Impazamo yomngcakazi
Inkolelo yokuba isiphumo “sesifikelwe lixesha” kuba kudala singaphumi.
Emva kwabomvu abalishumi amathuba omnyama asengu-18/37. Ivili aligcini rekhodi kwaye alityalwa nto.
Impazamo
Ukuba obomvuibhejiObomvuIbheji yemali elinganayo kumanani ali-18 abomvu. NgesiFrentshi: rouge.Funda yonke → uphume amaxesha alishumi, abadlali abaninzi baziva ukuba omnyamaibhejiOmnyamaIbheji yemali elinganayo kumanani ali-18 amnyama. NgesiFrentshi: noir.Funda yonke → “sele efikelwe lixesha” baze babheje ngokwalo ndlela. Abanye baziva ukuba obomvu “ushushu” baze babheje kuye. Bobabini baqiqa besuka kulandelelwano olusele luphelile besiya kumjikelo ongekenzeki. IbholaizixhoboIbholaIbhola encinci ephoswa emzileni ngokuchasene nerotha. Iibhola zanamhlanje zenziwe nge-ivorine okanye nge-Teflon, zi-18–21 mm.Funda yonke → ayazi ukuba yayiyintoni imijikelo elishumi yokugqibela; izikhewuizixhoboIsikhewuEsinye sezikhewu ezingama-37 ezinamanani kwirotha. Kwakhona: slot, cup.Funda yonke → zinobungakanani obufanayo nobezinabo kwiyure edlulileyo; amathubaizibaloAmathubaIthuba lesiphumo, ukusuka ku-0 ukuya ku-1 okanye ku-0% ukuya ku-100%. Inani elinye: 1/37 = 2.70%.Funda yonke → omnyama ngu-18/37 njengoko kwakusoloko kunjalo.
Kutheni ivakala iyinyani
Ngokuhamba kwexesha, inxalenye yabomvu neyabamnyama iyasondela ku-18/37 nganye. Umthetho wamanani amakhuluizibaloUmthetho wamanani amakhuluUmndilili weziphumo ezizimeleyo usondela kwixabiso elilindelekileyo njengoko inani lemizamo likhula.Funda yonke → uyakuqinisekisa oko. Kodwa ukusondela kwenzeka ngokuxutywa, hayi ngokulungiswa: emva kwemijikelo eyongezelelweyo eyi-1,000 abomvu abalishumi abongezelelweyo bayimpazamo yokujikelezisa kwinxalenye, hayi kuba omnyama ebambile, kodwa kuba isampulu ikhulile. Akukho ndlela yenza omnyama abe nokwenzeka ngakumbi, kwaye umthetho wamanani amakhulu awufuni enjalo.
Monte Carlo, 18 Agasti 1913
Omnyama waphuma amaxesha angama-26 ngokulandelelana etafileni ekwi-Casino de Monte-Carlo. Ukusukela malunga nomnyama weshumi elinesihlanu, abadlali bagalela kobomvu, bephinda kabini besiphinda kabini kwakhona, umjikelo ngamnye “uqinisekile ngakumbi” kunowangaphambili. Ikhasino yaphumelela izigidi zeefranc. Uluhlu lwalunamathuba angu-1 kwizigidi ezili-137 ukususela kumnyama wokuqala, kwaye amathuba okuba ekugqibeleni lwenzeke ndaweni ithile kwiikhasino zehlabathi ayephantse aqiniseke ngokupheleleyo. Ngenxa yoko impazamo yomngcakazi ikwabizwa ngokuba yimpazamo yaseMonte Carlo.
Akukho nto ingaqhelekanga. Kwenzeka kanye kwama-44.
Abadlali baqalisa ukuqaphela. Obomvu “sele efikelwe lixesha”.
Itafile ixinene. Iibheji kobomvu ziphindwa kabini emva kwelahleko nganye.
Ubutyebi bulahlekile. Omnyama omtsha ngamnye wenza obomvu avakale eqinisekile ngakumbi.
