Liphutsa lemgembuli
Inkholelo yekutsi umphumela lotsite “sewufike sikhatsi sawo” ngobe kadze ungaveli.
Ngemuva kwaletibovu letilishumi litfuba lalokumnyama lisengu-18/37. Lisondvo aligcini lirekhodi futsi alikweleti lutfo.
Liphutsa
Nangabe lokubovukubhejaBovuKubheja lokulingana nemali etinombolweni letingu-18 letibovu. NgesiFulentji: rouge.Fundza konkhe → sekuphume kalishumi, badlali labanyenti bativa shengatsi lokumnyamakubhejaMnyamaKubheja lokulingana nemali etinombolweni letingu-18 letimnyama. NgesiFulentji: noir.Fundza konkhe → “sekufike sikhatsi sako” bese babheja ngekuvumelana naloko. Labanye bativa shengatsi lokubovu “kuyashisa” bese babheja kuko. Bobabili bacabanga basuka ekulandzelaneni lokusekuphelile baya ekujikeleteni lokungakenteki. LibholatinsitaLibholaLibhola lelincane leliphoswa emzileni lihamba ngakulolunye luhlangotsi kune-rotor. Emabhola alamuhla ayi-ivorine noma i-Teflon, 18–21 mm.Fundza konkhe → alati kutsi kujikeleta lokulishumi lokwendlulile bekuyini; imigodzitinsitaUmgodziLesinye setikhala letingu-37 letinetinombolo ku-rotor. Kuphindze kutsiwe: slot, cup.Fundza konkhe → isalingana ngebukhulu nangelihora lelendlulile; litfubatibaloLitfubaLitfuba lekutsi umphumela wenteke, kusukela ku-0 kuya ku-1 noma ku-0% kuya ku-100%. Inombolo yinye: 1/37 = 2.70%.Fundza konkhe → lalokumnyama lingu-18/37 njengoba bekuhlala kunjalo.
Kungani kuva shengatsi kuliciniso
Esikhatsini lesidze tincenye talokubovu nalokumnyama tiyasondzela ku-18/37 ngayinye. Umtsetfo wetinombolo letinkhulutibaloUmtsetfo wetinombolo letinkhuluSilinganiso semiphumela letimele sisondzela linani lelilindzelekile njengoba linani lekuzama likhula.Fundza konkhe → uyakucinisekisa loko. Kodvwa kusondzela kwenteka ngekuhlanjululwa, hhayi ngekulungiswa: ngemuva kwekujikeleta lokungu-1,000 lokwengetiwe, letibovu letilishumi letengetiwe setincane kangangekutsi atibonakali encenyeni, hhayi ngobe lokumnyama kufinyelele kulokubovu kodvwa ngobe sampula sesikhulile. Ayikho indlela lenta lokumnyama kube nelitfuba lelikhulu, futsi umtsetfo wetinombolo letinkhulu awuyidzingi.
Monte Carlo, 18 Ingci 1913
Lokumnyama kwaphuma tikhatsi letingu-26 kulandzelana etafuleni e-Casino de Monte-Carlo. Kusukela cishe kulokumnyama kwelishumi nesihlanu, badlali bagcumela kulokubovu ngebunyenti, baphindza kabili baphindze futsi, kujikeleta ngakunye “kucinisekile kakhulu” kunalokwangembili. Likhasino lawina tigidzi tema-franc. Lolo luchungechunge belunelitfuba lelingu-1 etigidzini letingu-137 kusukela kulokumnyama kwekucala, futsi litfuba lekutsi ekugcineni lwenteke kulenye indzawo emakhasino emhlaba belicishe libe sicinisekiso. Ngiso sizatfu sekutsi liphutsa lemgembuli libitwe nangekutsi liphutsa lase-Monte Carlo.
Akumangalisi. Kwenteka kanye etikhatsini letingu-44.
Badlali bacala kucaphela. Lokubovu “sekufike sikhatsi sako”.
Litafula ligcwele. Emanani labhejwa kulokubovu aphindvwa kabili ngemuva kwekulahlekelwa ngakunye.
Kulahleka imali lenyenti. Lokumnyama lokusha ngakunye kwenta lokubovu kuve shengatsi kucinisekile kakhulu.
