Ensobi y'Abasiba Zzaala
Okukkiriza nti ekivaamu “kituuse” kubanga kimaze ebbanga nga tekirabise.
Oluvannyuma lw'emmyufu kkumi, obusoboka bw'enzirugavu bukyali 18/37. Nnamuziga tekuuma kiwandiiko era tebanjibwa kintu.
Ensobi
Singa emmyufuzzaalaEmmyufuZzaala ya emu ku emu ku nnamba 18 emmyufu. Mu Lufalansa: rouge.Soma byonna → evuddeyo emirundi kkumi, abazannyi bangi bawulira nti enzirugavuzzaalaEnzirugavuZzaala ya emu ku emu ku nnamba 18 enzirugavu. Mu Lufalansa: noir.Soma byonna → “etuuse” ne basiba ku yo. Abalala bawulira nti emmyufu “eyokya” ne basiba ku yo. Bombi balowooza okuva ku lunyiriri olwaggwa dda okudda ku kwetooloola okutannabaawo. AkapiiraebikozesebwaAkapiiraAkapiira akatono akakasukibwa mu lugudo nga kadduka mu ludda olukontana n'olwa rotor. Obupiira obw'omulembe bwa ivorine oba Teflon, mm 18–21.Soma byonna → tekamanyi kwetooloola kkumi okwayita kwali kutya; ebinnyaebikozesebwaEkinnyaKimu ku bisenge 37 ebiriko ennamba ku rotor. Era biyitibwa: slot, cup.Soma byonna → bikyali bya bunene bwe bumu nga bwe byali essaawa emu eyise; obusobokaokubalaObusobokaObusoboka bw'ekivaamu, okuva ku 0 okutuuka ku 1 oba 0% okutuuka ku 100%. Ennamba emu: 1/37 = 2.70%.Soma byonna → bw'enzirugavu buli 18/37 nga bulijjo.
Lwaki kiwulikika ng'ekituufu
Mu bbanga eddene, ebitundu by'emmyufu n'enzirugavu bisemberera ddala 18/37 buli kimu. Etteeka ly'emiwendo emineneokubalaEtteeka ly'emiwendo emineneEkigero ky'ebivaamu ebyetongodde kisemberera omuwendo ogusuubirwa ng'omuwendo gw'okugezaako gweyongera.Soma byonna → likikakasa. Naye okusembera kubaawo lwa kusaanuusa, so si lwa kutereeza: oluvannyuma lw'okwetooloola okulala 1,000, emmyufu ekkumi ez'okwongerako ziba nsobi ya kusemberezaamu omuwendo mu kitundu, so si lwa kuba nti enzirugavu yatuuka, wabula lwa kuba nti ekyokulabirako kyakula. Tewali nkola efuula enzirugavu kusoboka nnyo, era etteeka ly'emiwendo eminene teryetaaga nkola ng'eyo.
Monte Carlo, 18 Agusito 1913
Enzirugavu yavaayo emirundi 26 omuddiriŋŋanwa ku mmeeza mu Casino de Monte-Carlo. Okuva ku nzirugavu nga ey'ekkumi n'ettaano, abazannyi beeyiwa ku mmyufu, nga bakubisaamu bbiri era ne baddamu okukubisaamu bbiri, buli kwetooloola nga “kukakafu” okusinga okwasooka. Kaasino yawangula obukadde bwa faranga. Okuddiŋŋana okwo kwalina obusoboka bwa 1 ku bukadde 137 okuva ku nzirugavu esooka, era obusoboka nti kwandibaddewo wonna wonna mu kaasino z'ensi yonna bwali kumpi kimu. Y'ensonga lwaki ensobi y'abasiba zzaala era eyitibwa ensobi ya Monte Carlo.
Si kya kwewuunya. Kibaawo omulundi gumu ku 44.
Abazannyi batandika okukyetegereza. Emmyufu “etuuse”.
Emmeeza ejjudde abantu. Ssente za zzaala ku mmyufu zikubisibwamu bbiri oluvannyuma lwa buli kufiirwa.
Obugagga bufiiriddwa. Buli nzirugavu empya efuula emmyufu okuwulikika nga nkakafu okusingawo.