Uluhlu luyaphela. Ikhasino iphumelele izigidi zeefranc kubantu ababebheja ngokuchasene noluhlu olwalungenakho “ukwazi” ukuba luluhlu.
Isandla esishushu
Ukuxhasa umbala kuba ukuluhlu yimpazamo efanayo ejikiweyo: kulindeleke ukuba uluhlu luqhubeke endaweni yokuba luphele. Iingcali zengqondo ziyibiza ngokuba sisandla esishushuintsomiIsandla esishushuInkolelo yokuba uthotho lokuphumelela, okanye lwesiphumo esinye, lwenza esinye sibe nethuba elingaphezulu. Evilini yimpazamo yomngcakazi ejikiweyo.Funda yonke → (hot hand), ngokophando lwango-1985 lukaGilovich, Vallone noTversky olwakhangela uluhlu ekudubuleni kwebhola yomnyazi lwaza alwafumana nto ngaphaya kwethamsanqa. Ngo-2018 uMiller noSanjurjo babonisa ukuba uvavanyo ngokwalo lwalutyekele kwicala elinye: kwirekhodi emfutshane, inxalenye yokungena emva nje kokungena iphuma iphantsi kwezinga lilonke lomdubuli ngokomndilili, ngoko umdlali ongenaso kwaphela isandla esishushu ukhangeleka ebanda kancinci. Xa kulungisiwe, idatha efanayo ibonisa isandla esishushu esincinci. Umntu angafudumala; ivili alinamo imeko yokuba kuyo. Abanye abadlali bakholelwa kuzo zombini ngaxeshanye, ukuba uluhlu luyaqhubeka de lube “lude kakhulu” luze luphele. Kwivili elingenamkhethe yonke inguqulelo inexabiso elifanayo elilindelekileyoizibaloIxabiso elilindelekileyoIsiphumo esiphakathi kwibheji nganye ekuhambeni kwexesha elide. −1/37 yebheji kuyo yonke ibheji eqhelekileyo yaseYurophu.Funda yonke → nokukhetha umbala ngokuphosa ingqekembe: −2.70% yebheji.
Etafileni yokwenyani
UCroson noSundali (2005) babukela iiyure ezili-18 zevidiyo yokhuseleko yetafile enye eneqandaiviliIqandaIsikhewu esinye esiluhlaza esingagubungelwa yibheji yemali elinganayo, yedazini okanye yekholamu; umthombo wenzuzo yekhasino. Kwakhona: iqanda elinye, 0.Funda yonke → eliphindiweyo kwikhasino enkulu eReno: abadlali abali-139 bebeka iibheji ezingama-24,131. Kwiibheji zemali elinganayoibhejiIbheji yemali elinganayoObomvu/omnyama, angalinganiyo/alinganayo, aphezulu/aphantsi. Amanani ali-18, ihlawula u-1:1.Funda yonke →, abadlali babephantse bohlukane ngokulinganayo phakathi kokulandela uluhlu olufutshane nokuluchasa. Emva kwezintlanu zohlobo olunye ngokulandelelana babetyekela ekuchaseni uluhlu, kwaye emva kwezintandathu nangaphezulu, ama-85% eebheji zabo ayekwelinye icala. Kwaba badlali bafanayo babonisa isandla esishushu ngokwabo: emva kokuphumelela kumanani babegubungela amanani ali-13.6 kumjikelo olandelayo ngokomndilili, xa kuthelekiswa nali-9.2 emva kwelahleko. Ivili labo alizange libonise phawu lokuthambekela, ngoko akukho nto kwezi yatshintsha oko nabani na kubo wayenokukulindela.
