Lexrafa: tastratijit n rulit i yettrebḥen yal tikkelt
«Sɛiɣ anagraw i yettarbaḥen 80% n wakud.» Yezmer. Maca yettxesser idrimen.
Anagraw yezmer ad yerr tiɣimiyin n rrbeḥ d tid yettwafen s waṭas. Ur yezmir ara ad yerr azal yettwaṛǧan sennig n yilem, acku yal rrehn i yessersa d −1/37 n udrim-is, yerna azalen yettwaṛǧan ttwarnan. Inagrawen i yettarbaḥen s waṭas d wid i yettxesren aṭas mi ara xesren.
Ayen i d-yettwanna
Amenzay: deg kra n umkan tella tastratijit n rulit i yettarbaḥen yal tikkelt, anagraw n rrhun yettbeddilen ɣef leḥsab n yigmaḍ yezrin i yettarran rulit d urar n rrbeḥ. Abeggen i d-ttawin: azrar n tɣimiyin n rrbeḥ, avidyu ɣef wamek ara terbḥem deg rulit yal tikkelt, awal n yiwen i t-yeɛreḍen, tafelwit n yiwet n ddurt n zzher. Ayen i d-yettwanna s umata d tidet ɣer win i t-id-yennan; yettamen yis-s acku yeteddu alamma d tura.
Ayɣer d tuccḍa, s yiwet n tefyirt
Azalen yettwaṛǧantusnaktAzal yettwaṛǧanAlemmas n ugmuḍ n yal rrehn deg uɣawas aɣezfan. −1/37 n rrehn i yal rrehn amagnu awrupi.Ɣer akk → ttwarnan. Ma yella yal rrehn yesɛa EV = −1/37 n udrim-is, rrhun yemḍafaren, akken ma llan, sɛan EV = −1/37 n wayen akk yettwarehnen, akken yebɣu yili ulugen i yefran rrhun. Anagraw d alugen n ufran n rrhun. Ihi yal anagraw yesɛa EV = −1/37 n umḍan n rrhun meṛṛaidrimenAmḍan n rrhun meṛṛaTamerna n yidrimen yettwarhen deg yiwet n tɣimit neɣ deg yiwen wakud, s rrbeḥ i yettuɣalen yettwarhen. Daɣen: handle, action.Ɣer akk →. Wagi d alugen n tusnakt (Doob d Halmos sbeggnen-t deg yiseggasen n 1930; Thorp 1969 yenna-d tiwtilin), ur yesɛi ara ayen yeffɣen fell-as i yilugan yettḥerfin. Yiwet kan n twtilt i ilaqen ad tettwassen d talast tadday n rrehn: amedya n Thorp yettrehin $1 000 ɣef uzeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk →, sakin 90 n ssentimat, sakin 9 n ssentimat, akka ar taggara, yettenqas werǧin yeḥbes. S taprubabilit n 18/37 rrehn amezwaru yerbeḥ, amurar yeqqim s rrbeḥ i lebda, ɣas ma agmuḍ yettwaṛǧan yeqqim d −1/37 n wayen akk yettwarehnen. Talast tadday n ṭṭabla n tidet tessbedd ayagi, yerna yid-s yal asirem n uqqimi s rrbeḥ deg uɣawas aɣezfan.
Amlili deg uɣawas aɣezfan: alugen n wuṭṭunen imeqqranen deg rulit
Ayɣer yettban yeteddu
AsnernitastratijitAnagraw n usnerniYal alugen i yettbeddilen rrehn ɣef leḥsab n yigmaḍ yezrin. Asnerni deffir lexsara yessali-t deffir lexsara, asnerni deffir rrbeḥ deffir rrbeḥ.Ɣer akk → deffir lexsara yettarra tiɣimiyin n rrbeḥ d tid yettwafen s waṭas. MartingaletastratijitMartingaleAnagraw n usnerni i yessneggmen rrehn deffir yal lexsara. Walit taggayt n tstratijit i wayen i yettxemmem d wayen ur yettxemmim ara.Ɣer akk → seg $10 s talast n $500 tettfakk qrib 80% n tɣimiyin n 100 n tuzzyiwin s rrbeḥ n kra n yiferdisenidrimenAferdisRrehn agejdan s wacu i yettxeddem unagraw neɣ amurar. Inagrawen n usnerni ttwaglamen s yiferdisen akken ad ilin i yal ṭṭabla.Ɣer akk →. Amurar i tt-yesseqdacen ɛecrin n tɣimiyin yettarbaḥ seṭṭac seg-sent, yettmekti ayagi. Ukkuẓ n tɣimiyin yexsren, yal yiwet texser ugar n wayen rebḥent mraw n tɣimiyin n rrbeḥ, yerna leḥsab n ɛecrin n tɣimiyin ddaw n yilem. Anagraw ur ibeddel ara alemmas; yessenqel lexsarat ɣer kra n tɣimiyin timeqqranin anda yishel ad tent-isemmi yiwen zzher n diri.