Okuddiŋŋana kukoma. Kaasino ewangudde obukadde bwa faranga okuva ku bantu abaasiba okukontana n'okuddiŋŋana okutaasobola “kumanya” nti kuddiŋŋana.
Omukono ogwokya
Okusiba ku langi kubanga eri mu kuddiŋŋana y'ensobi y'emu nga ekyusiddwa: okuddiŋŋana kusuubirwa okugenda mu maaso mu kifo ky'okukoma. Bannabyamagezi g'omuntu bakiyita omukono ogwokyaenfumoOmukono ogwokyaOkukkiriza nti okuwangula okuddiriŋŋana, oba ekivaamu kimu okuddiŋŋana, kufuula ekirala okusoboka okusingawo. Ku nnamuziga y'ensobi y'abasiba zzaala ng'ekyusiddwa.Soma byonna →, okuva ku kunoonyereza kwa 1985 okwa Gilovich, Vallone ne Tversky okwanoonya okuddiŋŋana mu kukuba omupiira mu kasero ka basketball ne kutazuula kusukka ku kw'omukisa. Mu 2018 Miller ne Sanjurjo baalaga nti okukebera kwennyini kwali kukyamye: mu kiwandiiko ekimpi, ekitundu ky'okuyingiza amangu ddala oluvannyuma lw'okuyingiza kuvaamu wansi w'ekigero ky'omukubi kyonna ku kigero, kale omuzannyi atalina mukono gwokya n'akatono alabika ng'anyogoga katono. Nga kutereezeddwa, ebibalo bye bimu biraga omukono ogwokya omutono. Omuntu asobola okwongera amaanyi; nnamuziga talina mbeera ya mubiri gy'ayinza okubaamu. Abazannyi abamu bakkiriza byombi omulundi gumu, nti okuddiŋŋana kugenda mu maaso okutuusa lwe kuba “kuwanvu nnyo” oluvannyuma ne kukoma. Ku nnamuziga ow'obwenkanya, buli ngeri erina omuwendo ogusuubirwaokubalaOmuwendo ogusuubirwaEkivaamu eky'omu makkati ku buli zzaala mu bbanga eddene. −1/37 ya ssente za zzaala ku buli zzaala eya bulijjo eya Bulaaya.Soma byonna → gwe gumu n'okulonda langi ng'okasuse ssente: −2.70% za ssente za zzaala.
Ku mmeeza ey'amazima
Croson ne Sundali (2005) baatunuulira essaawa 18 eza vidiyo y'obukuumi okuva ku mmeeza emu eya zeeronnamuzigaZeeroEkinnya kimu ekya kiragala ekitabikkibwa zzaala ya emu ku emu, eya dazeni oba ey'empagi; y'ensibuko y'enkizo ya kaasino. Era eyitibwa: zeero emu, 0.Soma byonna → bbiri mu kaasino ennene mu Reno: abazannyi 139 nga basiba zzaala 24,131. Ku zzaala ya emu ku emuzzaalaZzaala ya emu ku emuEmmyufu/enzirugavu, ezitagabanyizika/ezigabanyizika, ennene/entono. Ennamba 18, esasula 1:1.Soma byonna →, abazannyi baali kumpi baagabanyizibwamu kyenkanyi wakati w'abagoberera okuddiŋŋana okumpi n'abakukontana. Oluvannyuma lw'ebifaanagana bitaano omuddiriŋŋanwa baasinga kusiba okukontana n'okuddiŋŋana, era oluvannyuma lwa mukaaga oba okusingawo, 85% ku zzaala zaabwe zaali ku ludda olulala. Abazannyi be bamu baalaga omukono ogwokya ku bo bennyini: oluvannyuma lw'okuwangula ku nnamba, baakwatanga ennamba 13.6 ku kwetooloola okuddako ku kigero, ku 9.2 oluvannyuma lw'okufiirwa. Nnamuziga waabwe teyalaga kabonero ka kusosola, kale tewali na kimu ku bino ekyakyusa kye bayinza okusuubira.
