Kukanganisa kweMubheji
Kutenda kuti mhedzisiro “yava kufanira kubuda” nekuti haina kuoneka kwechinguva.
Mushure metsvuku gumi mukana wenhema uchiri 18/37. Vhiri harichengeti rekodhi uye harina chikwereti.
Kukanganisa
Kana tsvukubhetiTsvukuBheti remubhadharo wakaenzana panhamba 18 tsvuku. ChiFrench: rouge.Verengai zvese → yabuda kagumi, vatambi vazhinji vanonzwa kuti nhemabhetiNhemaBheti remubhadharo wakaenzana panhamba 18 nhema. ChiFrench: noir.Verengai zvese → “yava kufanira kubuda” vobheja zvichienderana nazvo. Vamwe vanonzwa kuti tsvuku “inopisa” vobheja iyoyo. Vese vari kufunga kubva panhevedzo yakatopera kuenda pakutenderera kusati kwaitika. BhoramidziyoBhoraBhora diki rinokandwa mumugero richienda rimwe divi nerotor. Mabhora emazuva ano ndeeivorine kana Teflon, 18–21 mm.Verengai zvese → harizivi kuti kutenderera gumi kwekupedzisira kwaiva kupi; makombamidziyoGombaImwe yemakamuri 37 ane nhamba parotor. Mamwe mazita: slot, cup.Verengai zvese → akaenzana nezvaaiva awa yapfuura; mukanamasvomhuMukanaMukana wemhedzisiro, kubva pa0 kusvika pa1 kana 0% kusvika 100%. Nhamba imwe: 1/37 = 2.70%.Verengai zvese → wenhema i18/37 sezvawaigara wakaita.
Sei zvichinzwika sechokwadi
Munguva refu zviyero zvetsvuku nenhema zvinoswedera ku18/37 chimwe nechimwe. Mutemo wenhamba hurumasvomhuMutemo wenhamba huruAvhareji yemhedzisiro yakazvimirira inoswedera kukukosha kunotarisirwa sezvo huwandu hwekuedza huchikura.Verengai zvese → unozvivimbisa. Asi kuswedera kunoitika nekudzikiswa, kwete nekugadziriswa: mushure mekumwe kutenderera 1,000 tsvuku gumi dzakawedzerwa chikanganiso chidiki chekupatsanura muchiyero, kwete nekuti nhema yakabata asi nekuti sampuru yakakura. Hapana nzira inoita kuti nhema ive nemukana wakakura, uye mutemo wenhamba huru haudi imwe.
Monte Carlo, 18 Nyamavhuvhu 1913
Nhema yakabuda ka26 yakatevedzana patafura muCasino de Monte-Carlo. Kubva kunhema yegumi neshanu kana zvakadaro, vatambi vakaunganira patsvuku, vachipeta kaviri nekupetazve, kutenderera kwega kwega kuri “nechokwadi” kupfuura kwakapfuura. Kasino yakakunda mamiriyoni emafranc. Mutsara uyu waiva nemukana we1 mu137 miriyoni kubva panhema yekutanga, uye mukana wekuti waizozoitika kumwe kunhu mumakasino epasi rose waiva unenge mumwe. Ndicho chikonzero kukanganisa kwemubheji kuchinziwo kukanganisa kweMonte Carlo.
Hazvishamisi. Zvinoitika kamwe chete pa44.
Vatambi vanotanga kuona. Tsvuku “yava kufanira kubuda”.
Tafura yazara. Mari dzakabhejwa patsvuku dzinopetwa kaviri mushure mekurasikirwa kwega kwega.
Pfuma dzarasika. Nhema itsva yega yega inoita kuti tsvuku inzwike iine chokwadi kupfuura.
Mutsara unopera. Kasino yakunda mamiriyoni emafranc kubva kuvanhu vaibheja vachipikisa mutsara wakanga usingagoni “kuziva” kuti mutsara.
Ruoko runopisa
Kutsigira ruvara nekuti ruri pamutsara chikanganiso chimwe chete chakapindurudzwa: mutsara unotarisirwa kuenderera panzvimbo pekupera. Nyanzvi dzepfungwa dzinozviti ruoko runopisanganoRuoko runopisaKutenda kuti mutsara wekukunda, kana wemhedzisiro imwe, unoita kuti imwe zvakare ive nemukana wakawanda. Pavhiri ndiko kukanganisa kwemubheji kwakapindurudzwa.Verengai zvese → (hot hand), kubva paongororo ya1985 yaGilovich, Vallone naTversky yakatsvaga mitsara mukukanda kwebasketball isina kuwana inopfuura mhanza. Muna 2018 Miller naSanjurjo vakaratidza kuti bvunzo pachayo yakanga yakatsveyama: murekodhi pfupi, chikamu chekupinda mushure mekupinda chinobuda chiri pasi pechiyero chose chemukandi paavhareji, saka mutambi asina ruoko runopisa zvachose anoratidzika seakatonhora zvishoma. Pakugadziriswa, data rimwe chete rinoratidza ruoko runopisa rudiki. Munhu anogona kudziya; vhiri harina mamiriro ekuvamo. Vamwe vatambi vanotenda zvese zviri zviviri kamwe chete, kuti mutsara unoenderera kusvika “wareba zvakanyanya” wobva wapera. Pavhiri rakarurama shanduro yega yega ine kukosha kunotarisirwamasvomhuKukosha kunotarisirwaMhedzisiro yepakati pabheti rimwe nekufamba kwenguva refu. −1/37 yemari yakabhejwa pabheti rimwe nerimwe reEurope rakajairwa.Verengai zvese → kwakafanana nekusarudza ruvara nekukanda mari: −2.70% yemari yakabhejwa.
