Chinyengo cha Wotchova Juga
Chikhulupiriro chakuti zotsatira “zafika nthawi yake” chifukwa sizinatuluke kwa kanthawi.

Pambuyo pa zofiira khumi kuthekera kwa zakuda kudakali 18/37. Gudumu silisunga mbiri ndipo silikongola kanthu.
Chinyengocho
Ngati zofiirabetchaZofiiraBetcha la even-money pa manambala 18 ofiira. Mu Chifalansa: rouge.Werengani yonse → zatuluka ka khumi, osewera ambiri amaganiza kuti zakudabetchaZakudaBetcha la even-money pa manambala 18 akuda. Mu Chifalansa: noir.Werengani yonse → “zafika nthawi yake” ndipo amabetcha moteremo. Ena amaona kuti zofiira “zikutentha” ndipo amabetcha zimenezo. Onse akuganiza kuchokera ku zotsatizana zimene zatha kale kupita ku kuzungulira kumene sikunachitike. MpirazipangizoMpiraMpira waung’ono umene umaponyedwa mu njira motsutsana ndi rotor. Mipira yamakono ndi ya ivorine kapena Teflon, 18–21 mm.Werengani yonse → sudziwa kuti kuzungulira khumi komaliza kunali kotani; tibowozipangizoKabowoChimodzi mwa tibowo 37 tokhala ndi manambala pa rotor. Kamatchedwanso: slot, cup.Werengani yonse → n’tofanana kukula monga mmene tinalili ola lapitalo; kuthekeramasamuKuthekeraMwayi wa zotsatira, kuchokera 0 mpaka 1 kapena 0% mpaka 100%. Nambala imodzi: 1/37 = 2.70%.Werengani yonse → kwa zakuda ndi 18/37 monga mmene kwakhalira nthawi zonse.
N’chifukwa chiyani kumamveka ngati koona
Pa nthawi yayitali magawo a zofiira ndi zakuda amayandikiradi 18/37 iliyonse. Lamulo la manambala akuluakulumasamuLamulo la manambala akuluakuluAvareji ya zotsatira zodziyimira payokha imayandikira mtengo woyembekezeka pamene chiwerengero cha mayesero chikukula.Werengani yonse → limatsimikiza zimenezo. Koma kuyandikira kumachitika mwa kusungunula, osati mwa kukonza: pambuyo pa kuzungulira kwina 1,000 zofiira khumi zowonjezerazo ndi kachinthu kakang’ono m’gawo, osati chifukwa zakuda zinagwira koma chifukwa chitsanzo chinakula. Palibe njira imene imapangitsa zakuda kukhala zotheka kwambiri, ndipo lamulo la manambala akuluakulu silifuna njira yotere.
Monte Carlo, 18 August 1913
Zakuda zinatuluka ka 26 motsatizana pa tebulo lina mu Casino de Monte-Carlo. Kuyambira pa zakuda pafupifupi za khumi ndi zisanu, osewera anaunjikana pa zofiira, akuwirikiza ndi kuwirikizanso, kuzungulira kulikonse “kotsimikizika kwambiri” kuposa koyamba. Kasino inapambana mamiliyoni a ma franc. Zotsatizanazo zinali ndi kuthekera kwa 1 pa 137 miliyoni kuchokera pa zakuda zoyamba, ndipo kuthekera koti zichitike pamapeto pake kwinakwake m’makasino a padziko lonse kunali kwenikweni kumodzi. Ichi ndicho chifukwa chake chinyengo cha wotchova juga chimatchedwanso chinyengo cha Monte Carlo.
Palibe chachilendo. Zimachitika kamodzi pa 44.
Osewera ayamba kuzindikira. Zofiira “zafika nthawi yake”.
Tebulo ladzaza. Ndalama zobetcha pa zofiira zimawirikizidwa pambuyo pa kuluza kulikonse.
Chuma chatayika. Zakuda zatsopano zilizonse zimapangitsa zofiira kuoneka zotsimikizika kwambiri.