Ebweru wa kaasino
Okusika kwe kumu kulabika awasalibwawo ensonga ez'amazima. Clotfelter ne Cook (1993) baagoberera omuzannyo gw'ennamba ogwa buli lunaku ogwa Maryland: ssente ezisibibwa ku nnamba zaakendeera nnyo amangu ddala nga emaze okulondebwa era zaatwala emyezi okuddawo, newankubadde okulonda tekulina kijjukizo. Chen, Moskowitz ne Shue (2016) baakizuula mu bakugu. Abalamuzi b'abanoonya obubudamu mu Amerika baali basobola okugaana omusango okutuuka ku bitundu 3.3 ku kikumi okusingawo singa baali bakkirizza ogwasooka. Abalamuzi ba baseball baali tebasobola kwogera strike okutuuka ku bitundu 1.5 oluvannyuma lw'okwogera emu, era emirundi egisukka ebiri ku ekyo ku mipiira egy'okumpi. Mu kugezesa okw'oku ttaka n'abakozi b'ebbanja abaasasulwanga omuwendo ogutakyuka, okutuuka ku 9% ku kusalawo kwakyusibwa mu ngeri eno. Emisango gyajjanga mu nsengeka etategeerekeka, kale okusalawo okwasembayo tekwagamba kintu ku kuddako, nga okwetooloola okwasembayo bwe kutagamba kintu ku kuddako.
Ensobi y'abasiba zzaala ey'okukontana
Omufirosoofo Ian Hacking (1987) yatuuma ngeri ey'okusatu. Omuntu ayingira mu kisenge, n'alaba ddayisi bbiri nga zigwa mukaaga ne mukaaga, n'asalawo nti ziteekwa okuba nga zimaze okukasukibwa emirundi mingi. Buli kukasuka kusoboka kyenkanyi okuba mukaaga ne mukaaga, okusooka okw'akawungeezi oba okw'olukumi, kale ekyo ky'alaba tekigamba kintu ku bbanga omuzannyo lye gumaze. Mu roulette, ye muzannyi atuuka ku lubaawo olulaga emmyufu munaana n'asalawo nti emmeeza eteekwa okuba ng'emaze essaawa nnyingi nga yeetooloola okuzireeta. Ensobi eya bulijjo esoma ebyayita mu kwetooloola okuddako; eno esoma ekintu ekitatera kulabika mu byayita tewali yabiraba.
Munnabyamagezi g'omuntu eyakikkiriza
Ensobi eno ebaddeko abayivu abagiwolereza. Munnabyamagezi g'omuntu Omugirimaani Karl Marbe yayita mu bitabo bina eby'okuzaalibwa, buli kimu nga kirimu 49,152, n'azuula nti okuddiŋŋana okusinga obuwanvu okw'abalenzi oba okw'abawala omuddiriŋŋanwa kwali 17, n'asalawo nti okuddiŋŋana okuwanvu tekutera kubaawo okusinga omukisa bwe gukkiriza, kale nti okuddiŋŋana kufuula ekivaamu ekirala okusoboka okusingawo. Omukisa gwokka gugamba ekirala: mu kuzaalibwa 196,608, okuddiŋŋana kwa 17 oba okusingawo kulabika nga emirundi ena ku etaano. Marbe yali azudde ddala olunyiriri olutategeerekeka bwe lulabika. Epstein (2013) addamu okunyumya ensonga eno; Obusoboka bw'Emitendera gy'Ebivuddemu mu Roulette buwa engeri ya roulette.
Ensobi eno w'etakola
Singa nnamuziga yali asosola mu mubiri gwe, okwetooloola okwayita kwandibadde kulina amakulu, kubanga kwandibadde bujulizi ku binnya so si ku mukisa. Ekyo kye kiri mu Laabu, era kyetaaga okwetooloola nkumi na nkumi okuva ku nnamuziga omu amanyiddwa okusobola okugamba ekintu. Ku kuddiŋŋana kw'emmyufu kkumi ku nnamuziga atamanyiddwa, ensonga y'okusosola tesoboka nnyo okusinga ey'omukisa.
Ebibuuzo
Nedda. Ekwata ku kintu kyonna ekiddiŋŋana ekyetongodde: ddayisi, ssente ezikasukibwa, ennamba za lotto.
Ebitundu bijja kusemberera. Ekivuddemu kyo kijja kukyali nga −2.70% za ssente z'osibye.
