Erer zwer
Sa kroyans ki enn rezilta “bizin sorti” akoz li pa finn paret depi enn bon bout letan.
Apre dis rouz, probabilite nwar touzour 18/37. Rou-la pa gard okenn rezis ek li pa dwa nanye personn.
Erer-la
Si rouzpariRouzPari peman egal lor 18 nimero rouz. An franse: rouge.Lir tou → finn sorti dis fwa, boukou zwer santi ki nwarpariNwarPari peman egal lor 18 nimero nwar. An franse: noir.Lir tou → “bizin sorti” ek zot parye lor la. Lezot santi ki rouz “so” ek zot parye lor rouz. Toulede pe rezone depi enn sekans ki deza fini, lor enn tour ki pa ankor arive. Boul-laekipmanBoulTi boul ki lanse dan simen-la dan sans kontrer rotor. Zordi bann boul an ivorine ouswa Teflon, 18–21 mm.Lir tou → pa kone ki ti ena dan dis dernie tour; bann kazekipmanKazEnn bann 37 konpartiman avek nimero lor rotor. Osi: slot, cup.Lir tou → ena mem gran ki zot ti ena enn er de sa; probabilitematematikProbabiliteSans enn rezilta, depi 0 ziska 1 ouswa depi 0% ziska 100%. Enn nimero: 1/37 = 2.70%.Lir tou → nwar se 18/37 kouma touzour.
Kifer li paret vre
Lor enn long dire, proporsion rouz ek nwar vremem rapros 18/37 sakenn. Lalwa gran nonbmatematikLalwa gran nonbMwayenn bann rezilta independan aprose valer atandi kan nonb lesey ogmante.Lir tou → garanti sa. Me sa rapros-la fer par dilision, pa par koreksion: apre 1,000 tour anplis, sa dis rouz anplis-la vinn enn ti erer arondi dan proporsion-la, pa akoz nwar finn ratrap so reta me akoz lesantiyon-la finn grandi. Pena okenn mekanism ki fer nwar pli probab, ek lalwa gran nonb pa bizin enn.
Monte Carlo, 18 out 1913
Nwar ti sorti 26 fwa swivan lor enn latab dan Casino de Monte-Carlo. Depi apepre kinzyem nwar, bann zwer ti rant an mas lor rouz, zot ti doub ek redoub, sak tour “pli sir” ki sa enn avan. Kazino ti gagne plizir milyon fran. Sa seri-la ti ena enn probabilite 1 lor 137 milyon depi premie nwar, ek probabilite ki li ti pou arive enn zour enn kote dan bann kazino lemond ti preske enn. Se pou sa ki erer zwer osi apel erer Monte Carlo.
Nanye spesial. Arive enn fwa lor 44.
Bann zwer koumans remarke. Rouz “bizin sorti”.
Latab-la plin dimounn. Miz lor rouz doub apre sakenn pert.
Bann fortinn perdi. Sakenn nouvo nwar fer rouz paret pli sir.
Seri-la fini. Kazino finn gagne plizir milyon fran ar dimounn ki ti pe parye kont enn seri ki pa ti kapav “kone” ki li enn seri.
Lamin so
Parye lor enn koler akoz li lor enn seri, se mem erer-la lanver: ou atann ki seri-la kontinie olie fini. Bann psikolog apel sa lamin somitLamin soKrwar ki enn seri gin, ouswa enn seri mem rezilta, fer enn lot pli probab. Lor rou-la se erer zwer lanvers.Lir tou →, apre enn letid 1985 par Gilovich, Vallone ek Tversky ki ti rod seri dan tir baskett ek pa ti trouv nanye plis ki azar. An 2018 Miller ek Sanjurjo ti montre ki test-la limem pa ti ekilibre: dan enn ti rezis, proporsion tir rante zis apre enn tir rante sorti an mwayenn pli ba ki to zeneral zwer-la, alor enn zwer ki pena okenn lamin so ditou paret enpe fre. Apre koreksion, mem done-la montre enn lamin so modere. Enn dimounn kapav sof li; enn rou pena okenn form pou ena. Serten zwer kwar toulede an mem tan, ki enn seri kontinie ziska li vinn “tro long” ek lerla li fini. Lor enn rou zis, sakenn version ena mem valer atandimatematikValer atandiRezilta mwayen par pari lor enn long dire. −1/37 miz-la pou sak pari eropeen standar.Lir tou → ki swazir enn koler par zwe pil ouswa fas: −2.70% miz-la.