Akayad i yezmer yal yiwen ad t-yexdem
Asimulatur n tistratijiyin deg usmel-a yesselkam 10 000 n tɣimiyin n yal anagraw, neɣ n tengalt-nwen, deg yiwet n tsint. Sbeddet-t ɣef unagraw ideg tettamnem, ɣret alemmas. Lukan alemmas sennig n yilem i kra n uɣewwar, asebter-a ad t-yini. Yal aɣewwar, yal anagraw, yal talast n ṭṭablaṭṭablaTalast n ṭṭablaRrehn adday d rrehn afellay i yettwasirgen. Talast tafellayt d ayen i yeḥebsen inagrawen n usnegmu.Ɣer akk → ttaken alemmas n −2,70% n umḍan n rrhun meṛṛa rnu ahuzzu n tegnit. Awalen n yimdanen d tigrummiwin n yiwen; asimulatur d tigrummiwin n mraw igiman.
Anagraw ur nezmir ad yexser
Deg 1997, amaru n poker Mike Caro yessufeɣ-d anagraw n rulit akken ad yesseḍsu, Gambling Times tɛawed tessufeɣ-it deg 2001. D amuɣ n rrhun ara yettwaǧǧan: werǧin azeggaɣ neɣ aberkanrrehnAberkanRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen iberkanen. S tefransist: noir.Ɣer akk →, aryan neɣ uyug, neɣ ilmawenaḍebsiIlemTaxxamt 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 →; ulac uṭṭunen izeggaɣen iryanen, ulac uṭṭunen iberkanen iyugen; ulac acemma ɣef 30, neɣ ɣef wazrar aɣezfan n texxaminibenkanTaxxamtYiwet seg 37 n texxamin s wuṭṭunen ɣef uqerru yettezzin. Daɣen: slot, cup.Ɣer akk → seg 11 deg unezwer n temrilt alamma d 14 ɣef uḍebsi amarikani. Sdukklet ilugan, ur d-yeqqim ula d yiwen wuṭṭun. Tixxamin kan yellan beṛṛa n wazrar-nni d 0, 28, 9, 26, 30 d 2; 30 yettwagdel s yisem-is, wiyaḍ d ilem, d uyug d aberkan, neɣ d aryan d azeggaɣ. Amurar ara yeḍfren anagraw-a werǧin yettrehin, werǧin yettxesser. Lmaziyya-s d ilem, yerna d anagraw n rulit yiwen kan i d-yeqqaren tidet ɣef wamek i d-yettaweḍ.
Inagrawen s yismawen, yiwet n tefyirt i yal yiwen
Inagrawen i ttzenzen s yisem, neɣ am tsemselt n rrbeḥ n rulit, ur mgaraden ara. Yal yiwen d agraw n rrhun, yal rrehn ixelleṣ i uḍebsi 2,70%-ines. Bollman (2024) yessefhem kra seg-sen i uḍebsi amarikani, anda yal yiwen yettkellif 5,26%; da, ɣef uḍebsi awrupi.
Tidet
Inagrawen ttbeddilen udem n teɣimit: acḥal i terebḥem, acḥal meqqren yirbaḥen, acḥal i yella diri wayen n diri akk. D ifranen n tidet, yerna amurar yezmer ad yesmenyef yiwen n udem ɣef wayeḍ. Ayen ur ttbeddilen ara yinagrawen d ssuma, d 2,70% n wayen akk yettwarehnen, yerna acku inagrawen n usnerni rehhnen ugar n rrehn ur nettbeddiltastratijitRrehn ur nettbeddilRrehn n yiwen wazal deg yal tuzzya. D aswir ɣer wacu i yettwaserwas yal anagraw n usnerni.Ɣer akk →, xelleṣen ugar seg-s.
Isteqsiyen
Sḍis n wagguren n tɣimiyin yal ddurt d qrib 25 n tɣimiyin. Martingale tettarbaḥ 80% seg-sent. Tiɣimiyin yexsren ad d-asent, yerna d timeqqranin.
Alugen n usbeddi yessenqas amḍan n rrhun meṛṛa, ihi yessenqas lexsara yettwaṛǧantusnaktLexsara yettwaṛǧanAzal yettwaṛǧan seg tmerna n yidrimen yettwarhen; d alemmas n wayen yettwaxsar deg yiwet n tɣimit neɣ deg yiwen wakud.Ɣer akk →. Ur tt-yettarra ara sennig n yilem.
Mačči ɣef uḍebsi imsawi. Ɣef uḍebsi s umyaltanaritAḍebsi s umyalAḍebsi i deg ara xedmen yixeṣṣaṣen-is n lǧessa kra n texxamin ad d-ffɣent ugar n 1/37. D ayen yettwaxeṣṣren, ur yettwaf ara ala s yigiman n tuzzyiwin yettwarun.Ɣer akk →, d ugur n tfizikt wagi, mačči d anagraw.
Urar s tusnakt
Ɛerḍet-tent s yiman-nwen qbel. Yal tifrat tettwaffer; ldit-tt mi ara tilim twejdem.