Tewali tteeka lya kigero. Waliwo etteeka ly'emiwendo eminene, era likola lwa kusaanuusa.
Okwesanyusa n'Okubala
Gezaako bino ggwe kennyini okusooka. Buli kugonjoola kuzingiddwa; kuggulewo ng'oli mwetegefu.
Oluvannyuma lw'okukasuka ssente emirundi 10, eraga omutwe emirundi 7 n'omukira emirundi 3. Oluvannyuma lw'okukasuka 1,000, eraga omutwe 517 n'omukira 483. Omukira gwatuuka ku mutwe?
Laga okugonjoola
Eky'okuddamu Nedda. Enjawulo yakula okuva ku 4 okutuuka ku 34. Omugerageranyo gwokka gwe gwasemberera okwenkanankana.
Omugerageranyo gw'omutwe ku mukira gwakka okuva ku 7/3, nga 2.33, okutuuka ku 517/483, nga 1.07. Ekyo kye kiraga etteeka ly'emiwendo emineneokubalaEtteeka ly'emiwendo emineneEkigero ky'ebivaamu ebyetongodde kisemberera omuwendo ogusuubirwa ng'omuwendo gw'okugezaako gweyongera.Soma byonna → nga likola.
Enjawulo wakati waabyo yakula, okuva ku 4 okutuuka ku 34. Ne ssente ey'obwenkanya, enjawulo eya nga 30 oluvannyuma lw'okukasuka 1,000 ya bulijjo: enjawulo eya bulijjo ekula kumpi ng'ekikolo kya kkuudraati eky'omuwendo gw'okukasuka, ate omugerageranyo gutereera okudda ku 1.
Tewali kyazzaayo mukira. Omutwe omungi ogwasooka gwakendeezebwa okukasuka 990 okwaddako, so tegwatereezebwa.
Kasuka ssente emirundi ena era otunuulire bwesalazi okukasuka okujja amangu ddala oluvannyuma lw'omutwe. Kitundu ki ku ebyo eky'omutwe? Kibale ku buli emu ku nnyiriri 16 ezisoboka era ofune ekigero ky'ebitundu. Kiri 50%?
Laga okugonjoola
Eky'okuddamu Nedda. Kiri 17/42, nga 40.5%. Bw'otunuulira bw'otyo, ssente ey'obwenkanya erabika ng'ennyogoga oluvannyuma lw'omutwe.
Wandiika ennyiriri 16 (H = omutwe, T = omukira). Bbiri ku zo, TTTT ne TTTH, tezirina mutwe mu kukasuka okusatu okusooka, n'olwekyo tewali kiddirira mutwe; kino kirekawo 14.
Mu buli lumu, twala okukasuka okuddirira omutwe ozuule kitundu ki eky'omutwe. HHHH ewa 3 ku 3. HHHT ewa 2 ku 3. HTHT ewa 0 ku 2. Ng'oyita mu zonna 14: ennyiriri mukaaga ziwa 0, nnya ziwa 1/2, lumu luwa 2/3 ate ssatu ziwa 1 (HHHH, THHH ne TTHH).
Gatta ebitundu: 4 × 1/2 + 2/3 + 3 = 17/3. Gabanya na 14: 17/42 ≈ 40.5%.
Tewali kukasuka kusinza mukira; buli kumu kuli 50–50. Okuwunzika kuva mu kufuna ekigero olunyiriri ku lunyiriri: olunyiriri olujjudde omutwe lulina okukasuka kungi okutunuulirwa naye lubalibwa omulundi gumu, kye kimu n'olunyiriri olulina omutwe gumu gwokka. Miller ne Sanjurjo (2018) baalaga nti okunoonyereza kwa 1985 ku “mukono ogwokya” (hot hand) kwapima abazannyi baakwo aba basketball mu ngeri eno, n'olwekyo abazannyi abaalabika ng'abatalina mitendera gya kuyingiza egisinga egy'omukisa gwokka, mu butuufu baagibanga nayo katono.
Eky'okusesa
Kusaanuusa, so si kutereeza. Nnamuziga tebanjibwa kintu.
Ensibuko
- 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.”