Iphutha lomgembuli
Inkolelo yokuthi umphumela othile “usufike isikhathi sawo” ngoba kade ungaveli.
Ngemuva kwezibomvu eziyishumi amathuba okumnyama asengu-18/37. Isondo aligcini rekhodi futhi alikweletanga lutho.
Iphutha
Uma okubomvuukubhejaBomvuUkubheja okulingana nemali ezinombolweni eziyi-18 ezibomvu. NgesiFulentshi: rouge.Funda konke → sekuphume kayishumi, abadlali abaningi bazizwa sengathi okumnyamaukubhejaMnyamaUkubheja okulingana nemali ezinombolweni ezimnyama eziyi-18. NgesiFulentshi: noir.Funda konke → “sekufike isikhathi sakho” bese bebheja ngokuvumelana nalokho. Abanye bazizwa sengathi okubomvu “kuyashisa” bese bebheja kukho. Bobabili bacabanga besuka ekulandelaneni okusekuphelile beya ekujikelezeni okungakenzeki. IbholaokokusebenzaIbholaIbhola elincane eliphonswa emzileni libheke ngakolunye uhlangothi lwe-rotor. Amabhola esimanje enziwa nge-ivorine noma nge-Teflon, angu-18–21 mm.Funda konke → alazi ukuthi ukujikeleza okuyishumi okudlule bekuyini; amagodiokokusebenzaIgodiEsinye sezikhala ezingu-37 ezinezinombolo ku-rotor. Kubuye kuthiwe: slot, cup.Funda konke → asalingana ngobukhulu nangehora elidlule; amathubaizibaloAmathubaIthuba lomphumela, kusukela ku-0 kuya ku-1 noma ku-0% kuya ku-100%. Inombolo eyodwa: 1/37 = 2.70%.Funda konke → okumnyama angu-18/37 njengoba bekuhlale kunjalo.
Kungani kuzwakala kuyiqiniso
Esikhathini eside izingxenye zokubomvu nokumnyama ziyasondela ku-18/37 ngayinye. Umthetho wezinombolo ezinkuluizibaloUmthetho wezinombolo ezinkuluIsilinganiso semiphumela ezimele sisondela enanini elilindelekile njengoba inani lemizamo likhula.Funda konke → uyakuqinisekisa lokho. Kodwa ukusondela kwenzeka ngokuhlanjululwa, hhayi ngokulungiswa: ngemuva kokujikeleza okungu-1,000 okwengeziwe, izibomvu eziyishumi ezengeziwe sezincane kangangokuthi azibonakali engxenyeni, hhayi ngoba okumnyama kufinyelele kokubomvu kodwa ngoba isampula likhulile. Ayikho indlela eyenza okumnyama kube namathuba amakhulu, futhi umthetho wezinombolo ezinkulu awuyidingi.
Monte Carlo, 18 Agasti 1913
Okumnyama kwaphuma izikhathi ezingu-26 ngokulandelana etafuleni e-Casino de Monte-Carlo. Kusukela cishe kokumnyama kweshumi nanhlanu, abadlali bagxumela kokubomvu ngobuningi, bephinda kabili baphinde futhi, ukujikeleza ngakunye “kuqiniseke kakhulu” kunokwangaphambili. Ikhasino yawina izigidi zama-franc. Lolo chungechunge lwalunamathuba angu-1 ezigidini ezingu-137 kusukela kokumnyama kokuqala, futhi amathuba okuthi ekugcineni lwenzeke kwenye indawo emakhasino omhlaba ayecishe abe yisiqiniseko. Yisona sizathu sokuthi iphutha lomgembuli libizwe nangokuthi iphutha lase-Monte Carlo.
Akumangalisi. Kwenzeka kanye ezikhathini ezingu-44.
Abadlali baqala ukuqaphela. Okubomvu “sekufike isikhathi sakho”.
Itafula ligcwele. Amanani abhejwa kokubomvu aphindwa kabili ngemuva kokuhlulwa ngakunye.
Kulahleka imali eningi. Okumnyama okusha ngakunye kwenza okubomvu kuzwakale kuqiniseke kakhulu.