Ngaphandle kwekhasino
Lo mtsalane ufanayo uvela apho kwenziwa khona izigqibo zokwenyani. UClotfelter noCook (1993) balandela umdlalo wamanani wemihla ngemihla waseMaryland: imali ebhejwa kwinani yehla kakhulu kwakamsinya nje emva kokuba lizotyiwe kwaye yathatha iinyanga ukubuyela, nangona ukuzoba kungenankumbulo. UChen, Moskowitz noShue (2016) bayifumana phakathi kweengcali. Iijaji zaseMelika ezigweba iimbacu zazinokwenzeka ukuba zale ityala ngamanqaku epesenti angama-3.3 ngaphezulu ukuba zivume elingaphambili. Oonompire bebaseball babenokwenzeka ngamanqaku ali-1.5 ngaphantsi ukuba babize i-strike emva kokubiza enye, kwaye ngaphezu kokuphindwe kabini koko kwiibhola ezisondeleyo. Kuvavanyo lwasentsimini namagosa emali-mboleko ahlawulwa umrhumo omiselweyo, ukuya kuma-9% ezigqibo zaguqulwa ngale ndlela. Amatyala ayefika ngolandelelwano olungacwangciswanga, ngoko isigqibo sokugqibela sasingathethi nto ngesilandelayo, kanye njengokuba umjikelo wokugqibela ungathethi nto ngolandelayo.
Impazamo yomngcakazi eguqulweyo
Isithandi-sobulumko u-Ian Hacking (1987) wanika igama kwinguqulelo yesithathu. Umntu ungena egumbini, abone idayisi ezimbini ziwa zibonisa izithandathu ezimbini aze agqibe kwelokuba kufuneka ukuba sele ziphoswe amaxesha amaninzi. Ukuphosa ngakunye kunamathuba alinganayo okuba zizithandathu ezimbini, nokuba kokokuqala ngobusuku okanye kwewaka, ngoko oko akubonayo akuthethi nto ngokuba umdlalo udlalwe ixesha elingakanani. Kwi-roulette ngumdlali ofika kwibhodi ebonisa abomvu abasibhozo aze agqibe kwelokuba itafile kufuneka ibijikeleziswa iiyure ukuze ibavelise. Impazamo eqhelekileyo ifaka okudlulileyo kumjikelo olandelayo; le ifaka into enqabileyo ebonwayo kwixesha elidlulileyo ekungekho mntu walibonayo.
Ingcali yengqondo eyayikholelwa kuyo
Impazamo iye yaba nabakhuseli abafundileyo. Ingcali yengqondo yaseJamani uKarl Marbe yahlola iirejista ezine zokuzalwa ezingama-49,152 nganye, yafumanisa ukuba olona luhlu lude lwamakhwenkwe okanye lwamantombazana ngokulandelelana lwalungu-17, yaza yagqiba kwelokuba uluhlu olude lunqabile kunokuba ithamsanqa livumela, ngoko uluhlu lwenza esinye isiphumo sibe nokwenzeka ngakumbi. Ithamsanqa lodwa lithi akunjalo: kukuzalwa okuli-196,608 uluhlu lwe-17 nangaphezulu luvela malunga namaxesha amane kwamahlanu. UMarbe wayefumene kanye oko kukhangeleka ngako ulandelelwano olungacwangciswanga. U-Epstein (2013) ulibalisa kwakhona eli tyala; iphepha elithi Amathuba oluhlu lweziphumo kwi-roulette linika inguqulelo ye-roulette.
Apho impazamo ingasebenziyo
Ukuba ivili belithambekile ngokwasemzimbeni, imijikelo edlulileyo ibiya kunika ulwazi, kuba ibiya kuba bubungqina ngezikhewu kunokuba bube ngethamsanqa. Leso sisihloko seLebhu ye-roulette, kwaye kufuneka imijikelo engamawaka kwivili elinye elaziwayo ukuze kuthethwe nantoni na. Kuluhlu lwabomvu abalishumi kwivili elingaziwayo, ingcaciso yokuthambekela ayinakwenzeka kangako kunaleyo yethamsanqa.
Imibuzo
Hayi. Isebenza kuyo nayiphi na into ephindaphindwayo ezimeleyo: idayisi, iingqekembe, amanani elotho.
Iinxalenye ziya kusondelelana. Isiphumo sakho siya kuhlala simalunga ne-−2.70% yoko ukubhejileyo.
