Ikosa ry'Umukinnyi w'Urusimbi
Kwizera ko igisubizo “kigeze igihe” kubera ko kimaze igihe kitagaragara.
Nyuma y'imitukura icumi, amahirwe y'umukara aracyari 18/37. Uruziga ntirubika amateka kandi nta cyo rubereyemo umwenda.
Ikosa
Iyo umutukuitegaUmutukuItega ryishyura kimwe ku kindi ku mibare 18 y'umutuku. Mu Gifaransa: rouge.Soma byose → umaze gusohoka inshuro icumi, abakinnyi benshi bumva ko umukaraitegaUmukaraItega ryishyura kimwe ku kindi ku mibare 18 y'umukara. Mu Gifaransa: noir.Soma byose → “ugeze igihe” bagatega bakurikije ibyo. Abandi bumva ko umutuku “ushyushye” bakawutegaho. Bombi batekereza bahereye ku ruhererekane rwarangiye bajya ku izunguruka ritarabaho. AgapiraibikoreshoAgapiraAgapira gato koherezwa mu nzira kerekeza mu cyerekezo kinyuranye n'icya rotor. Udupira tw'iki gihe dukozwe muri ivorine cyangwa Teflon, mm 18–21.Soma byose → ntikazi uko amazunguruka icumi aheruka yagenze; utuzuibikoreshoAkazuKamwe mu tuzu 37 twanditseho imibare turi kuri rotor. Nanone: slot, cup.Soma byose → dufite ingano imwe n'iyo twari dufite mu isaha ishize; amahirweimibareAmahirweAmahirwe y'igisubizo, kuva kuri 0 kugeza kuri 1 cyangwa kuva kuri 0% kugeza kuri 100%. Umubare umwe: 1/37 = 2,70%.Soma byose → y'umukara ni 18/37 nk'uko buri gihe yari ari.
Impamvu bisa n'ukuri
Mu gihe kirekire ibipimo by'umutuku n'umukara byegera koko 18/37 kuri buri kimwe. Itegeko ry'imibare mininiimibareItegeko ry'imibare mininiImpuzandengo y'ibisubizo byigenga yegera agaciro gateganyijwe uko umubare w'amagerageza wiyongera.Soma byose → ribyemeza. Ariko kwegerana kubaho binyuze mu kuvangwa, si mu gukosorwa: nyuma y'andi mazunguruka 1.000, imitukura icumi y'inyongera iba ikosa ryo kuzengurutsa mu gipimo, si uko umukara wafashe umutuku ahubwo ni uko icyitegererezo cyakuze. Nta buryo butuma umukara ugira amahirwe menshi, kandi itegeko ry'imibare minini ntiribukeneye.
Monte Carlo, ku wa 18 Kanama 1913
Umukara wasohotse inshuro 26 zikurikiranye ku meza yo muri Casino de Monte-Carlo. Kuva ku mukara wa cumi na gatanu, abakinnyi barundanyije amatega ku mutuku, bakuba kabiri inshuro nyinshi, buri zunguruka “ryizewe kurushaho” kurusha iryabanje. Kazino yatsindiye miliyoni z'amafaranga y'Igifaransa. Urwo ruhererekane rwari rufite amahirwe ya 1 muri miliyoni 137 uhereye ku mukara wa mbere, kandi amahirwe y'uko rwazabaho amaherezo ahantu runaka muri kazino zo ku isi yari hafi rimwe. Ni yo mpamvu ikosa ry'umukinnyi w'urusimbi ryitwa kandi ikosa rya Monte Carlo.
Nta gitangaza. Biba rimwe muri 44.
Abakinnyi batangira kubibona. Umutuku “ugeze igihe”.
Ameza yuzuye abantu. Amatega ku mutuku akubwa kabiri nyuma ya buri gihombo.
Imitungo iratakara. Buri mukara mushya utuma umutuku wumvikana nk'uwizewe kurushaho.