Anagraw n taḍsa n Mike Caro n 1997 i uḍebsi amarikani yegdel azeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk → d uberkanrrehnAberkanRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen iberkanen. S tefransist: noir.Ɣer akk →, aryan d uyug, d 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 →; uṭṭunen iryanen izeggaɣen d uṭṭunen iyugen iberkanen; uṭṭun 30; d yal taxxamtibenkanTaxxamtYiwet seg 37 n texxamin s wuṭṭunen ɣef uqerru yettezzin. Daɣen: slot, cup.Ɣer akk → deg ubrid seg 11, s tnila n yisegnan n temrilt, ar 14. Seqdecet ilugan yiwen yiwen. Anwi wuṭṭunen i d-yeqqimen i rrehn?
Sken-d tifrat
Tiririt Ulac. Anagraw werǧin yettrehin, ihi lmaziyya-s d ilem s tidet.
Agdel n uzeggaɣ, uberkan, uryan, uyug d yilmawen yeǧǧa uṭṭunen iman-nsen d yigrawen imecṭaḥ seg 1 ar 36.
Ulac iryanen izeggaɣen, ulac iyugen iberkanen: qqimen iyugen izeggaɣen (12, 14, 16, 18, 30, 32, 34, 36) d iryanen iberkanen (11, 13, 15, 17, 29, 31, 33, 35): sṭac n wuṭṭunen. Agdel n 30 yeǧǧa xmesṭac.
Ɣef uḍebsi amarikani, abrid seg 11 s tnila n yisegnan n temrilt ar 14 iḍebber 32 seg 38 n texxamin. Sḍis-nni yellan beṛṛa-s d 0, 28, 9, 26, 30 d 2. Xmesṭac-nni yeqqimen llan akk daxel n ubrid, ihi alugen aneggaru yekkes-iten daɣen. Anagraw ur nettrehin ara d netta kan i ur nettexsar ara, d ayagi i yebɣa ad d-yini Caro.
Kryptos yesselkam kraḍ n MartingaletastratijitMartingaleAnagraw n usnerni i yessneggmen rrehn deffir yal lexsara. Walit taggayt n tstratijit i wayen i yettxemmem d wayen ur yettxemmim ara.Ɣer akk → deg yiwet n tikkelt, yiwen ɣef yal tayuga n rrhun s lexlaṣ imsawirrehnRrehn s lexlaṣ imsawiAzeggaɣ/aberkan, aryan/uyug, afellay/adday. 18 n wuṭṭunen, ixelleṣ 1:1.Ɣer akk → (afellay neɣ adday, aryan neɣ uyug, azeggaɣ neɣ aberkan), s rrhun 1, 2, 4, 8, 16, 32 d uḥbas deffir sḍis n lexsarat. Ṭṭfet yiwen seg kraḍ-nni ɣef uḍebsi awrupi. Acḥal n tikkal i yexser sḍis-nni n rrhun, acḥal i yettawi yiwet n tunnḍa s ulemmas, d acḥal i d tasgunt-a seg yedrimen yettwarehnen?
Sken-d tifrat
Tiririt Yexser sḍis-nni qrib yiwet n tikkelt deg 55 n tunnḍiwin, 1,83% n wakud, u ayagi yetteklif 63 n yiferdisenidrimenAferdisRrehn agejdan s wacu i yettxeddem unagraw neɣ amurar. Inagrawen n usnerni ttwaglamen s yiferdisen akken ad ilin i yal ṭṭabla.Ɣer akk →. S ulemmas, tunnḍa texser qrib 0,17 n uferdis seg 6,42 n yiferdisen yettwarehnen: 2,70%, ssuma n yal rrehn ɣef uḍebsi.
Rrehn yexser s tprubabilit n 19/37, s yilem. Sḍis ṭṭafaren: (19/37)⁶ = 0,0183, qrib 1 seg 55, syin rrhun 1 + 2 + 4 + 8 + 16 + 32 = 63 ruḥen. Ma ulac, tunnḍa tekfa s rrbeḥ d +1 n uferdis.
Alemmas: 1 × (1 − 0,0183) − 63 × 0,0183 = 1 − 64 × 0,0183 = −0,17 n uferdis.
Idrimen yettwarehnen: rrehn amezwaru yettwasers yal tikkelt, wis sin deffir lexsara kan, akka akka: 1 + 2 × (19/37) + 4 × (19/37)² + … + 32 × (19/37)⁵ = 6,42 n yiferdisen. U −0,17/6,42 = −2,70%.
Sḍis-nni n tuzzyiwin yettwarun sbadunt kan anta tama i yal rrehn, u aḍebsi ur yezmir ara ad ten-yissin. Aselkem n kraḍ-nni yessnernay s kraḍ idrimen yettwarehnen d lexsara talemmast yid-sen. Bollman (2024) yexdem anagraw ɣef uḍebsi amarikani, anda yal yiwen seg-sen yexser sḍis ṭṭafaren 2,1% n wakud.
Taḍsa i usgunfu
Rrbeḥ s waṭas d rrbeḥ n yedrimen d imḍanen yemgaraden.
Iɣbula
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Doob, J. L. “Note on probability.”
- Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.”
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed.