Tuccḍa n umqemmer
Amenzay belli agmuḍ «yewweḍ-d wakud-is» acku ur d-yettban ara kra n wakud.
Deffir mraw n uzeggaɣ, taprubabilit n uberkan teqqim 18/37. Aḍebsi ur yettaru acemma, ur yettrus ula d ttlaba.
Tuccḍa
Ma yella uzeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk → yeffeɣ-d mraw n tikkal, aṭas n yimuraren ttḥulfun belli aberkanrrehnAberkanRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen iberkanen. S tefransist: noir.Ɣer akk → «yewweḍ-d wakud-is», ttrehinen fell-as. Wiyaḍ ttḥulfun belli azeggaɣ «yeḥma», ttrehinen fell-as. Akk ttxemmimen seg wazrar yekfan yakan ɣer tuzzya ur neḍri ara. TakurtibenkanTakurtTakurt tamecṭuḥt i yettwaḍeqqren deg ubrid mgal aqerru yettezzin. Tikurin n tura d ivorine neɣ d Teflon, 18–21 mm.Ɣer akk → ur teẓri ara anta-tent mraw n tuzzyiwin ineggura; tixxaminibenkanTaxxamtYiwet seg 37 n texxamin s wuṭṭunen ɣef uqerru yettezzin. Daɣen: slot, cup.Ɣer akk → sɛant yiwet n tiddi am yiwet n tsaɛett aya; taprubabilittusnaktTaprubabilitAzal n yiwen ugmuḍ ad d-yeḍru, seg 0 ɣer 1 neɣ seg 0% ɣer 100%. Yiwen wuṭṭun: 1/37 = 2,70%.Ɣer akk → n uberkan d 18/37 am yal tikkelt.
Ayɣer yettban d tidet
Deg uɣawas aɣezfan, tifesniwin n uzeggaɣ d uberkan qerrbent s tidet ɣer 18/37 yal yiwet. Alugen n wuṭṭunen imeqqranentusnaktAlugen n wuṭṭunen imeqqranenAlemmas n yigmaḍ imanayen yettqerrib ɣer wazal yettwaṛǧan mi ara yettimɣur umḍan n tirmitin.Ɣer akk → yeḍmen ayagi. Maca aqerreb yeḍṛu s usfesi, mačči s useɣti: deffir 1 000 n tuzzyiwin nniḍen, mraw-nni n uzeggaɣ ugar d tuccḍa n useẓḍi deg tfesna, mačči acku aberkan yuɣal-d, maca acku tagrumma temɣer. Ulac tamacint i yettarran aberkan s taprubabilit meqqren, yerna alugen n wuṭṭunen imeqqranen ur yesra ara yiwet.
Monte Carlo, 18 ɣuct 1913
Aberkan yeffeɣ-d 26 n tikkal yeṭṭafaren ɣef yiwet n ṭṭabla deg Casino de Monte-Carlo. Seg qrib aberkan wis xmesṭac, imuraren ɣlin ɣef uzeggaɣ, s sin d s sin tikkelt nniḍen, yal tuzzya «teṣḥa ugar» n tin yezrin. Lkazinu terbeḥ imelyunen n yifranken. Azrar-nni yesɛa taprubabilit n 1 seg 137 n yimelyunen seg uberkan amezwaru, yerna taprubabilit ad yeḍru ɣer taggara deg kra n umkan deg lkazinu n umaḍal tella qrib d yiwen. D wagi i d sebba i yettusemman tuccḍa n umqemmer daɣen tuccḍa n Monte Carlo.
Ulac ayen yesweḥcen. Yeḍṛu yiwet n tikkelt seg 44.
Imuraren bdan ttwalin. Azeggaɣ «yewweḍ-d wakud-is».
Ṭṭabla teččur. Rrhun ɣef uzeggaɣ ttnernin s sin deffir yal lexsara.
Aṭas n yedrimen i yexsren. Yal aberkan amaynut yettarra azeggaɣ yettban d aṣeḥḥan ugar.
