Juumre Fijoowo Kaalis
Hoolaade wonde njeñtudi ina “hewtii” sabu ummaaki ko ɓooyi.
Caggal boɗeeje sappo, porobabilite ɓaleere ina woni tawo 18/37. Taarorde ndee winndataa hay huunde, ndee yoɓetaake hay huunde.
Juumre ndee
So boɗeerepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof → ummiima laabi sappo, fijooɓe heewɓe ina keɓtina wonde ɓaleerepariƁaleerePari njoɓdi fotndi e limooje 18 ɓaleeje. E Farayse: noir.Tar fof → ina “hewtii” ɓe ngaɗa pari e mayre. Woɓɓe ina keɓtina wonde boɗeere ina “wuli” ɓe ngaɗa pari e mayre. Ɓe ɗiɗo fof ina ƴeewndoo jokkondiral timmungal ngam taarol ngol waɗaaki tawo. BalkuutorɗeBalBal tokoosal werlaangal e laawol ngol e laawol rotoor ngol. Balli jamaanu hannde ko ivorine walla Teflon, 18–21 mm.Tar fof → ngal anndaa ko taarle sappo sakkitiiɗe ɗee ngoni; cuuɗikuutorɗeSuuduGootel e cuuɗi 37 limoraaɗi e rotoor. Ina noddee kadi: wenndu, kopp.Tar fof → ɗii ina poti mawneeki e no ɗi ngonnoo waktu ɓennuɗo; porobabilitematematikPorobabiliteSahaa njeñtudi, immorde 0 haa 1 walla 0% haa 100%. Limoore wootere: 1/37 = 2,70%.Tar fof → ɓaleere ko 18/37 no woniri kala sahaa.
Ko waɗi ɗum ina wayi no goonga
E juuta, feccere boɗeeje e ɓaleeje ina ɓadoo 18/37 kala. Sariya limooje mawɗematematikSariya limooje mawɗeHakkundeere njeñtuɗi ceertuɗi ina ɓadoo njaru fodaandu tuma nde limoore etaaɗe ɓeydotoo.Tar fof → ina tabitina ɗum. Kono ɓadagol ngol ina waɗa e lattinde ndiyam, wonaa e feewnude: caggal taarle 1 000 goɗɗe, boɗeeje sappo ɓeydiiɗe ɗee ko juumre hiisa e feccere ndee, wonaa sabu ɓaleere tawtii, kono sabu misal ngal mawni. Alaa masiŋ waɗata ɓaleere ina ɓura sahaa, sariya limooje mawɗe kadi sokliraa ɗum.
Monte-Carlo, 18 Ut 1913
Ɓaleere ummiima laabi 26 jokkondirɗi e taabal e Casino de Monte-Carlo. Gila ɓaleere sappo e joyaɓere hedde, fijooɓe ina ndenndii e boɗeere, ina ɗiɗiɓna, ina ɗiɗiɓna kadi, kala taarol ina “ɓura goongaaji” e ngol ɓennungol. Kasino dañii miliyoŋaaji faraŋ. Jokkondiral ngal jogii ko porobabilite 1 e nder miliyoŋaaji 137 gila ɓaleere aranndeere, porobabilite wonde ɗum ina waɗoo sakket e nokku e kasinooji aduna kadi ko hedde gooto. Ɗum woni ko waɗi juumre fijoowo kaalis ina noddee kadi juumre Monte-Carlo.
Huunde aadanteende. Ina waɗa laawol gootol e nder 44.
Fijooɓe ina fuɗɗa tiiɗnaade. Boɗeere ina “hewtii”.
Taabal ngal ina heewi. Pariiji e boɗeere ina ɗiɗiɓnee caggal kala majjere.
Jawdi majjii. Kala ɓaleere hesere ina waɗa boɗeere ina keɓtinee ɓurde goongaaji.
Jokkondiral ngal ina gasa. Kasino dañii miliyoŋaaji faraŋ e yimɓe waɗooɓe pari e dow jokkondiral ngal waawaano “anndude” wonde ko jokkondiral.
Jungo wulngo
Tammbaade noone sabu ina e jokkondiral ko juumre wootere ndee huccitinaande: ina fodee jokkondiral ngal ina jokkoo, wonaa gasde. Ganndo miijo neɗɗo ina noddira ɗum jungo wulngomiijo juumɗoJungo wulngoHoolaare wonnde dañe jokkondirɗe, walla njeñtudi wootiri ina jokkondiri, ina ɓeyda porobabilite goɗndi. E taarorde ko juumre fijoowo kaalis huccitinaande.Tar fof →, caggal jaŋde 1985 Gilovich, Vallone e Tversky ɗi ndaarnoo jokkondire e fiɗgol bal e basket, ɗi njiyaani hay ɗe ɓuri sahaa. E 2018 Miller e Sanjurjo kolliri wonde ƴeewndo ngoo e hoore mum ooñiino: e winndannde gaɗaande, feccere dañe ɗe ngaddi caggal dañal ina woni les feccere fof fiɗoowo e hakkundeere, ɗuum waɗi fijoowo mo alaa jungo wulngo fof ina wayi no jaangi seeɗa. So feewnaama, keɓe ɗee ina kolla jungo wulngo seeɗa. Neɗɗo ina waawi wulde; taarorde alaa ngonka ngo woni e mum. Fijooɓe woɓɓe ina njogii hoolaare ɗiɗi ɗee e sahaa gootal: jokkondiral ina jokkoo haa “juuta no feewi” refti gasa. E taarorde peewnde kala mbaadi ina jogii njaru fodaandumatematikNjaru fodaanduNjeñtudi hakkundeere e kala pari e juuta. −1/37 pari ngam kala pari Orop laawol.Tar fof → wootu ndun e suɓaade noone e jaaɓugol pees kaalis: −2,70% pari.
