Khaladka Khamaarlaha
Aaminaadda in natiijo ay “waqtigeedii timid” sababtoo ah muddo ma soo bixin.
Toban casaan kadib itimaalka madow weli waa 18/37. Giraangirtu diiwaan ma hayso, waxna kuma laha.
Khaladka
Haddii casaansharadCasaanSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee casaanka ah. Faransiis: rouge.Akhri dhammaan → toban jeer soo baxay, ciyaartoy badan waxay dareemaan in madowsharadMadowSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee madow. Faransiis: noir.Akhri dhammaan → uu “waqtigiisii yimid” waxayna ku sharadsadaan sidaas. Kuwo kale waxay dareemaan in casaan uu “kulul yahay” wayna ku sharadsadaan. Labaduba waxay ka fikirayaan taxane horey u dhammaaday oo ay u gudbinayaan wareeg aan weli dhicin. KubbadduqalabKubbadKubbadda yar ee lagu tuuro jidka iyada oo ka soo horjeedda rotor-ka. Kubbadaha casriga ah waa ivorine ama Teflon, 18–21 mm.Akhri dhammaan → ma garanayso waxa ay ahaayeen tobankii wareeg ee u dambeeyay; godadkuqalabGodMid ka mid ah 37-ka qol ee lambarrada leh ee rotor-ka. Sidoo kale: slot, cup.Akhri dhammaan → waa isla cabbirkii ay ahaayeen saacad ka hor; itimaalkaxisaabItimaalFursadda natiijo, 0 ilaa 1 ama 0% ilaa 100%. Hal lambar: 1/37 = 2.70%.Akhri dhammaan → madow waa 18/37 sidii uu had iyo jeer ahaa.
Sababta ay run ugu ekaato
Muddada dheer saamiyada casaan iyo madow mid kastaa wuxuu isugu soo dhowaadaa 18/37. Sharciga tirooyinka waaweynxisaabSharciga tirooyinka waaweynCelceliska natiijooyinka madaxbannaan wuxuu u soo dhowaadaa qiimaha la filayo marka tirada tijaabooyinku korodho.Akhri dhammaan → ayaa dammaanad ka qaada. Laakiin isku-soo-dhowaanshuhu wuxuu ku dhacaa khafiifin, ma aha sixid: 1,000 wareeg oo kale kadib tobanka casaan ee dheeriga ahi waa khalad yar oo saamiga ku jira, ma aha sababtoo ah madow ayaa la soo gaaray ee waa sababtoo ah muunadda ayaa korortay. Ma jiro hab ka dhiga madow mid ka itimaal badan, sharciga tirooyinka waaweynna uma baahna mid.
Monte Carlo, 18 Agoosto 1913
Madow wuxuu soo baxay 26 jeer oo isku xiga miis ku yaal Casino de Monte-Carlo. Laga bilaabo qiyaastii madowga shan iyo tobnaad, ciyaartoydu waxay ku qulquleen casaan, iyagoo labanlaabaya oo mar kale labanlaabaya, wareeg kastaa “ka hubsan yahay” kii ka horreeyay. Kasiinadu waxay ku guuleysatay malaayiin faran. Taxanahu wuxuu lahaa itimaal 1 ka mid ah 137 milyan laga bilaabo madowgii ugu horreeyay, itimaalka in uu ugu dambeyn meel uun ka dhaco kasiinooyinka adduunka oo dhanna wuxuu ahaa ku dhawaad hal. Taasi waa sababta khaladka khamaarlaha sidoo kale loogu yeero khaladka Monte Carlo.
Caadi. Wuxuu dhacaa hal mar 44-kiiba.
Ciyaartoydu waxay bilaabaan inay dareemaan. Casaan ayaa “waqtigiisii yimid”.
Miisku waa buuxaa. Sharadyada casaanka waa la labanlaabaa khasaare kasta kadib.
Hanti badan ayaa luntay. Madow kasta oo cusub wuxuu casaan ka dhigaa mid la dareemo inuu ka hubsan yahay.
Taxanuhu wuu dhammaadaa. Kasiinadu waxay ku guuleysatay malaayiin faran oo ka timid dad ku sharadsanayay taxane aan “ogaan karin” inuu taxane yahay.
Gacanta kulul
Taageeridda midab sababtoo ah wuxuu ku jiraa taxane waa isla khaladkaas oo la rogay: taxanaha waxaa laga filayaa inuu sii socdo halkii uu dhammaan lahaa. Cilmi-nafsiyaqaannadu waxay ugu yeeraan gacan kululkhuraafaadGacan kululAaminaadda ah in taxane guulo ah, ama hal natiijo, uu mid kale ka dhigo mid u badan. Giraangirta waa khaladka khamaarlaha oo la rogay.Akhri dhammaan →, kadib daraasad 1985 ah oo ay sameeyeen Gilovich, Vallone iyo Tversky oo raadisay taxanayaal toogashada kubbadda koleyga waxna kama helin wax dhaafsiisan nasiib. 2018 Miller iyo Sanjurjo waxay muujiyeen in tijaabadu lafteedu ay janjeertay: diiwaan gaaban, qaybta soo galidda isla markiiba ka dambeysa soo galid waxay celcelis ahaan ka hoosaysaa heerka guud ee toogtaha, sidaas darteed ciyaartoy aan gacan kulul gabi ahaanba lahayn wuxuu u muuqdaa mid xoogaa qabow. Marka la saxo, isla xogtaasi waxay muujinaysaa gacan kulul oo dhexdhexaad ah. Qof wuu kululaan karaa; giraangirtu ma laha xaalad ay ku jirto. Ciyaartoy qaarkood waxay isku mar haystaan labada aaminaad, in taxane sii socdo ilaa uu “aad u dheeraado” kadibna dhammaado. Giraangir caddaalad ah, nooc kastaa wuxuu leeyahay isla qiimaha la filayoxisaabQiimaha la filayoCelceliska natiijada sharad kasta muddada dheer. −1/37 ee sharadka sharad kasta oo Yurub caadi ah.Akhri dhammaan → ee dooridda midab adigoo tuuraya qadaadiic: −2.70% sharadka.
Miis dhab ah
Croson iyo Sundali (2005) waxay daawadeen 18 saacadood oo muuqaal amni ah oo ka yimid hal miis laba-ebergiraangirEberHal godka cagaaran ee aan daboolin sharad lacag isle'eg ah, dersin ama tiir; isha faa'iidada kasiinada. Sidoo kale: single zero, 0.Akhri dhammaan → ah oo ku yaal kasiino weyn oo Reno ah: 139 ciyaartoy oo dhigay 24,131 sharad. Sharadyada lacag isle'egsharadSharad lacag isle'eg ahCasaan/madow, kisi/dhaban, sare/hoose. 18 lambar, wuxuu bixiyaa 1:1.Akhri dhammaan →, ciyaartoydu waxay u qaybsanaayeen si qiyaas ahaan siman inta raacda taxanayaal gaagaaban iyo inta ka soo horjeedda. Shan isku nooc ah oo isku xiga kadib waxay u janjeereen ka soo horjeedka taxanaha, lix ama ka badan kadibna, 85% sharadyadoodu waxay ahaayeen dhinaca kale. Isla ciyaartoydaas waxay muujiyeen gacanta kulul ee ku saabsan naftooda: guul lambarrada kadib waxay daboolayeen 13.6 lambar wareegga xiga celcelis ahaan, marka loo eego 9.2 khasaare kadib. Giraangirtoodu ma muujin wax calaamad eex ah, sidaas darteed waxaas midkoodna ma beddelin waxa midkoodna filan karay.