Azrar yekfa. Lkazinu terbeḥ imelyunen n yifranken seg yimdanen i yettrehinen mgal wazrar ur nezmir ad «yeẓer» belli d azrar.
Afus yeḥman
Rrehn ɣef yini acku yella deg wazrar d yiwet n tuccḍa yettwaqelben: ttraǧun azrar ad ikemmel deg umkan ad yekfu. Imussnawen n tasnilest semman-as afus yeḥmanlexrafaAfus yeḥmanTaɛqidt dakken azrar n rrbeḥ, neɣ n yiwen ugmuḍ, ad yerr wayeḍ ad d-yeffeɣ ugar. Ɣef uḍebsi, d tuccḍa n umqemmer yettwaqelben.Ɣer akk →, seg yiwet n tezrawt n 1985 n Gilovich, Vallone d Tversky i yettnadin izrar deg uḍeggeṛ n basketball, ur d-ufin acemma ugar n zzher. Deg 2018 Miller d Sanjurjo sbeggnen belli akayad s timmad-is yemyal: deg usekles awezlan, amur n tuṭṭfiwin deffir tuṭṭfa yettas-d ddaw tafesna tamatut n uḍeggaṛ s ulemmas, ihi amurar war afus yeḥman akk yettban cwiṭ d asemmaḍ. Mi yettwaseɣti, isefka-nni s timmad-nsen sbeggnen-d afus yeḥman amecṭuḥ. Amdan yezmer ad yeḥmu; aḍebsi ulac ɣur-s lḥala. Kra n yimuraren ttamnen s snat n tmenziyin deg yiwet n tikkelt, belli azrar ikemmel alamma yuɣal «d aɣezfan aṭas» sakin ad yekfu. Ɣef uḍebsi imsawi, yal lqem yesɛa yiwen wazal yettwaṛǧantusnaktAzal yettwaṛǧanAlemmas n ugmuḍ n yal rrehn deg uɣawas aɣezfan. −1/37 n rrehn i yal rrehn amagnu awrupi.Ɣer akk → am ufran n yini s uḍeggeṛ n uṣurdi: −2,70% n udrim n rrehn.
Ɣef ṭṭabla n tidet
Croson d Sundali (2005) walan 18 n tsaɛtin n tvidyut n tɣellist n yiwet n ṭṭabla s sin yilmawenaḍebsiIlemTaxxamt tazegzawt tasuft ur yeṭṭif ula d yiwen n rrehn s lexlaṣ imsawi, n ddzina neɣ n tgejdit; d aɣbalu n lmaziyya n lkazinu. Daɣen: yiwen yilem, 0.Ɣer akk → deg lkazinu tameqqrant deg Reno: 139 n yimuraren i yessersen 24 131 n rrhun. Ɣef rrhun s lexlaṣ imsawirrehnRrehn s lexlaṣ imsawiAzeggaɣ/aberkan, aryan/uyug, afellay/adday. 18 n wuṭṭunen, ixelleṣ 1:1.Ɣer akk →, imuraren bḍan qrib s wazgen gar uḍfar n yizrar iwezlanen d umgal-nsen. Deffir semmus n yiwet n tewsit yeṭṭafaren, mlan ɣer umgal n wazrar, deffir sḍis neɣ ugar, 85% n rrhun-nsen llan ɣef tama nniḍen. Imuraren-nni s timmad-nsen sbeggnen-d afus yeḥman ɣef yiman-nsen: deffir rrbeḥ ɣef wuṭṭunen, ṭṭfen 13,6 n wuṭṭunen deg tuzzya d-iteddun s ulemmas, mgal 9,2 deffir lexsara. Aḍebsi-nsen ur d-yesskan ula d yiwet n tazmilt n umyal, ihi ayagi akk ur ibeddel ara ayen yezmer ad yettraǧu yal yiwen seg-sen.