Luchungechunge luyaphela. Likhasino seliwine tigidzi tema-franc kubantfu labebabheja bamelene neluchungechunge lolungakhonanga “kwati” kutsi luluchungechunge.
Sandla lesishisako
Kusekela umbala ngobe useluchungechungeni kuliphutsa lelifanako leliphendvuliwe: kulindzeleke kutsi luchungechunge luchubeke esikhundleni sekuphela. Tati tengcondvo tikubita ngekutsi sandla lesishisakoinganekwaneSandla lesishisakoInkholelo yekutsi luchungechunge lwekuwina, noma lwemphumela munye, lwenta lokunye kube nematfuba lamanyenti. Elisondvweni liphutsa lemgembuli lelibhekiswe ngalokuphambene.Fundza konkhe → (hot hand), ngemuva kwelucwaningo lwanga-1985 lwa-Gilovich, Vallone na-Tversky lolwafuna luchungechunge ekushayeni libhola le-basketball futsi lwangalutfoli ngetulu kwenhlanhla. Nga-2018 Miller na-Sanjurjo bakhombisa kutsi kuhlola ngekwako bekuchemile: erekhodini lelifishane, incenye yekungena ngekushesha ngemuva kwekungena iba ngaphansi kwelizinga lemshayi lilonkhe ngesilinganiso, ngako umdlali longenaso nhlobo sandla lesishisako ubukeka shengatsi uyabanda kancane. Nangabe kulungisiwe, idatha lefanako ikhombisa sandla lesishisako lesincane. Umuntfu angafudvumala; lisondvo alinaso simo sekushisa noma sekubanda. Labanye badlali bakholelwa kuto tombili tinkholelo ngesikhatsi sinye, kutsi luchungechunge luchubeka luze lube “lude kakhulu” bese luyaphela. Elisondvweni lelilungile yonkhe inguculo inelinani lelilindzelekiletibaloLinani lelilindzelekileUmphumela wesilinganiso ngekubheja ngakunye ngekuhamba kwesikhatsi lesidze. −1/37 yelinani lelibhejiwe kuko konkhe kubheja lokujwayelekile kwaseYurophu.Fundza konkhe → lelifanako nekukhetsa umbala ngekuphosa luhlavu lwemali: −2.70% welinani lelibhejwako.
Etafuleni langempela
Croson na-Sundali (2005) babukela emahora langu-18 evidiyo yekuvikela yelitafula linye lelinelicandzalisondvoLicandzaUmgodzi munye loluhlata longambonjwa kubheja lokulingana nemali, kwelidazini noma kwelikholamu; umtfombo wenzuzo yelikhasino. Kuphindze kutsiwe: licandza linye, 0.Fundza konkhe → lelikabili elikhasino lelikhulu e-Reno: badlali labangu-139 babheja tikhatsi letingu-24,131. Ekubhejeni lokulingana nemalikubhejaKubheja lokulingana nemaliLokubovu/lokumnyama, lengalingani/lelinganako, phansi/etulu. Tinombolo letingu-18, kukhokha 1:1.Fundza konkhe →, badlali bebacishe bahlukane ngalokulinganako emkhatsini wekulandzela luchungechunge lolufishane nekuluphikisa. Ngemuva kwemiphumela lemihlanu lefanako kulandzelana batsambekela ekuphikiseni luchungechunge, futsi ngemuva kwesitfupha noma ngetulu, 85% wekubheja kwabo bewukulolunye luhlangotsi. Badlali labafanako bakhombisa sandla lesishisako ngabo ngekwabo: ngemuva kwekuwina etinombolweni bambotsa tinombolo letingu-13.6 ekujikeleteni lokulandzelako ngesilinganiso, nangabe kucatsaniswa na-9.2 ngemuva kwekulahlekelwa. Lisondvo labo belingakhombisi luphawu lwekuchema, ngako kute kuloku lokwashintja loko noma ngubani wabo bekangakulindzela.