Kasiinada dibaddeeda
Isla jiidashadaas waxay ka muuqataa meelaha go'aanno dhab ah lagu gaaro. Clotfelter iyo Cook (1993) waxay raaceen ciyaarta lambarrada maalinlaha ah ee Maryland: lacagta lagu sharadsaday lambar si xoog ah bay hoos ugu dhacday isla marka la soo saaro, bilooyin bayna qaadatay inay soo kabato, inkastoo bixintu aysan lahayn xusuus. Chen, Moskowitz iyo Shue (2016) waxay ka heleen xirfadleyda dhexdooda. Garsoorayaasha magangalyada Mareykanka waxay ahaayeen ilaa 3.3 dhibcood boqolley oo ka itimaal badan inay diidaan kiis haddii ay oggolaadeen kii ka horreeyay. Garsoorayaasha baseball-ka waxay ahaayeen 1.5 dhibcood oo ka itimaal yar inay ku dhawaaqaan strike mid ku dhawaaqid kadib, in ka badan labanlaab marka tuuristu dhow tahay. Tijaabo goob ah oo ay ka qaybgaleen saraakiisha amaahda oo lagu bixiyay khidmad go'an, ilaa 9% go'aannada ayaa sidan loo rogay. Kiisaska waxay u yimaadeen si nasiib ah, sidaas darteed go'aankii u dambeeyay waxba kama sheegin kan xiga, sida wareeggii u dambeeyay aanu waxba uga sheegin kan xiga.
Khaladka khamaarlaha ee rogan
Faylasuuf Ian Hacking (1987) wuxuu magacaabay nooc saddexaad. Qof ayaa qol soo gala, arka labo laadh oo ku dhacay lix-lix, wuxuuna go'aamiyaa in mar hore marar badan la tuuray. Tuuris kastaa waa isku itimaal inay noqoto lix-lix, ha ahaato tii ugu horreysay fiidka ama tii kunaad, sidaas darteed muuqaalku waxba kama sheego inta ciyaartu socotay. Roulette-ka waa ciyaartoyga yimaada loox muujinaya siddeed casaan oo go'aamiya in miisku saacado wareegayay si uu u soo saaro. Khaladka caadiga ahi wuxuu wixii hore u akhriyaa wareegga xiga; kanina wuxuu muuqaal dhif ah u akhriyaa wixii hore oo aan qofna arkin.
Cilmi-nafsiyaqaan rumaysnaa
Khaladku wuxuu lahaa difaacayaal aqoon leh. Cilmi-nafsiyaqaanka Jarmalka ah Karl Marbe wuxuu baaray afar diiwaan oo mid kastaa ka kooban yahay 49,152 dhalasho, wuxuu ogaaday in taxanaha ugu dheer ee wiilal ama gabdho isku xiga uu ahaa 17, wuxuuna go'aamiyay in taxanayaasha dhaadheer ay ka dhif badan yihiin inta nasiibku oggol yahay, sidaas darteed taxane wuxuu ka dhigaa natiijada kale mid ka itimaal badan. Nasiibka keligiis ayaa si kale u sheega: 196,608 dhalasho gudahood taxane 17 ama ka badan ah wuxuu soo muuqdaa qiyaastii afar jeer shantiiba. Marbe wuxuu helay sida saxda ah ee taxane nasiib ahi u eg yahay. Epstein (2013) ayaa kiiska dib u sheegay; Itimaalka Taxanayaasha ee Roulette ayaa bixiya nooca roulette-ka.
Meesha khaladku aanu khuseyn
Haddii giraangirtu jir ahaan eex lahaan lahayd, wareegyadii hore waxay noqon lahaayeen kuwo xog leh, sababtoo ah waxay caddeyn u noqon lahaayeen godadka halkii nasiibka. Taasi waa mawduuca Shaybaarka Roulette, waxayna u baahan tahay kumanaan wareeg oo ka yimid hal giraangir oo la aqoonsaday si wax loo sheego. Taxane toban casaan ah oo giraangir aan la aqoon ah, sharraxaadda eexdu aad bay uga itimaal yar tahay ta nasiibka.
Su'aalo
Maya. Wuxuu khuseeyaa dhacdo kasta oo madaxbannaan oo soo noqnoqota: laadhka, qadaadiicda, lambarrada bakhtiyaanasiibka.