Beṛṛa n lkazinu
Yiwen ujbad-a yettban-d anda ttwaṭṭfent tegrayin n tidet. Clotfelter d Cook (1993) ḍefren urar n wuṭṭunen n yal ass n Maryland: idrimen yettwarehnen ɣef wuṭṭun ṣubben aṭas mi kan yeffeɣ-d, ṭṭfen agguren akken ad d-uɣalen, ɣas akken tuffɣa ulac ɣur-s takatut. Chen, Moskowitz d Shue (2016) ufan-tt ɣer yimesnalen. Inezzarfiyen n usigez deg Marikan llan alamma d 3,3 n tfesniwin s taprubabilit meqqren ad gin taluft ma yella qeblen tin yezwaren. Inezzarfiyen n baseball llan 1,5 n tfesniwin s taprubabilit tamecṭuḥt ad inin strike deffir mi qqaren yiwen, ugar n sin n tikkal ɣef tiyitiwin iqerben. Deg tirmit deg wakal s yineɣlifen n ttlaba ixellṣen s ssuma yettwasbedden, alamma d 9% n tegrayin ttwaqelbent akka. Tiluɣa ttasent-d s umyizwer agacuran, ihi tagrayt taneggarut ur d-teqqar acemma ɣef tin d-iteddun, am tuzzya taneggarut ur d-teqqar acemma ɣef tin d-iteddun.
Tuccḍa tamettiwt n umqemmer
Amussnaw n tfelsafit Ian Hacking (1987) yessemma lqem wis kraḍ. Yiwen yekcem ɣer tzeqqa, iwala sin n zzhaṛ ɣlin s sḍis d sḍis, yenna-d belli ttwaḍeggren aṭas n tikkal yakan. Yal aḍeggeṛ yesɛa yiwet n taprubabilit ad yili sḍis d sḍis, amezwaru n tmeddit neɣ wis agim, ihi tamuɣli ur d-teqqar acemma ɣef acḥal aya i yebda wurar. Deg rulit d amurar i d-yewwḍen ɣer tfelwit i yesskanayen tam n uzeggaɣ yenna-d belli ṭṭabla ilaq tezzi tisaɛtin akken ad ten-id-tessufeɣ. Tuccḍa tamagnut teqqar ayen yezrin deg tuzzya d-iteddun; tagi teqqar tamuɣli yettwafen qlil deg wayen yezrin ur yiwala yiwen.
Amussnaw n tasnilest i yumnen yis-s
Tuccḍa-a tesɛa imeḥḥaḍen imusnawen. Amussnaw n tasnilest Amalman Karl Marbe yesmuqel ukkuẓ n yiseklasen n 49 152 n tlalit yal yiwen, yufa-d belli azrar aɣezfan akk n yiqcicen neɣ n teqcicin yeṭṭafaren d 17, yenna-d belli izrar iɣezfanen ttwafen qlil ugar n wayen yeqqar zzher, ihi azrar yettarra agmuḍ nniḍen s taprubabilit meqqren. Zzher s yiman-is yeqqar ayen nniḍen: deg 196 608 n tlalit, azrar n 17 neɣ ugar yettban-d qrib ukkuẓ n tikkal seg semmus. Marbe yufa-d ayen kan i d udem n yigmaḍ igacuranen yemḍafaren. Epstein (2013) yɛawed-d taqsiḍt; Taprubabilit n yizrar deg rulit tefka-d lqem n rulit.
Anida ur tettwasnas ara tuccḍa
Lukan aḍebsi yemyal s tfizikt, tuzzyiwin yezrin ad sɛunt azal, acku ad ilint d abeggen ɣef texxamin, mačči ɣef zzher. D asentel n Tanarit, yerna yesra igiman n tuzzyiwin seg yiwen uḍebsi yettwassnen akken ad d-yini kra. I wazrar n mraw n uzeggaɣ ɣef uḍebsi ur nettwassen ara, asefhem s umyal yesɛa taprubabilit drus aṭas n win s zzher.
Isteqsiyen
Ala. Tettwasnas ɣef yal aneḍru amanay yettuɛawaden: zzhaṛ, iṣurdiyen, uṭṭunen n lotri.