Zotsatizana zatha. Kasino yapambana mamiliyoni a ma franc kuchokera kwa anthu obetcha motsutsana ndi zotsatizana zimene sizikanatha “kudziwa” kuti zinali zotsatizana.
Dzanja lotentha (hot hand)
Kuthandizira mtundu chifukwa ukutsatizana ndi kulakwa komweko kotembenuzidwa: zotsatizana zikuyembekezeka kupitirira m’malo motha. Akatswiri a maganizo amazitcha dzanja lotenthanthanoDzanja lotenthaChikhulupiriro chakuti kupambana motsatizana, kapena zotsatira zimodzimodzi motsatizana, kumapangitsa china kukhala chotheka kwambiri. Pa gudumu ndi chinyengo cha wotchova juga chotembenuzidwa.Werengani yonse →, potsatira kafukufuku wa 1985 wa Gilovich, Vallone ndi Tversky amene anafufuza zotsatizana pa kuponya mpira wa basketball ndipo sanapeze zina kupatula za mwangozi. Mu 2018 Miller ndi Sanjurjo anaonetsa kuti mayesowo anali opendekeka: m’mbiri yaifupi, gawo la kugunda pambuyo pa kugunda limatuluka pansi pa mlingo wonse wa woponya pa avareji, choncho wosewera wopanda dzanja lotentha konse amaoneka wozizira pang’ono. Atakonzedwa, zambiri zomwezo zimaonetsa dzanja lotentha pang’ono. Munthu angathe kutentha; gudumu lilibe mkhalidwe woti likhalemo. Osewera ena amakhulupirira zonse ziwiri nthawi imodzi, kuti zotsatizana zimapitirira mpaka “zitalika kwambiri” kenako zimatha. Pa gudumu lachilungamo mtundu uliwonse wa chikhulupiriro uli ndi mtengo woyembekezekamasamuMtengo woyembekezekaZotsatira zapakati pa betcha lililonse pa nthawi yayitali. −1/37 ya ndalama zobetcha pa betcha lililonse la ku Ulaya wamba.Werengani yonse → wofanana ndi kusankha mtundu poponya ndalama: −2.70% ya ndalama zobetcha.
Pa tebulo lenileni
Croson ndi Sundali (2005) anaonera maola 18 a vidiyo ya chitetezo kuchokera pa tebulo limodzi la zirogudumuZiroKabowo kamodzi kobiriwira kamene betcha la even-money, dazeni kapena mzati siliphimba; gwero la phindu la kasino. Imatchedwanso: ziro imodzi, 0.Werengani yonse → ziwiri m’kasino yaikulu ku Reno: osewera 139 akuika mabetcha 24,131. Pa mabetcha a even-moneybetchaBetcha la even-moneyZofiira/zakuda, osakhala awiriawiri/awiriawiri, okwera/otsika. Manambala 18, amalipira 1:1.Werengani yonse →, osewera anali ogawanika pafupifupi mofanana pakati pa kutsatira zotsatizana zazifupi ndi kuzitsutsa. Pambuyo pa zisanu za mtundu umodzi motsatizana anapendekera motsutsana ndi zotsatizanazo, ndipo pambuyo pa zisanu ndi chimodzi kapena kuposa, 85% ya mabetcha awo anali mbali ina. Osewera omwewo anaonetsa dzanja lotentha pa iwo eni: pambuyo popambana pa manambala anaphimba manambala 13.6 pa kuzungulira kotsatira pa avareji, poyerekeza ndi 9.2 pambuyo poluza. Gudumu lawo silinaonetse chizindikiro cha kukondera, choncho palibe chimene chinasintha zimene aliyense wa iwo akanayembekezera.