Uchungechunge luyaphela. Ikhasino isiwine izigidi zama-franc kubantu ababheja ngokumelene nochungechunge olungakwazanga “ukwazi” ukuthi luwuchungechunge.
Isandla esishisayo
Ukusekela umbala ngoba usochungechungeni kuyiphutha elifanayo eliphenduliwe: kulindeleke ukuthi uchungechunge luqhubeke esikhundleni sokuphela. Izazi zengqondo zikubiza ngokuthi isandla esishisayoinganekwaneIsandla esishisayoInkolelo yokuthi uchungechunge lokuwina, noma lomphumela owodwa, lwenza okunye kube namathuba amakhulu. Esondweni kuyiphutha lomgembuli eliphenduliwe.Funda konke → (hot hand), ngemuva kocwaningo lwango-1985 lwe-Gilovich, Vallone no-Tversky olwafuna uchungechunge ekushayeni ibhola lomnqakiswano (basketball) futhi lwangalutholi ngaphezu kwenhlanhla. Ngo-2018 u-Miller no-Sanjurjo bakhombisa ukuthi ukuhlola uqobo kwakuchemile: kurekhodi elifushane, ingxenye yokungena ngokushesha ngemuva kokungena iba ngaphansi kwezinga lomshayi lilonke ngokwesilinganiso, ngakho umdlali ongenaso nhlobo isandla esishisayo ubukeka ebanda kancane. Uma kulungisiwe, idatha efanayo ikhombisa isandla esishisayo esincane. Umuntu angafudumala; isondo alinaso isimo sokushisa noma sokubanda. Abanye abadlali bakholelwa kuzo zombili izinkolelo ngesikhathi esisodwa, ukuthi uchungechunge luqhubeka luze lube “lude kakhulu” bese luyaphela. Esondweni elinobulungiswa yonke inguqulo inenani elilindelekileizibaloInani elilindelekileUmphumela ovamile ekubhejeni ngakunye esikhathini eside. U-−1/37 wenani elibhejwayo kukho konke ukubheja okujwayelekile kwaseYurophu.Funda konke → elifanayo nokukhetha umbala ngokuphonsa uhlamvu lwemali: −2.70% wenani elibhejwayo.
Etafuleni langempela
U-Croson no-Sundali (2005) babuka amahora angu-18 evidiyo yokuphepha yetafula elilodwa elineqandaisondoIqandaIgodi elilodwa eliluhlaza elingambozwa ukubheja okulingana nemali, okwedazini noma okwekholamu; umthombo wenzuzo yekhasino. Kubuye kuthiwe: iqanda elilodwa, 0.Funda konke → eliphindiwe ekhasino enkulu e-Reno: abadlali abangu-139 bebheja izikhathi ezingu-24,131. Ekubhejeni okulingana nemaliukubhejaUkubheja okulingana nemaliBomvu/mnyama, engalingani/elinganayo, phezulu/phansi. Izinombolo eziyi-18, kukhokha u-1:1.Funda konke →, abadlali babecishe bahlukane ngokulinganayo phakathi kokulandela uchungechunge olufushane nokuluphikisa. Ngemuva kwemiphumela emihlanu efanayo ngokulandelana bathambekela ekuphikiseni uchungechunge, futhi ngemuva kwesithupha noma ngaphezulu, u-85% wokubheja kwabo wawukolunye uhlangothi. Abadlali abafanayo bakhombisa isandla esishisayo ngabo uqobo: ngemuva kokuwina ezinombolweni bamboza izinombolo ezingu-13.6 ekujikelezeni okulandelayo ngokwesilinganiso, uma kuqhathaniswa no-9.2 ngemuva kokuhlulwa. Isondo labo lalingakhombisi luphawu lokuchema, ngakho akukho kulokhu okwashintsha lokho noma ubani wabo ayengakulindela.