Ngaphandle kwelikhasino
Lokudvonsa lokufanako kuyavela lapho kwentiwa khona tincumo tangempela. Clotfelter na-Cook (1993) balandzela umdlalo wetinombolo welilanga ngalinye wase-Maryland: imali lebhejwa enombolweni yehla kakhulu ngekushesha nje nayidvonswe futsi yatsatsa tinyanga kute ibuyele, nanoma kudvonswa kungenayo inkhumbulo. Chen, Moskowitz na-Shue (2016) bakutfola kulabangochwepheshe. Emajaji ekukhoseliswa (asylum) ase-United States bekanelitfuba lelingaba ngemaphuzu langu-3.3 emaphesenti lelikhulu lekwala licala nangabe bekavumile lelingembili. Bonompempe be-baseball bebanelitfuba lelincane ngemaphuzu langu-1.5 lekubita i-strike ngemuva kwekubita yinye, futsi ngetulu kwekuphindvwe kabili kwaloko emabhola lasondzelene. Elucwaningweni lwasendzaweni netikhulu temalimboleko letikhokhelwa imali lengagucuki, kwagucuka ngalendlela tincumo letifika ku-9%. Emacala bekafika ngekulandzelana lokungahlelekile, ngako sincumo sekugcina besingasho lutfo ngalesilandzelako, njengobe nje kujikeleta kwekugcina kungasho lutfo ngalokulandzelako.
Liphutsa lemgembuli leliphambene
Sati sefilosofi Ian Hacking (1987) waniketa ligama enguculweni yesitsatfu. Umuntfu ungena ekamelweni, abone emadayisi lamabili awela kulasitfupha ombili bese aphetsa ngekutsi kufanele kutsi asaphoswe tikhatsi letinyenti. Konkhe kuphosa kunelitfuba lelilinganako lekuba ngulasitfupha ombili, kwekucala kwalobusuku noma kwenkhulungwane, ngako loko lakubonako akusho lutfo ngekutsi umdlalo sewuchubeke sikhatsi lesingakanani. Ku-roulette ngumdlali lofika ebhodini lelikhombisa letibovu letisiphohlongo bese ancuma kutsi litafula kufanele kutsi belilokhu lijikeleta emahora kute litikhicite. Liphutsa lelijwayelekile lifundza lokwendlulile ekujikeleteni lokulandzelako; lelo lisebentisa intfo lengavamile lelibonako kucagela lokwendlulile lokungabonwanga muntfu.
Sati sengcondvo lesasikholelwa kulo
Lelophutsa libe nebavikeli labafundzile. Sati sengcondvo saseJalimane Karl Marbe sahlola emarejista lamane ekutalwa langu-49,152 ngalinye, satfola kutsi luchungechunge lolude kakhulu lwebafana noma lwemantfombatana kulandzelana belungu-17, futsi saphetsa ngekutsi luchungechunge lolude luyivelakancane kunaloko lokuvunyelwa yinhlanhla, ngako luchungechunge lwenta lomunye umphumela ube nelitfuba lelikhulu. Inhlanhla yodvwa itsi akunjalo: ekutalweni lokungu-196,608 luchungechunge lwalabangu-17 noma ngetulu luvela cishe kane kuletisihlanu. Marbe besatfole kanye indlela kulandzelana lokungahlelekile lokubukeka ngayo. Epstein (2013) uphindze alandzise lendzaba; likhasi Ematfuba eluchungechunge ku-roulette liniketa inguculo ye-roulette.
Lapho liphutsa lingasebenti khona
Kube lisondvo belichemile ngekwesakhiwo, kujikeleta lokwendlulile bekutawuba nelwati, ngobe bekutawuba bufakazi ngemigodzi kunekutsi kube ngenhlanhla. Leso sihloko seLilabhorethri, futsi sidzinga kujikeleta lokutinkhulungwane elisondvweni linye lelatiwako kute kushiwo lokutsite. Eluchungechungeni lwaletibovu letilishumi elisondvweni lelingatiwa, inchazelo yekuchema inelitfuba lelincane kakhulu kunenchazelo yenhlanhla.
Imibuto
Cha. Lisebenta kunoma ngusiphi sehlakalo lesitimele lesiphindvwako: emadayisi, tinhlavu temali, tinombolo telotho.