Saamiyadu way isu soo dhowaan doonaan. Natiijadaadu weli waxay noqon doontaa qiyaastii −2.70% waxa aad sharadsatay.
Ma jiro sharci celcelisyo. Waxaa jira sharciga tirooyinka waaweyn, wuxuuna ku shaqeeyaa khafiifin.
Madadaalo Xisaabeed
Marka hore adigu isku day. Xal kasta waa qarsoon yahay; fur marka aad diyaar u tahay.
10 tuur kadib qadaadiic ayaa muujisa 7 madax iyo 3 dabo. 1,000 tuur kadib waxay muujisaa 517 madax iyo 483 dabo. Dabadu ma soo gaartay?
Muuji xalka
Jawaab Maya. Farqigu wuxuu ka koray 4 ilaa 34. Saamiga oo keliya ayaa u soo dhowaaday siman.
Saamiga madaxa iyo dabada wuxuu ka dhacay 7/3, qiyaastii 2.33, ilaa 517/483, qiyaastii 1.07. Taasi waa sharciga tirooyinka waaweynxisaabSharciga tirooyinka waaweynCelceliska natiijooyinka madaxbannaan wuxuu u soo dhowaadaa qiimaha la filayo marka tirada tijaabooyinku korodho.Akhri dhammaan → oo shaqeynaya.
Farqiga u dhexeeya wuu koray, 4 ilaa 34. Qadaadiic caddaalad ah, farqi qiyaastii 30 ah 1,000 tuur kadib waa caadi: farqiga caadiga ahi wuxuu qiyaas ahaan u koraa sida xididka labajibbaarka ee tirada tuurista, halka saamigu u dego dhanka 1.
Waxba dabada dib uma soo jiidin. Badnaanshihii hore ee madaxa waxaa qasay 990-ka tuur ee xigay, lama sixin.
Qadaadiic tuur afar jeer oo eeg oo keliya tuurista si toos ah madax u xigta. Qeybtee ka mid ah kuwaas ayaa madax ah? U xisaabi mid kasta oo ka mid ah 16-ka taxane ee suurtagalka ah, kadibna qaado celceliska qaybaha. Ma 50% baa?
Muuji xalka
Jawaab Maya. Waa 17/42, qiyaastii 40.5%. Sidan marka loo eego, qadaadiic caddaalad ah waxay u muuqataa inay qaboobayso madax kadib.
Qor 16-ka taxane. Laba ka mid ah, TTTT iyo TTTH, madax kuma laha saddexda tuur ee ugu horreeya, sidaa darteed waxba madax ma xigaan; taasi waxay reebaysaa 14.
Mid kasta, qaado tuurista madax xigta oo hel qaybta madaxa ah. HHHH waxay bixisaa 3 ka mid ah 3. HHHT waxay bixisaa 2 ka mid ah 3. HTHT waxay bixisaa 0 ka mid ah 2. Marka la dhex maro dhammaan 14-ka: lix taxane waxay bixiyaan 0, afar waxay bixiyaan 1/2, mid wuxuu bixiyaa 2/3, saddexna waxay bixiyaan 1 (HHHH, THHH iyo TTHH).
Isku dar qaybaha: 4 × 1/2 + 2/3 + 3 = 17/3. U qaybi 14: 17/42 ≈ 40.5%.
Tuur kasta dabada uma janjeedho; mid kastaa waa 50–50. Janjeeradu waxay ka timaadaa celcelinta taxane taxane: taxane madax ka buuxo wuxuu leeyahay tuurro badan oo la eego laakiin hal mar ayuu tirsadaa, sida taxane leh hal mid oo keliya. Miller iyo Sanjurjo (2018) waxay muujiyeen in daraasaddii gacanta kulul ee 1985 ay ciyaartoydeedii kubbadda koleyga sidan ku cabbirtay, sidaa darteed ciyaartoy u muuqday inaysan ka taxane badnayn fursadda dhab ahaantii waxay ahaayeen xoogaa taxane badan.
Kaftan yar
Khafiifin, ma aha sixid. Giraangirtu waxba kuma laha.
Ilaha
- 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.”