Lor enn vre latab
Croson ek Sundali (2005) ti get 18 er video sekirite enn latab doub zerorouZeroSel kaz ver ki okenn pari peman egal, douzenn ouswa kolonn pa kouver; sours lavantaz kazino. Osi: enn sel zero, 0.Lir tou → dan enn gran kazino Reno: 139 zwer ki ti fer 24,131 pari. Lor pari peman egalpariPari peman egalRouz/nwar, inper/per, ot/ba. 18 nimero, peye 1:1.Lir tou →, zwer ti apepre divize egal ant sa bann ki swiv ti seri ek sa bann ki parye kont zot. Apre sink parey swivan, zot ti plito parye kont seri-la, ek apre sis ouswa plis, 85% zot pari ti lor lot kote. Mem bann zwer-la ti montre lamin so lor zot mem: apre enn gin lor nimero, zot ti kouver 13.6 nimero lor tour swivan an mwayenn, kont 9.2 apre enn pert. Zot rou pa ti montre okenn sign defo, alor nanye ladan pa ti sanz seki okenn ladan ti kapav atann.
Deor kazino
Mem latraksion-la paret kot vre desizion pran. Clotfelter ek Cook (1993) ti swiv zwe nimero sakzour Maryland: larzan ki dimounn parye lor enn nimero ti bes for-for depi ki li ti tire ek ti pran plizir mwa pou remonte, alor ki tiraz-la pena memwar. Chen, Moskowitz ek Shue (2016) ti trouv li parmi profesionel. Bann ziz azil Lamerik ti ziska 3.3 pwen pousantaz pli probab pou refiz enn dosie si zot ti aksepte sa enn avan. Bann arbit baseball ti 1.5 pwen mwins probab pou anons enn strike apre ki zot ti anons enn, ek plis ki de fwa sa lor bann lanse sere. Dan enn lexperyans lor terin avek ofisie pre ki ti gagn enn fre fix, ziska 9% desizion ti ranverse koumsa. Bann dosie ti vinn dan enn lord aleatwar, alor dernie desizion pa ti dir nanye lor swivan, parey kouma dernie tour pa dir nanye lor tour swivan.
Erer zwer envers
Filozof Ian Hacking (1987) ti nom enn trwazyem version. Enn kikenn rant dan enn lasam, trouv enn per de tom lor doub sis ek konklir ki zot inn bizin deza zete boukou fwa. Sakenn zete ena mem sans pou donn doub sis, premie zete laswar ouswa milyem, alor sa vizion-la pa dir nanye lor depi komie letan zwe-la pe dire. Dan roulet, se zwer ki arive divan enn tablo ki montre wit rouz ek deside ki latab-la inn bizin pe tourne depi plizir er pou prodir zot. Erer ordiner-la lir lepase dan tour swivan; sa enn-la lir enn vizion rar dan enn lepase ki personn pa finn trouve.
Enn psikolog ki ti kwar ladan
Erer-la finn ena defanser savan. Psikolog alman Karl Marbe ti pas lor kat rezis 49,152 nesans sakenn, ti trouve ki pli long seri garson ouswa tifi swivan ti 17, ek ti konklir ki long seri pli rar ki azar permet, alor ki enn seri fer lot rezilta pli probab. Azar tousel dir lekontrer: dan 196,608 nesans, enn seri 17 ouswa plis paret apepre kat fwa lor sink. Marbe ti trouv egzakteman figir enn sekans aleatwar. Epstein (2013) rakont sa ka-la ankor; Probabilite bann seri donn versio roulet.