E taabal goonga
Croson e Sundali (2005) ndaarii waktuuji 18 widewo reentaari taabal seerotaarordeSeeroSuudu haako wootere nde hay pari njoɓdi fotndi, sappo e ɗiɗi walla kolon kuuɓataa; ko ɗum woni iwdi ɓural kasino. Ina noddee kadi: seero gooto, 0.Tar fof → ɗiɗi gootal e kasino mawɗo to Reno: fijooɓe 139 waɗooɓe pariiji 24 131. E pariiji njoɓdi fotndipariPari njoɓdi fotndiBoɗeere/ɓaleere, peccotaake/peccotoonde, mawɗe/tokooseeje. Limooje 18, ina yoɓa 1:1.Tar fof →, fijooɓe ina pecciino hedde potngol hakkunde rewɓe jokkondire gaɗaaɗe e luurdooɓe ɗe. Caggal noone wootere laabi joy jokkondirɗi ɓe ooñaama e luurde jokkondiral ngal, caggal jeegom walla ko ɓuri, 85% pariiji maɓɓe ina ngonnoo e geɗal goɗngal. Fijooɓe gooto ɓeen kolliri jungo wulngo e hoore maɓɓe: caggal dañal e limooje ɓe kuuɓnoo limooje 13,6 e taarol garoowol e hakkundeere, ndeen ko 9,2 caggal majjere. Taarorde maɓɓe holliraa hay maande ooñol, ɗuum waɗi hay huunde e ɗum waylitaani ko hay gooto e maɓɓe waawnoo fodaade.
Caggal kasino
Foodagol gootol ngol ina yiyee ɗo kuuɓtodi goonga ina mbaɗee. Clotfelter e Cook (1993) njokkii fijo limooje ñalnde kala Maryland: kaalis pariyaaɗo e limoore ina ustoo no feewi nde ndee yaltii, ina ɓooya lebbi ado rutteede, tawa yaltinngol ngol alaa jejjitaare. Chen, Moskowitz e Shue (2016) tawii ɗum e nder gannduɓe golle. Ñaawooɓe dañgol hisnaare Dowlaaji Dentuɗi Amerik ina ɓura haa poyaaji 3,3 salaade dosiye so ɓe jaɓii ngo ado mum. Ñaawooɓe baseball ina ustoo poyaaji 1,5 e wiyde strike caggal wiyde gooto, e ko ɓuri laabi ɗiɗi ɗum e fiɗɗe ɓadiiɗe. E ƴeewndo e nder golle e kurtiiɓe ñamaleeje yoɓeteeɓe njoɓdi fotndi, haa 9% kuuɓtodi ina mbaylitaa e ndee laawol. Dosiyeeji ɗii ina ngarnoo e doggol sahaa, ɗuum waɗi kuuɓtodi sakkitiindi wiyaani hay huunde e ndi garooti, no taarol sakkitiingol wiyataa hay huunde e ngol garoowol.
Juumre fijoowo kaalis huccitinaande
Ganndo filosofi Ian Hacking (1987) inndii mbaadi tataɓol. Neɗɗo ina naata e suudu, ina yi’a deeji ɗiɗi ina njana jeegom e jeegom, ina sikka wonde ɗi njaltinaama laabi keewɗi ado. Kala jaltinngol ina foti sahaa wonde jeegom e jeegom, ngol aranngol e jemma oo walla ngol ujunereewol, ɗuum waɗi ko o yi’i wiyaa hay huunde e no fijo ngoo ɓooyiri. E ruleet ko fijoowo hewtoyɗo e tabalo hollirɗo boɗeeje jeetati, sikki wonde taabal ngal ina taarnoo waktuuji ngam addude ɗe. Juumre aadanteende ndee ina janngira ko ɓenni e taarol garoowol; ndee ina janngira huunde nde heewaa e ko ɓenni ko hay gooto yi’aani.