Ngaphandle kwekhasino
Lokhu kudonsa okufanayo kuyavela lapho kwenziwa khona izinqumo zangempela. U-Clotfelter no-Cook (1993) balandela umdlalo wezinombolo wansuku zonke wase-Maryland: imali ebhejwa enombolweni yehla kakhulu ngokushesha nje uma idonswe futhi yathatha izinyanga ukuze ibuyele, nakuba ukudonswa kungenayo inkumbulo. U-Chen, Moskowitz no-Shue (2016) bakuthola kochwepheshe. Amajaji okukhoseliswa (asylum) ase-United States ayenamathuba angaba amaphuzu angu-3.3 ephesenti aphezulu okwenqaba icala uma ayevumile elangaphambili. Onompempe be-baseball babenamathuba aphansi ngamaphuzu angu-1.5 okubiza i-strike ngemuva kokubiza eyodwa, futhi ngaphezu kokuphindwe kabili kwalokho kumabhola asondelene. Ocwaningweni lwasensimini nezikhulu zemalimboleko ezikhokhelwa imali engaguquki, kwaguqulwa ngale ndlela izinqumo ezifika ku-9%. Amacala ayefika ngokulandelana okungahleliwe, ngakho isinqumo sokugcina sasingasho lutho ngesilandelayo, njengoba nje ukujikeleza kokugcina kungasho lutho ngokulandelayo.
Iphutha lomgembuli eliphambene
Isazi sefilosofi u-Ian Hacking (1987) waqamba inguqulo yesithathu. Umuntu ungena egumbini, abone amadayisi amabili ewela kweziyisithupha zombili bese ephetha ngokuthi kumele ukuthi asephonswe izikhathi eziningi. Konke ukuphonsa kunamathuba alinganayo okuba yiziyisithupha zombili, okokuqala kwakusihlwa noma okwenkulungwane, ngakho lokho akubonayo akusho lutho ngokuthi umdlalo usuqhubeke isikhathi esingakanani. Ku-roulette kungumdlali ofika ebhodini elikhombisa izibomvu eziyisishiyagalombili bese enquma ukuthi itafula kumele ukuthi belilokhu lijikeleza amahora ukuze lizikhiqize. Iphutha elijwayelekile lifunda okwedlule ekujikelezeni okulandelayo; leli lisebenzisa into engavamile elibonayo ukuqagela okwedlule okungabonwanga muntu.
Isazi sengqondo esasikholelwa kulo
Leli phutha libe nabavikeli abafundile. Isazi sengqondo saseJalimane u-Karl Marbe sahlola amarejista amane okuzalwa angu-49,152 ilinye, sathola ukuthi uchungechunge olude kakhulu lwabafana noma lwamantombazane ngokulandelana lwalungu-17, futhi saphetha ngokuthi uchungechunge olude luyivelakancane kunalokho okuvunyelwa yinhlanhla, ngakho uchungechunge lwenza omunye umphumela ube namathuba amakhulu. Inhlanhla yodwa ithi akunjalo: ekuzalweni okungu-196,608 uchungechunge lwabangu-17 noma ngaphezulu luvela cishe kane kwezinhlanu. U-Marbe wayethole kanye indlela ukulandelana okungahleliwe okubukeka ngayo. U-Epstein (2013) uphinda alandise leli cala; ikhasi elithi Amathuba ochungechunge ku-roulette linikeza inguqulo ye-roulette.
Lapho iphutha lingasebenzi khona
Ukube isondo belichemile ngokwesakhiwo, ukujikeleza okudlule bekungaba nolwazi, ngoba bekungaba wubufakazi ngamagodi kunokuba kube ngenhlanhla. Leso yisihloko seLabhorethri ye-roulette, futhi sidinga ukujikeleza okuyizinkulungwane esondweni elilodwa elaziwayo ukuze kushiwo okuthile. Ochungechungeni lwezibomvu eziyishumi esondweni elingaziwa, incazelo yokuchema inamathuba amancane kakhulu kunencazelo yenhlanhla.
Imibuzo
Cha. Lisebenza kunoma yisiphi isenzakalo esizimele esiphindwayo: amadayisi, izinhlamvu zemali, izinombolo zelotho.
Izingxenye zizosondelana. Umphumela wakho uzobe usacishe ube ngu-−2.70% walokho okubhejile.
