai ʻa e 14.
ʻI he taki taha, toʻo ʻa e ngaahi lī ʻoku hoko hili ha ʻulu pea kumi ʻa e konga ʻoku ʻulu. ʻOku ʻomai ʻe he HHHH ʻa e 3 ʻi he 3. ʻOku ʻomai ʻe he HHHT ʻa e 2 ʻi he 3. ʻOku ʻomai ʻe he HTHT ʻa e 0 ʻi he 2. ʻI hono vakai ki he 14 kotoa: ko e hokohoko ʻe ono ʻoku ʻomai ʻa e 0, fā ʻoku ʻomai ʻa e 1/2, taha ʻoku ʻomai ʻa e 2/3 pea tolu ʻoku ʻomai ʻa e 1 (HHHH, THHH mo e TTHH).
Tānaki ʻa e ngaahi konga: 4 × 1/2 + 2/3 + 3 = 17/3. Vahe ʻaki ʻa e 14: 17/42 ≈ 40.5%.
ʻOku ʻikai ha lī ʻoku poupou ki he hiku; ʻoku 50–50 ʻa e taki taha. ʻOku tupu ʻa e hehema mei hono fai ʻo e ʻavalisi ʻo hokohoko ki he hokohoko: ko ha hokohoko ʻoku fonu ʻi he ʻulu ʻoku lahi hono ngaahi lī ke sio ki ai ka ʻoku lau tuʻo taha pē, tatau mo ha hokohoko ʻoku ʻulu pē ʻe taha ai. Naʻe fakahā ʻe Miller mo Sanjurjo (2018) naʻe fua ʻe he ako ʻo e 1985 ki he nima vela ʻa hono kau vaʻinga pasiketipolo ʻi he founga ni, ko ia ko e kau vaʻinga naʻe hā ʻoku ʻikai ke nau hokohoko lahi ange ʻi he meʻa taʻefakataumuʻa naʻa nau hokohoko lahi ange ʻi ha meʻa siʻi.
Meʻa fakaoli
Fakavaivaiʻi, ʻo ʻikai fakatonutonu. ʻOku ʻikai ha meʻa ʻoku moʻua ai ʻa e veʻeteka.
Ngaahi Maʻuʻanga
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Schwartz, D. G. Roll the Bones: The History of Gambling.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Croson, R. & Sundali, J. “The gambler’s fallacy and the hot hand: empirical data from casinos.”
- Chen, D. L., Moskowitz, T. J. & Shue, K. “Decision making under the gambler’s fallacy: evidence from asylum judges, loan officers, and baseball umpires.”
- Clotfelter, C. T. & Cook, P. J. “The ‘gambler’s fallacy’ in lottery play.”
- Gilovich, T., Vallone, R. & Tversky, A. “The hot hand in basketball: on the misperception of random sequences.”
- Miller, J. B. & Sanjurjo, A. “Surprised by the hot hand fallacy? A truth in the law of small numbers.”
- Hacking, I. “The inverse gambler’s fallacy: the argument from design. The anthropic principle applied to Wheeler universes.”