Patafura chaiyo
Croson naSundali (2005) vakatarisa maawa 18 evhidhiyo yekuchengetedza kubva patafura imwe yezerovhiriZeroGomba rimwe chete rakasvibira risingafukidzwi nebheti remubhadharo wakaenzana, redozeni kana rekoramu; ndiko kunobva chikamu chekasino. Mamwe mazita: zero imwe, 0.Verengai zvese → mbiri pakasino hombe muReno: vatambi 139 vachiisa mabheti 24,131. Pamabheti emubhadharo wakaenzanabhetiBheti remubhadharo wakaenzanaTsvuku/nhema, isina kuenzana/yakaenzana, dzepamusoro/dzepasi. Nhamba 18, rinobhadhara 1:1.Verengai zvese →, vatambi vakanga vakaganika zvakaenzana pakati pekutevera mitsara mipfupi nekuipikisa. Mushure mezvishanu zvakafanana zvakatevedzana vakazendamira kupikisa mutsara, uye mushure metanhatu kana kupfuura, 85% yemabheti avo yaiva kune rumwe rutivi. Vatambi vamwe chete ava vakaratidza ruoko runopisa pamusoro pavo pachavo: mushure mekukunda panhamba vakafukidza nhamba 13.6 pakutenderera kunotevera paavhareji, kana zvichienzaniswa ne9.2 mushure mekurasikirwa. Vhiri ravo raisaratidza chiratidzo chekutsauka, saka hapana chezvi chakachinja zvaigona kutarisirwa neani zvake.
Kunze kwekasino
Kukwevera ikoko kunooneka panoitwa sarudzo chaidzo. Clotfelter naCook (1993) vakatevera mutambo wenhamba wezuva nezuva weMaryland: mari yaibhejwa panhamba yakadonha zvikuru ichangobva kudhirowa uye yakatora mwedzi kuti idzoke, kunyange kudhirowa kusina ndangariro. Chen, Moskowitz naShue (2016) vakazviwana pakati penyanzvi. Vatongi vekupotera muUnited States vaiva nemukana unosvika 3.3 percentage points wekuramba nyaya kana vakanga vabvuma yapfuura. Vatongi vebaseball vaiva nemukana mudiki ne1.5 points wekudaidza strike mushure mekudaidza imwe, uye kakapetwa kanopfuura kaviri pakukanda kwakaoma kutonga. Muedzo wemunda nevashandi vezvikwereti vanobhadharwa mari yakatarwa, kusvika 9% yesarudzo dzakapidigurwa nenzira iyi. Nyaya dzaiuya nenhevedzo isina hurongwa, saka sarudzo yekupedzisira yakanga isingatauri chinhu pamusoro peinotevera, sekutenderera kwekupedzisira kusingatauri chinhu pamusoro pekunotevera.
Kukanganisa kwemubheji kwakapindurudzwa
Muzivi Ian Hacking (1987) akatumidza shanduro yechitatu. Mumwe munhu anopinda mukamuri, anoona dhayisi mbiri dzichimhara pamatanhatu maviri oti dzinofanira kunge dzatokandwa kakawanda. Kukanda kwega kwega kune mukana wakaenzana wekuva matanhatu maviri, kwekutanga kwemanheru kana kwechiuru, saka kuona ikoko hakutauri chinhu pamusoro pekuti mutambo wanga uchienderera kwenguva yakareba sei. PaRoulette ndiye mutambi anosvika pabhodhi rinoratidza tsvuku sere oti tafura inofanira kunge yanga ichitenderera kwemaawa kuti iburitse izvozvo. Kukanganisa kwakajairwa kunoverenga zvakapfuura mukutenderera kunotevera; uku kunoverenga chinhu chisingawanzoonekwa muzvakapfuura zvisina akazviona.