Uruhererekane rurarangira. Kazino yatsindiye miliyoni z'amafaranga y'Igifaransa ku bantu bategaga barwanya uruhererekane rutashoboraga “kumenya” ko ari uruhererekane.
Ukuboko gushyushye
Gushyigikira ibara kubera ko riri mu ruhererekane ni rya kosa rimwe rihindukiye: uruhererekane ruteganywa gukomeza aho kurangira. Abahanga mu mitekerereze babyita ukuboko gushyushyeigihuhaUkuboko gushyushyeKwizera ko uruhererekane rw'intsinzi, cyangwa rw'igisubizo kimwe, rutuma ikindi gishoboka kurushaho. Ku ruziga ni ikosa ry'umukinnyi w'urusimbi rihindukiye.Soma byose →, bakurikije ubushakashatsi bwo mu 1985 bwa Gilovich, Vallone na Tversky bwashakishije uruhererekane mu gutera umupira muri basketball maze ntibubone urenze amahirwe. Mu 2018 Miller na Sanjurjo bagaragaje ko isuzuma ubwaryo ryari ribogamye: mu nyandiko ngufi, igice cy'ibitego biterwa nyuma y'igitego gisohoka munsi y'igipimo rusange cy'uwatera ku mpuzandengo, bityo umukinnyi udafite ukuboko gushyushye na gato agaragara nk'ukonje gato. Bimaze gukosorwa, amakuru amwe agaragaza ukuboko gushyushye guto. Umuntu ashobora gushyuha; uruziga nta miterere rugira rwabamo. Abakinnyi bamwe bizera byombi icyarimwe, ko uruhererekane rukomeza kugeza rubaye “rurerure cyane” hanyuma rukarangira. Ku ruziga ruboneye buri buryo bufite agaciro gateganyijweimibareAgaciro gateganyijweIgisubizo mpuzandengo kuri buri tega mu gihe kirekire. −1/37 y'itega kuri buri tega risanzwe ry'i Burayi.Soma byose → kamwe no guhitamo ibara utera igiceri: −2,70% by'itega.
Ku meza nyayo
Croson na Sundali (2005) barebye amasaha 18 y'amashusho y'umutekano y'ameza amwe ya zeruuruzigaZeruAkazu kamwe k'icyatsi katafatwa n'itega ryishyura kimwe ku kindi, irya dazeni cyangwa iry'inkingi; ni ho inyungu ya kazino ikomoka. Nanone: zeru imwe, 0.Soma byose → ebyiri muri kazino nini y'i Reno: abakinnyi 139 bateze amatega 24.131. Ku matega yishyura kimwe ku kindiitegaItega ryishyura kimwe ku kindiUmutuku/umukara, itabangikanye/ibangikanye, minini/mito. Imibare 18, ryishyura 1:1.Soma byose →, abakinnyi bari bagabanyijemo hafi kimwe hagati yo gukurikira uruhererekane rugufi no kururwanya. Nyuma y'ibisubizo bitanu bisa bikurikiranye bahengamiraga ku kurwanya uruhererekane, kandi nyuma y'atandatu cyangwa arenga, 85% by'amatega yabo yari ku rundi ruhande. Abo bakinnyi bamwe bagaragazaga ukuboko gushyushye kuri bo ubwabo: nyuma yo gutsinda ku mibare, bafataga imibare 13,6 ku izunguruka rikurikira ku mpuzandengo, ugereranyije na 9,2 nyuma yo gutsindwa. Uruziga rwabo nta kimenyetso cy'ukubogama rwagaragazaga, bityo nta na kimwe muri ibyo cyahinduye icyo umwe muri bo yashoboraga kwitega.