Awukho umthetho wezilinganiso. Kukhona umthetho wezinombolo ezinkulu, futhi usebenza ngokuhlanjululwa.
Ubumnandi bezibalo
Zama lezi ngokwakho kuqala. Isixazululo ngasinye sifihliwe; sivule uma usukulungile.
Ngemuva kokuphonswa kayi-10 uhlamvu lwemali lukhombisa amakhanda angu-7 nemisila emi-3. Ngemuva kokuphonswa okungu-1,000 lukhombisa amakhanda angu-517 nemisila engu-483. Ingabe imisila yafinyelela amakhanda?
Bonisa isixazululo
Impendulo Cha. Igebe lakhula lisuka ku-4 laya ku-34. Isilinganiso kuphela esasondela ekulinganeni.
Isilinganiso samakhanda nemisila sehla sisuka ku-7/3, cishe u-2.33, saya ku-517/483, cishe u-1.07. Lokho ngumthetho wezinombolo ezinkuluizibaloUmthetho wezinombolo ezinkuluIsilinganiso semiphumela ezimele sisondela enanini elilindelekile njengoba inani lemizamo likhula.Funda konke → usebenza.
Igebe phakathi kwakho lakhula, lisuka ku-4 laya ku-34. Ngohlamvu lwemali olulungile igebe elingaba ngu-30 ngemuva kokuphonswa okungu-1,000 liyinto evamile: igebe elivamile likhula cishe ngempande yesikwele yenani lokuphonswa, kanti isilinganiso sizinza sibheke ku-1.
Akukho okwabuyisela imisila emuva. Ukweqa kwamakhanda kwasekuqaleni kwahlanjululwa wukuphonswa okungu-990 okulandelayo, akuzange kulungiswe.
Phonsa uhlamvu lwemali kane bese ubheka kuphela ukuphonswa okulandela ngokushesha ikhanda. Yiyiphi ingxenye yalokho engamakhanda? Kubale kukho konke ukulandelana okungu-16 okungenzeka bese uthatha isilinganiso sezingxenye. Ingabe kungu-50%?
Bonisa isixazululo
Impendulo Cha. Kungu-17/42, cishe u-40.5%. Uma kubhekwa ngale ndlela, uhlamvu lwemali olulungile lubonakala lubanda ngemuva kwekhanda.
Bhala uhlu lokulandelana okungu-16 (H = ikhanda, T = umsila). Okubili kwakho, i-TTTT ne-TTTH, akunalo ikhanda ekuphonsweni kokuqala okuthathu, ngakho akukho okulandela ikhanda; lokho kushiya okungu-14.
Kukho ngakunye, thatha ukuphonswa okulandela ikhanda bese uthola ingxenye engamakhanda. I-HHHH inikeza 3 kwezi-3. I-HHHT inikeza 2 kwezi-3. I-HTHT inikeza 0 kwezi-2. Uma udlula kukho konke okungu-14: ukulandelana okuyisithupha kunikeza u-0, okune kunikeza u-1/2, okukodwa kunikeza u-2/3 kanti okuthathu kunikeza u-1 (HHHH, THHH ne-TTHH).
Hlanganisa izingxenye: 4 × 1/2 + 2/3 + 3 = 17/3. Hlukanisa ngo-14: 17/42 ≈ 40.5%.
Akukho kuphonswa okuthanda umsila; ngakunye kungu-50–50. Ukutsheka kuvela ekuthatheni isilinganiso ngokulandelana ngakunye: ukulandelana okugcwele amakhanda kunokuphonswa okuningi okungabhekwa kodwa kubalwa kanye, kufana nokulandelana okunelilodwa kuphela. U-Miller no-Sanjurjo (2018) bakhombisa ukuthi ucwaningo lwango-1985 lwe-hot hand lwalukale abadlali balo be-basketball ngale ndlela, ngakho abadlali ababebonakala bengenalo uchungechunge oluningi kunethuba empeleni babenalo kancane uchungechunge oluningi.
Okokuhlekisa
Ukuhlanjululwa, hhayi ukulungiswa. Isondo alikweletanga lutho.
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.”