Tifesniwin ad qerrbent. Agmuḍ-nwen ad yeqqim qrib −2,70% n wayen i terehnem.
Ulac alugen n yilemmasen. Yella walugen n wuṭṭunen imeqqranen, yerna yetteddu s usfesi.
Urar s tusnakt
Ɛerḍet-tent s yiman-nwen qbel. Yal tifrat tettwaffer; ldit-tt mi ara tilim twejdem.
Deffir 10 n tegrin, aṣurdi yesskan-d 7 n wudmawen d 3 n tɣiltin. Deffir 1 000 n tegrin, yesskan-d 517 n wudmawen d 483 n tɣiltin. Tiɣiltin ṭṭfent-d deg-sen?
Sken-d tifrat
Tiririt Ala. Amgired yemɣer seg 4 ar 34. D assaɣ kan i yqerben ɣer umsawi.
Assaɣ n wudmawen ɣef tɣiltin yeɣli seg 7/3, qrib 2,33, ar 517/483, qrib 1,07. D alugen n wuṭṭunen imeqqranentusnaktAlugen n wuṭṭunen imeqqranenAlemmas n yigmaḍ imanayen yettqerrib ɣer wazal yettwaṛǧan mi ara yettimɣur umḍan n tirmitin.Ɣer akk → i yettxeddmen.
Amgired gar-asen yemɣer, seg 4 ar 34. S uṣurdi imsawi, amgired n qrib 30 deffir 1 000 n tegrin d ayen n yal ass: amgired amagnu yettimɣur qrib am uẓar amkuẓ n umḍan n tegrin, ma d assaɣ yerseḥ ɣer 1.
Ulac ayen i d-yerran tiɣiltin. Udmawen i d-yugaren di tazwara ttwaxelḍen deg 990-nni n tegrin d-iteddun, ur ttwaseɣten ara.
Ḍeqqret aṣurdi ukkuẓ n tikkal u walit kan tigrin i d-yeddan deffir wudem. Acḥal seg-sent d udmawen? Ḥesbet-tt i yal yiwet seg 16 n yimyizwaren i yezmren ad ilint u ṭṭfet alemmas n tesgunin. D 50%?
Sken-d tifrat
Tiririt Ala. D 17/42, qrib 40,5%. Ma twalam akka, aṣurdi imsawi yettban yesmeḍ deffir wudem.
Arut 16 n yimyizwaren (H d udem, T d tiɣilt). Snat seg-sent, TTTT d TTTH, ur sɛint ara udem deg kraḍ n tegrin timezwura, ihi ulac ayen i d-yeddan deffir wudem; qqimen 14.
Deg yal yiwet, ṭṭfet tigrin i d-yeddan deffir wudem u afet-d tasgunt n wudmawen. HHHH tettak-d 3 seg 3. HHHT tettak-d 2 seg 3. HTHT tettak-d 0 seg 2. Ma tɛeddam ɣef 14-nni meṛṛa: sḍis n yimyizwaren ttak-d 0, ukkuẓ ttak-d 1/2, yiwen yettak-d 2/3 u kraḍ ttak-d 1 (HHHH, THHH d TTHH).
Rnut tisgunin: 4 × 1/2 + 2/3 + 3 = 17/3. Bḍut ɣef 14: 17/42 ≈ 40,5%.
Ulac tigri i yesmenyafen tiɣilt; yal yiwet d 50–50. Amyal d-yekka seg walemmas n yal amyizwer weḥd-s: amyizwer yeččuren d udmawen yesɛa aṭas n tegrin ara twalim maca yettwaḥseb yiwet n tikkelt, am umyizwer s yiwen kan. Miller d Sanjurjo (2018) sseknen-d belli tazrawt n 1985 ɣef «afus yeḥman» tektal imuraren-is n basketball s tarrayt-a, ihi imuraren i yettbanen ur sɛin ara izrar ugar n zzher sɛan-ten s tidet cwiṭ ugar.
Taḍsa i usgunfu
Asfesi, mačči aseɣti. Aḍebsi ur yettrus acemma.
Iɣbula
- 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.”