Ganndo miijo neɗɗo hoolaaɗo ɗum
Juumre ndee jogiima faabooɓe gannduɓe. Ganndo miijo neɗɗo Almaañ Karl Marbe ƴeewtii kaaye winndannde nay, kala e majje ko jibinannde 49 152, tawi jokkondiral ɓurngal juutde sukaaɓe worɓe walla rewɓe jokkondirɓe ko 17, sikki wonde jokkondire juutɗe ina ɓura famɗude e ko sahaa newnani, ɗuum waɗi jokkondiral ina waɗa njeñtudi goɗndi ina ɓura sahaa. Sahaa tan ina wiya ko woɗɗi ɗum: e jibinannde 196 608, jokkondiral 17 walla ko ɓuri ina ummoo hedde laabi nay e nder joy. Marbe tawii ko jokkondiral sahaa wayi ko feewi. Epstein (2013) ina hokka ndee daarol; Porobabilite Jokkondire e Ruleet ina hokka mbaadi ruleet.
Ɗo juumre ndee huutortaake
So taarorde ndee ooñiino e ɓalli mum, taarle ɓennuɗe ina ndokkatno kabaruuji, sabu ɗe ngonata seedeeji e cuuɗi ɗii, wonaa e sahaa. Ɗum ko yiyannde Laboratuwaar, ina sokli ujunaaji taarle e taarorde wootere anndaande ado wiyde hay huunde. E jokkondiral boɗeeje sappo e taarorde nde anndaaka, firo ooñol ngol ina ɓura famɗude sahaa e firo sahaa ngol no feewi.
Naamne
Alaa. Ina huutoree e kala huunde ceertunde fuɗɗitotoonde: deeji, pees kaalis, limooje lotori.
Fecce ɗee ina ɓadoo. Njeñtudi maa ina wona tawo hedde −2,70% ko waɗ-ɗaa pari.
Alaa sariya hakkundeere. Ko sariya limooje mawɗe woodi, ngal ina gollira lattinde ndiyam.
Weltaare e Matematik
Etu ɗum hoore maa adii. Kala jaabawol ina suuɗii; uddit ɗum so a heblii.
Caggal werlagol laabi 10, piyees ina holla fas 7 e pil 3. Caggal werlagol laabi 1 000 ina holla fas 517 e pil 483. Hol pil yettii fas?
Hollu jaabawol ngol
Jaabawol Alaa. Ceerndugol ngol ɓeydii iwde 4 haa 34. Fecceere ndee tan ɓadii potde.
Fecceere fas e pil jippii iwde 7/3, hedde 2,33, haa 517/483, hedde 1,07. Ɗum ko sariya limooje mawɗematematikSariya limooje mawɗeHakkundeere njeñtuɗi ceertuɗi ina ɓadoo njaru fodaandu tuma nde limoore etaaɗe ɓeydotoo.Tar fof → ina golla.
Ceerndugol hakkunde maɓɓe ɓeydii, iwde 4 haa 34. E piyees potɗo, ceerndugol hedde 30 caggal werlagol 1 000 ko ordinaare: ceerndugol ngol ina mawna hedde e rasin karre keewal werlagol, nde fecceere ndee ina ɓada 1.
Hay huunde ruttaani pil. Ɓuri fas gadanɗo ina saakaa e werlagol 990 garooji ɗii, wonaa feewnaa.
Werlo piyees laabi nay, ndaar tan werlagol jokkiiɗi fas. Feccere honnde e majji ko fas? Hiisa ɗum e kala e jokkondire 16 waawooje ɗee, ƴettu hakkundeere fecceeje ɗee. Hol ko 50%?
Hollu jaabawol ngol
Jaabawol Alaa. Ko 17/42, hedde 40,5%. E ndee ndaarngal, piyees potɗo ina sikkee ina jaangoo caggal fas.
Limto jokkondire 16 ɗee (F = fas, P = pil). Ɗiɗi e majji, PPPP e PPPF, alaa fas e werlagol tati adanɗi, ndeen hay huunde jokkaani fas; 14 ina keddoo.
E kala e majji, ƴettu werlagol jokkiiɗi fas, yiytu feccere ko fas. FFFF ina rokka 3 e 3. FFFP ina rokka 2 e 3. FPFP ina rokka 0 e 2. E yahde e 14 ɗee fof: jokkondire jeegom ina rokka 0, nay ina rokka 1/2, gootal ina rokka 2/3, tati ina rokka 1 (FFFF, PFFF e PPFF).
Hawtu fecceeje ɗee: 4 × 1/2 + 2/3 + 3 = 17/3. Feccu e 14: 17/42 ≈ 40,5%.
Alaa werlagol ɓurɗo yiɗde pil; kala ko 50–50. Ooñol ngol ina iwa e ƴettude hakkundeere jokkondiral e jokkondiral: jokkondiral heewngal fas ina jogii werlagol keewɗi ndaareteeɗi kono ina limee laawol gootol, hono jokkondiral jogiingal fas gootol tan. Miller e Sanjurjo (2018) kolliino wonde ƴeewndo jungo wulngo hitaande 1985 betiino fijooɓe basket mum e ndee laawol, ndeen fijooɓe sikkaaɓe ɓurtaa sahaa e jokkondire dañe ina ɓurnoo ɗum seeɗa e goonga.
Ƴeewndo weltinoowo
Lattinde, wonaa feewnude. Taarorde ndee yoɓetaake hay huunde.
Iwdi
- 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.”