Tincenye titawusondzelana. Umphumela wakho utawube usacishe ube ngu-−2.70% waloko lokubhejile.
Awukho umtsetfo wetilinganiso. Kukhona umtsetfo wetinombolo letinkhulu, futsi usebenta ngekuhlanjululwa.
Bumnandi betibalo
Zama loku ngekwakho kucala. Sixazululo ngasinye sifihliwe; sivule nawukulungele.
Ngemuva kwekuphonsa lokuli-10 inhlavu yemali ikhombisa tinhloko leti-7 nemisila le-3. Ngemuva kwekuphonsa lokungu-1,000 ikhombisa tinhloko letingu-517 nemisila lengu-483. Ingabe imisila yafinyelela?
Khombisa sixazululo
Imphendvulo Cha. Sikhala sakhula kusuka ku-4 saya ku-34. Kusondzela kulingana kuphela silinganiso.
Silinganiso setinhloko kumisila sehla kusuka ku-7/3, cishe 2.33, saya ku-517/483, cishe 1.07. Loko ngumtsetfo wetinombolo letinkhulutibaloUmtsetfo wetinombolo letinkhuluSilinganiso semiphumela letimele sisondzela linani lelilindzelekile njengoba linani lekuzama likhula.Fundza konkhe → usebenta.
Sikhala emkhatsini wato sakhula, kusuka ku-4 saya ku-34. Ngenhlavu yemali lelinganako sikhala lesicishe sibe ngu-30 ngemuva kwekuphonsa lokungu-1,000 sijwayelekile: sikhala lesivamile sikhula cishe ngempandze yesikwele yelinani lekuphonsa, kantsi silinganiso sitinta kubhekisa ku-1.
Kute lokwabuyisela imisila emuva. Kwenyuka kwekucala kwetinhloko kwahlanjululwa kuphonsa lokungu-990 lokulandzelako, hhayi kwalungiswa.
Phonsa inhlavu yemali kane bese ubuka kuphela kuphonsa lokulandzela inhloko (H = inhloko, T = umsila). Yincenye lengakanani yaloko letinhloko? Kubale kuko konkhe kulandzelana lokungu-16 lokungenteka bese utsatsa silinganiso setincenye. Ingabe ngu-50%?
Khombisa sixazululo
Imphendvulo Cha. Ngu-17/42, cishe 40.5%. Nawubuka ngalendlela, inhlavu yemali lelinganako ibonakala shengatsi iyabanda ngemuva kwenhloko.
Bhala luhlu lwekulandzelana lokungu-16. Kubili kuko, TTTT na-TTTH, akunayo inhloko kuphonsa kwekucala lokutsatfu, ngako kute lokulandzela inhloko; loko kushiya 14.
Kuko ngakunye, tsatsa kuphonsa lokulandzela inhloko bese utfola incenye letinhloko. HHHH iniketa 3 ku-3. HHHT iniketa 2 ku-3. HTHT iniketa 0 ku-2. Nawudzabula kuko konkhe lokungu-14: kulandzelana lokusitfupha kuniketa 0, lokune kuniketa 1/2, kunye kuniketa 2/3 bese lokutsatfu kuniketa 1 (HHHH, THHH na-TTHH).
Hlanganisa tincenye: 4 × 1/2 + 2/3 + 3 = 17/3. Hlukanisa nga-14: 17/42 ≈ 40.5%.
Kute kuphonsa lokuvuna umsila; kuphonsa ngakunye kungu-50–50. Kuchema kuvela ekutseni silinganiso kulandzelana ngakunye: kulandzelana lokugcwele tinhloko kunekuphonsa lokunyenti lokungabukwa kodvwa kubalwa kanye, lokufanako nekulandzelana lokunenhloko yinye. Miller na-Sanjurjo (2018) bakhombisa kutsi lucwaningo lwa-1985 lwesandla lesishisako belukala badlali balo be-basketball ngalendlela, ngako badlali lebebabonakala bangenaluchungechunge kakhulu kunelitfuba bebanaluchungechunge kancane ngempela.
Lokuhlekisako
Kuhlanjululwa, hhayi kulungiswa. Lisondvo alikweleti lutfo.
Imitfombo
- 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.”