Akukho mthetho womndilili. Kukho umthetho wamanani amakhulu, kwaye usebenza ngokuxutywa.
Ukonwaba ngezibalo
Qala uzizame ngokwakho. Isisombululo ngasinye sisongiwe; sivule xa ukulungele.
Emva kokuphosa ingqekembe amaxesha ali-10 ibonisa iintloko ezi-7 nemisila emi-3. Emva kokuphosa okuyi-1,000 ibonisa iintloko ezingama-517 nemisila engama-483. Ingaba imisila yabamba?
Bonisa isisombululo
Impendulo Hayi. Umsantsa wakhula ukusuka kwi-4 ukuya kuma-34. Ngumlinganiselo kuphela owasondela ekulinganeni.
Umlinganiselo weentloko kwimisila wehla ukusuka ku-7/3, malunga no-2.33, ukuya ku-517/483, malunga no-1.07. Lowo ngumthetho wamanani amakhuluizibaloUmthetho wamanani amakhuluUmndilili weziphumo ezizimeleyo usondela kwixabiso elilindelekileyo njengoko inani lemizamo likhula.Funda yonke → usebenza.
Umsantsa phakathi kwazo wakhula, ukusuka kwi-4 ukuya kuma-34. Ngengqekembe engenamkhethe umsantsa omalunga nama-30 emva kokuphosa okuyi-1,000 uqhelekile: umsantsa oqhelekileyo ukhula malunga nengcambu yesikwere yenani lokuphosa, ngelixa umlinganiselo uzinza ngakuye u-1.
Akukho nto yabuyisa imisila. Ukongezeka kweentloko kwasekuqaleni kwaxutywa kukuphosa okungama-990 okulandelayo, akuzange kulungiswe.
Phosa ingqekembe amaxesha amane uze ujonge kuphela ukuphosa okuza emva nje kwentloko. Yeyiphi inxalenye yezo eziintloko? Yisebenze kulandelelwano ngalunye kwezi-16 ezinokubakho uze uthathe umndilili weenxalenye. Ingaba ngama-50%?
Bonisa isisombululo
Impendulo Hayi. Ngu-17/42, malunga nama-40.5%. Xa kujongwa ngale ndlela, ingqekembe engenamkhethe ibonakala ibanda emva kwentloko.
Dwelisa ulandelelwano oluli-16 (H yintloko, T ngumsila). Olubini kulo, TTTT no-TTTH, alunantloko kukuphosa kokuqala okuthathu, ngoko akukho nto ilandela intloko; kusala ali-14.
Kulandelelwano ngalunye, thatha ukuphosa okulandela intloko uze ufumane inxalenye eziintloko. HHHH inika ezi-3 kwezi-3. HHHT inika ezi-2 kwezi-3. HTHT inika u-0 kwezi-2. Ukuhamba kuzo zonke ezili-14: ulandelelwano oluthandathu lunika u-0, olune lunika u-1/2, olunye lunika u-2/3 kwaye oluthathu lunika u-1 (HHHH, THHH no-TTHH).
Dibanisa iinxalenye: 4 × 1/2 + 2/3 + 3 = 17/3. Yahlula ngali-14: 17/42 ≈ 40.5%.
Akukho kuphosa kuthanda umsila; nganye ingama-50–50. Ukutyekela kuvela ekuthatheni umndilili ulandelelwano ngolandelelwano: ulandelelwano oluzele ziintloko lunokuphosa okuninzi okunokujongwa kodwa lubalwa kanye, ngokufanayo nolandelelwano olunye kuphela. UMiller noSanjurjo (2018) babonisa ukuba uphando lwesandla esishushu lwango-1985 lwalulinganise abadlali balo bebhola yomnyazi ngale ndlela, ngoko abadlali ababonakala bengenaluhlu lude ngaphezu kwethamsanqa ngokwenene babenoluhlu ngakumbi kancinci.
Uncumo
Ukuxutywa, hayi ukulungiswa. Ivili alityalwa nto.
Imithombo
- 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.”