Hanze ya kazino
Iyo mbaraga imwe igaragara aho ibyemezo nyabyo bifatirwa. Clotfelter na Cook (1993) bakurikiranye umukino w'imibare wa buri munsi wa Maryland: amafaranga ategwa ku mubare yagabanukaga cyane ukimara gutomborwa kandi agatwara amezi kugira ngo asubire uko yari ari, nubwo itombora ritagira ububiko bw'ibyabaye. Chen, Moskowitz na Shue (2016) babisanze mu banyamwuga. Abacamanza b'ubuhungiro bo muri Leta Zunze Ubumwe za Amerika bashoboraga kwanga ikirego kugeza ku manota 3,3 ku ijana kurushaho iyo bari bemeye icyabanje. Abasifuzi ba baseball bashoboraga kuvuga strike amanota 1,5 munsi nyuma yo kuyivuga, kandi birenze kabiri ibyo ku majugunywa y'umupira yegeranye. Mu igerageza ryakorewe mu kazi n'abashinzwe inguzanyo bahembwa amafaranga adahinduka, kugeza kuri 9% by'ibyemezo byahindukaga gutyo. Ibirego byazaga mu buryo butunguranye, bityo icyemezo giheruka nta cyo cyavugaga ku gikurikira, nk'uko izunguruka riheruka nta cyo rivuga ku rikurikira.
Ikosa ry'umukinnyi w'urusimbi rihindukiye
Umuhanga mu bya filozofiya Ian Hacking (1987) yise uburyo bwa gatatu. Umuntu yinjira mu cyumba, akabona udusoro tubiri tugwa kuri gatandatu na gatandatu maze agasoza ko twagomba kuba twarajugunywe inshuro nyinshi mbere. Buri jugunywa rifite amahirwe angana yo kuba gatandatu kabiri, iryambere ry'umugoroba cyangwa irya gihumbi, bityo ibyo yabonye nta cyo bivuga ku gihe umukino umaze. Muri roulette ni umukinnyi ugera ku kibaho kigaragaza imitukura umunani agafata umwanzuro ko ameza agomba kuba amaze amasaha azunguruka kugira ngo ayitange. Ikosa risanzwe rishyira ibyahise mu izunguruka rikurikira; iri rishyira ikintu kidakunze kubaho mu byahise nta muntu wabonye.
Umuhanga mu mitekerereze wabyizeraga
Iri kosa ryagize abarishyigikira b'abahanga. Umuhanga mu mitekerereze w'Umudage Karl Marbe yasuzumye ibitabo bine by'ivuka birimo ivuka 49.152 buri kimwe, asanga uruhererekane rurerure rw'abahungu cyangwa rw'abakobwa bakurikiranye ari 17, maze asoza ko uruhererekane rurerure rudakunze kubaho kurusha uko amahirwe abyemera, bityo uruhererekane rugatuma ikindi gisubizo kigira amahirwe menshi. Amahirwe yonyine avuga ibindi: mu ivuka 196.608, uruhererekane rwa 17 cyangwa rurenga rugaragara hafi inshuro enye muri eshanu. Marbe yari yabonye neza neza uko impererekane itunguranye isa. Epstein (2013) asubiramo iyi nkuru; Amahirwe y'Uruhererekane rw'Ibisubizo muri Roulette itanga uburyo bwa roulette.
Aho iri kosa ridakora
Iyo uruziga rubogamye mu buryo bufatika, amazunguruka yahise yaba afite amakuru, kuko yaba ari ikimenyetso ku tuzu aho kuba ku mahirwe. Iyo ni yo ngingo ya Laboratwari, kandi bisaba amazunguruka ibihumbi yo ku ruziga rumwe rwamenyekanye kugira ngo hagire icyo bivuga. Ku ruhererekane rw'imitukura icumi ku ruziga rutazwi, impamvu y'ukubogama ntishoboka cyane kurusha iy'amahirwe.
Ibibazo
Oya. Rireba ikintu cyose cyigenga gisubirwamo: udusoro, ibiceri, imibare ya tombola.
Ibipimo bizegerana. Igisubizo cyawe kizaba kikiri hafi −2,70% by'ibyo wategeye.