Kot erer-la pa aplike
Si rou-la ti ena enn defo fizik, bann tour pase ti pou donn linformasion, akoz zot ti pou enn prev lor bann kaz olie lor lasans. Sa se sizet Laboratwar-la, ek li bizin plizir milye tour lor enn sel rou idantifie pou dir kiksoz. Pou enn seri dis rouz lor enn rou ki ou pa kone, explikasion defo boukou mwins probab ki explikasion azar.
Kestion
Non. Li aplik pou nimport ki evennman independan ki repete: de, pies, nimero loto.
Proporsion-la pou rapros. Ou rezilta pou touzour apepre −2.70% seki ou finn parye.
Pena okenn lalwa bann mwayenn. Ena enn lalwa gran nonb, ek li marse par dilision.
Lamizman ar matematik
Esey rezoud zot ou mem avan. Sakenn solision kase; ouver li kan ou pare.
Apre 10 lanse, enn pies montre 7 fas ek 3 pil. Apre 1,000 lanse, li montre 517 fas ek 483 pil. Eski pil inn rattrap fas?
Montre solision-la
Repons Non. Lekar-la inn grandi depi 4 ziska 34. Zis rapor-la inn vinn pli pre egalite.
Rapor fas lor pil inn bes depi 7/3, apepre 2.33, ziska 517/483, apepre 1.07. Samem lalwa gran nonbmatematikLalwa gran nonbMwayenn bann rezilta independan aprose valer atandi kan nonb lesey ogmante.Lir tou → ki pe azir.
Lekar ant zot inn grandi, depi 4 ziska 34. Avek enn pies zis, enn lekar apepre 30 apre 1,000 lanse se normal: lekar tipik grandi apepre kouma rasinn kare nonb lanse, alor ki rapor-la stabiliz ver 1.
Nanye pa finn tir pil deryer. Sirplis fas o koumansman inn dilie par 990 lanse swivan, pa koriz.
Lans enn pies kat fwa ek get zis bann lanse ki vinn drwat apre enn fas. Ki proporsion ladan fas? Kalkil li pou sakenn lor 16 sekans posib ek pran mwayenn bann proporsion. Eski li 50%?
Montre solision-la
Repons Non. Li 17/42, apepre 40.5%. Gete dan sa fason-la, enn pies zis paret vinn fre apre enn fas.
Fer lalis 16 sekans. De ladan, PPPP ek PPPF, pena okenn fas dan trwa premie lanse, alor nanye pa swiv enn fas; sa les 14.
Dan sakenn, pran bann lanse ki swiv enn fas ek trouv proporsion ki fas. FFFF donn 3 lor 3. FFFP donn 2 lor 3. FPFP donn 0 lor 2. Kan pas lor tou 14: sis sekans donn 0, kat donn 1/2, enn donn 2/3 ek trwa donn 1 (FFFF, PFFF ek PPFF).
Azout bann proporsion: 4 × 1/2 + 2/3 + 3 = 17/3. Divize par 14: 17/42 ≈ 40.5%.
Okenn lanse pa favoriz pil; sakenn 50–50. Lapant-la sorti dan fer mwayenn sekans par sekans: enn sekans ranpli fas ena boukou lanse pou gete me konte enn fwa, parey kouma enn sekans avek enn sel. Miller ek Sanjurjo (2018) finn montre ki letid 1985 lor lamin so ti mezir so bann zwer baskett dan sa fason-la, alor bann zwer ki ti paret pa plis an seri ki lazar ti an realite enpe plis an seri.
Enpe riye
Dilision, pa koreksion. Rou-la pa dwa nanye.
Sours
- 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.”