Kunja kwa kasino
Kukoka komweko kumaonekera kumene zisankho zenizeni zimapangidwa. Clotfelter ndi Cook (1993) anatsatira masewera a manambala a tsiku ndi tsiku a Maryland: ndalama zobetchedwa pa nambala zinatsika kwambiri itangotulutsidwa ndipo zinatenga miyezi kuti zibwerere, ngakhale kuti kutulutsa kulibe kukumbukira. Chen, Moskowitz ndi Shue (2016) anachipeza pakati pa akatswiri. Oweruza a milandu yopempha chitetezo (asylum) ku United States anali ndi mwayi wokwera mpaka 3.3 percentage points wokana mlandu ngati anavomereza wapitawo. Oyimbira a baseball anali ndi mwayi wotsika ndi 1.5 points woyimba strike atangoyimba ina, ndipo kuposa kuwirikiza kawiri pa maponyedwe a mkangano. M’kuyesa kwa m’munda ndi akuluakulu a ngongole olipidwa malipiro osasintha, mpaka 9% ya zisankho zinatembenuzidwa motere. Milanduyo inabwera mwachisawawa, choncho chisankho chomaliza sichinanene kanthu za chotsatira, monga momwe kuzungulira komaliza sikunena kanthu za kotsatira.

Chinyengo cha wotchova juga chotembenuzidwa
Katswiri wa nzeru Ian Hacking (1987) anatchula mtundu wachitatu. Munthu walowa m’chipinda, waona madayisi awiri akugwera pa sikisi ziwiri ndipo wamaliza kuti ayenera kuti aponyedwa kale kambirimbiri. Kuponya kulikonse kuli ndi mwayi wofanana wotuluka sikisi ziwiri, koyamba madzulo kapena ka chikwi, choncho chooneka chimenecho sichinena kanthu za kutalika kwa nthawi imene masewera akhala akuchitika. Mu roulette ndi wosewera amene afika pa bolodi loonetsa zofiira zisanu ndi zitatu ndipo asankha kuti tebulo liyenera kuti lakhala likuzungulira kwa maola kuti zichitike. Chinyengo chamba chimawerenga zakale mu kuzungulira kotsatira; ichi chimawerenga chooneka chosowa m’zakale zimene palibe anaziona.
Katswiri wa maganizo amene anachikhulupirira
Chinyengochi chakhala ndi oteteza ophunzira. Katswiri wa maganizo wa ku Germany Karl Marbe anafufuza m’mabuku anayi olembera obadwa, iliyonse ya obadwa 49,152, anapeza kuti zotsatizana zazitali kwambiri za anyamata kapena za atsikana motsatizana zinali 17, ndipo anamaliza kuti zotsatizana zazitali ndi zosowa kuposa mmene mwangozi kumalolera, kotero kuti zotsatizana zimapangitsa zotsatira zina kukhala zotheka kwambiri. Mwangozi kokha kumanena mosiyana: pa obadwa 196,608 zotsatizana za 17 kapena kuposa zimaonekera pafupifupi kanayi pa kasanu. Marbe anapeza ndendende mmene zotsatizana zachisawawa zimaonekera. Epstein (2013) amafotokozanso nkhaniyi; Kuthekera kwa Zotsatizana mu Roulette imapereka mtundu wa roulette.

Kumene chinyengo sichigwira ntchito
Ngati gudumu likanakhala lokondera mwakuthupi, kuzungulira kwakale kukanakhala ndi chidziwitso, chifukwa kukanakhala umboni wokhudza tibowo osati wokhudza mwayi. Imeneyo ndi nkhani ya Labu ya Roulette, ndipo imafuna kuzungulira masauzande kuchokera pa gudumu limodzi lodziwika kuti inene chilichonse. Pa zofiira khumi motsatizana pa gudumu losadziwika, kufotokoza kwa kukondera n’kosatheka kwambiri kuposa kwa mwangozi.
Mafunso
Ayi. Chimakhudza chochitika chilichonse chobwerezedwa chodziyimira payokha: madayisi, ndalama zoponya, manambala a lotale.
Magawo adzayandikirana. Zotsatira zanu zidzakhalabe pafupifupi −2.70% ya zimene munabetcha.