Nyanzvi yepfungwa yakazvitenda
Kukanganisa uku kwakave nevadziviriri vakadzidza. Nyanzvi yepfungwa yekuGermany Karl Marbe akapfuura nemarejista mana ekuberekwa 49,152 rimwe nerimwe, akawana kuti mutsara wakareba kupfuura yose wevakomana kana wevasikana vakatevedzana waiva 17, akati mitsara mirefu haiwanzoitiki kupfuura zvinobvumirwa nemhanza, saka mutsara unoita kuti imwe mhedzisiro ive nemukana wakakura. Mhanza yega inotaura zvimwe: mukuberekwa 196,608 mutsara we17 kana kupfuura unooneka kunenge kana pashanu. Marbe akanga awana chaizvo zvinoratidzika senhevedzo isina hurongwa. Epstein (2013) anotaurazve nyaya iyi; Mukana weMitsara yeMhedzisiro muRoulette unopa shanduro yeRoulette.
Pasingashandi kukanganisa uku
Dai vhiri raitsauka nechimiro, kutenderera kwakapfuura kwaizopa ruzivo, nekuti kwaizova humbowo pamusoro pemakomba kwete pamusoro pemhanza. Ndiyo nyaya yeLab, uye inoda zviuru zvekutenderera kubva pavhiri rimwe rinozivikanwa kuti itaure chimwe chinhu. Kumutsara wetsvuku gumi pavhiri risingazivikanwi, tsananguro yekutsauka ine mukana mudiki zvikuru pane yemhanza.
Mibvunzo
Kwete. Kunoshanda kuchiitiko chipi nechipi chakazvimirira chinodzokororwa: dhayisi, mari, nhamba dzerotari.
Zviyero zvichaswedera. Mhedzisiro yenyu ichiri kunenge −2.70% yezvamakabheja.
Hapana mutemo weavhareji. Pane mutemo wenhamba huru, uye unoshanda nekudzikiswa.
Kutamba neMasvomhu
Edzai izvi imi pachenyu pekutanga. Mhinduro yega yega yakapetwa; ivhurei kana magadzirira.
Mushure mekukandwa 10 mari yesimbi inoratidza musoro ka7 nemuswe ka3. Mushure mekukandwa 1,000 inoratidza musoro ka517 nemuswe ka483. Muswe wakabata here?
Ratidza mhinduro
Mhinduro Kwete. Musiyano wakakura kubva pa4 kusvika pa34. Chiyero chete ndicho chakaswedera pedyo nekuenzana.
Chiyero chemusoro nemuswe chakadonha kubva pa7/3, anenge 2.33, kusvika pa517/483, anenge 1.07. Ndiwo mutemo wenhamba hurumasvomhuMutemo wenhamba huruAvhareji yemhedzisiro yakazvimirira inoswedera kukukosha kunotarisirwa sezvo huwandu hwekuedza huchikura.Verengai zvese → uri kushanda.
Musiyano uri pakati pazvo wakakura, kubva pa4 kusvika pa34. Nemari yesimbi yakaenzana, musiyano unenge 30 mushure mekukandwa 1,000 wakajairika: musiyano wakajairika unokura zvichienderana nesquare root yehuwandu hwekukandwa, nepo chiyero chichigadzikana chichienda ku1.
Hapana chakadzosa muswe. Kuwanda kwemusoro kwekutanga kwakadzikiswa nekukandwa 990 kwakatevera, hakuna kugadziriswa.
Kandai mari yesimbi kana motarisa chete kukanda kunouya mushure memusoro. Chikamu chakadii chazvo chiri musoro? Chiverengei pamitsara yose 16 inogoneka motora avhareji yezvikamu. I50% here?
Ratidza mhinduro
Mhinduro Kwete. I17/42, anenge 40.5%. Kana zvatariswa nenzira iyi, mari yesimbi yakaenzana inoratidzika seinotonhora mushure memusoro.
Nyorai mitsara 16 (H = musoro, T = muswe). Miviri yayo, TTTT neTTTH, haina musoro pakukanda kutatu kwekutanga, saka hapana chinotevera musoro; panosara 14.
Pane imwe neimwe, torai kukanda kunotevera musoro motsvaga chikamu chiri musoro. HHHH inopa 3 pa3. HHHT inopa 2 pa3. HTHT inopa 0 pa2. Tichipfuura nemose 14: mitsara mitanhatu inopa 0, mina inopa 1/2, umwe unopa 2/3 uye mitatu inopa 1 (HHHH, THHH neTTHH).
Wedzerai zvikamu: 4 × 1/2 + 2/3 + 3 = 17/3. Kamurai ne14: 17/42 ≈ 40.5%.
Hapana kukanda kunofarira muswe; kwega kwega i50–50. Kurereka kunobva pakuita avhareji mutsara nemutsara: mutsara uzere nemisoro une kukanda kwakawanda kwekutarisa asi unoverengwa kamwe chete, zvakafanana nemutsara une umwe chete. Miller naSanjurjo (2018) vakaratidza kuti chidzidzo che1985 che“ruoko runopisa” (hot hand) chakayera vatambi vacho vebasketball nenzira iyi, saka vatambi vaiita sevasina mitsara kupfuura mukana vainge vachitova nemitsara zvishoma.
Kuseka zvishoma
Kudzikiswa, kwete kugadziriswa. Vhiri harina chikwereti.
Zvinyorwa
- 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.”