Nta tegeko ry'impuzandengo ribaho. Hariho itegeko ry'imibare minini, kandi rikora binyuze mu kuvangwa.
Kwishimisha n'Imibare
Banza ubigerageze ubwawe. Buri gisubizo kirapfunyitse; ugifungure igihe witeguye.
Nyuma yo gutera igiceri inshuro 10, cyerekana umutwe inshuro 7 n'inyuma inshuro 3. Nyuma yo kugitera inshuro 1.000, cyerekana umutwe 517 n'inyuma 483. Ese inyuma zafashe umutwe?
Erekana igisubizo
Igisubizo Oya. Itandukaniro ryavuye kuri 4 rigera kuri 34. Igipimo ni cyo cyonyine cyegereye uburinganire.
Igipimo cy'umutwe ku nyuma cyavuye kuri 7/3, hafi 2,33, kigera kuri 517/483, hafi 1,07. Ibyo ni itegeko ry'imibare mininiimibareItegeko ry'imibare mininiImpuzandengo y'ibisubizo byigenga yegera agaciro gateganyijwe uko umubare w'amagerageza wiyongera.Soma byose → rikora.
Itandukaniro hagati yabyo ryariyongereye, kuva kuri 4 kugeza kuri 34. Ku giceri kitabogamye, itandukaniro rya hafi 30 nyuma yo kugitera inshuro 1.000 ni ibisanzwe: itandukaniro risanzwe ryiyongera hafi nk'umuzi kare w'umubare w'inshuro cyatewe, mu gihe igipimo cyegera 1.
Nta kintu cyagaruye inyuma ngo zifate umutwe. Ubwiyongere bw'umutwe bwo mu ntangiriro bwarenzweho n'inshuro 990 zakurikiyeho, ntibwakosowe.
Tera igiceri inshuro enye maze urebe gusa inshuro ziza ako kanya nyuma y'umutwe (H = umutwe, T = inyuma). Ni ikihe gice cy'izo kiba umutwe? Kibare kuri buri ruhererekane muri 16 rushoboka maze ufate impuzandengo y'ibyo bice. Ese ni 50%?
Erekana igisubizo
Igisubizo Oya. Ni 17/42, hafi 40,5%. Urebye utyo, igiceri kitabogamye gisa n'igikonja nyuma y'umutwe.
Andika impererekane 16. Ebyiri muri zo, TTTT na TTTH, nta mutwe zifite mu nshuro eshatu za mbere, bityo nta kintu gikurikira umutwe; hasigara 14.
Muri buri rumwe, fata inshuro zikurikira umutwe maze ushake igice kiba umutwe. HHHH itanga 3 kuri 3. HHHT itanga 2 kuri 3. HTHT itanga 0 kuri 2. Unyuze kuri zose uko ari 14: impererekane esheshatu zitanga 0, enye zitanga 1/2, imwe itanga 2/3 naho eshatu zigatanga 1 (HHHH, THHH na TTHH).
Teranya ibice: 4 × 1/2 + 2/3 + 3 = 17/3. Gabanya na 14: 17/42 ≈ 40,5%.
Nta nshuro n'imwe ishyigikira inyuma; buri imwe ni 50–50. Ukubogama guturuka ku gufata impuzandengo uruhererekane ku rundi: uruhererekane rwuzuye imitwe rufite inshuro nyinshi zo kureba ariko rubarwa rimwe, kimwe n'uruhererekane rufite imwe gusa. Miller na Sanjurjo (2018) berekanye ko ubushakashatsi bwo mu 1985 ku kuboko gushyushye (hot hand) bwapimye abakinnyi babwo ba basketball muri ubu buryo, bityo abakinnyi basaga n'abatagira uruhererekane kurusha amahirwe mu by'ukuri bari barufite gato kurushaho.
Akanya k'urwenya
Kuvangwa, si ugukosorwa. Uruziga nta mwenda rufite.
Inkomoko
- 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.”