Palibe lamulo la avareji. Pali lamulo la manambala akuluakulu, ndipo limagwira ntchito mwa kusungunula.
Masamu Osangalatsa
Yesani nokha choyamba. Yankho lililonse labisika; litsegulireni mukakonzeka.
Pambuyo pa kuponya ndalama ka 10 ikusonyeza mitu 7 ndi michira 3. Pambuyo pa kuponya ka 1,000 ikusonyeza mitu 517 ndi michira 483. Kodi michira inapeza mitu?
Onetsani yankho
Yankho Ayi. Kusiyana kunakula kuchokera pa 4 kufika pa 34. Chiyerekezo chokha ndicho chinayandikira kufanana.
Chiyerekezo cha mitu ndi michira chinatsika kuchokera pa 7/3, pafupifupi 2.33, kufika pa 517/483, pafupifupi 1.07. Limenelo ndi lamulo la manambala akuluakulumasamuLamulo la manambala akuluakuluAvareji ya zotsatira zodziyimira payokha imayandikira mtengo woyembekezeka pamene chiwerengero cha mayesero chikukula.Werengani yonse → likugwira ntchito.
Kusiyana pakati pawo kunakula, kuchokera pa 4 kufika pa 34. Ndi ndalama yachilungamo kusiyana kwa pafupifupi 30 pambuyo pa kuponya 1,000 n’kwanthawi zonse: kusiyana kwanthawi zonse kumakula pafupifupi ndi muzu wa chiwerengero cha kuponya, pamene chiyerekezo chimakhazikika kuyandikira 1.
Palibe chimene chinakoka michira kubwerera. Mitu yochuluka yoyambirira inasungunulidwa ndi kuponya 990 kotsatira, osati kukonzedwa.
Ponyani ndalama kanayi ndipo yang’anani kuponya kokha kumene kumabwera pambuyo pa mutu. Kodi ndi gawo lanji la kumeneko limene ndi mitu? Werengerani pa ndandanda iliyonse mwa 16 zotheka ndipo tengani avareji ya magawowo. Kodi ndi 50%?
Onetsani yankho
Yankho Ayi. Ndi 17/42, pafupifupi 40.5%. Poyang’ana motere, ndalama yachilungamo imaoneka ngati ikuzizira pambuyo pa mutu.
Lembani ndandanda 16 (H = mutu, T = mchira). Ziwiri mwa izo, TTTT ndi TTTH, zilibe mutu m’kuponya katatu koyamba, choncho palibe chimene chimatsatira mutu; zimenezo zimasiya 14.
Pa iliyonse, tengani kuponya kotsatira mutu ndipo pezani gawo limene ndi mitu. HHHH imapereka 3 mwa 3. HHHT imapereka 2 mwa 3. HTHT imapereka 0 mwa 2. Kudutsa zonse 14: ndandanda zisanu ndi imodzi zimapereka 0, zinayi zimapereka 1/2, imodzi imapereka 2/3 ndipo zitatu zimapereka 1 (HHHH, THHH ndi TTHH).
Phatikizani magawo: 4 × 1/2 + 2/3 + 3 = 17/3. Gawani ndi 14: 17/42 ≈ 40.5%.
Palibe kuponya kumene kumakonda michira; kulikonse ndi 50–50. Kupendekeka kumachokera pa kutenga avareji ndandanda ndi ndandanda: ndandanda yodzaza ndi mitu ili ndi kuponya kochuluka koyang’ana koma imawerengedwa kamodzi, mofanana ndi ndandanda yokhala ndi umodzi wokha. Miller ndi Sanjurjo (2018) anasonyeza kuti kafukufuku wa “dzanja lotentha” wa 1985 anayeza osewera ake a basketball motere, choncho osewera amene ankaoneka kuti alibe zotsatizana kuposa mwangozi kwenikweni anali ndi zotsatizana pang’ono.
Nthabwala yopumitsa

Kusungunula, osati kukonza. Gudumu silikongola kanthu.
Magwero
- 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.”