Tusnakt n rulit · Aseqdec · 7 tsd

Azal yettwaṛǧan n rrhun s wawal

Voisins, tiers, orphelinsFR · tagzemtOrphelins«Igujilen»: tam n wuṭṭunen i d-yeqqimen deffir voisins d tiers: 17, 34, 6 d 1, 20, 14, 31, 9.Ɣer akk →, lǧiran d jeu zéro, yal yiwen yettwaḥseb alamma d −1/37-ines i yal ajiṭun.

Tiririt tawezlant

Rrhun s wawal d isemlilen n rrhun imagnuten s taẓayt ur nemsawa, ihi lexlaṣ-nsen yettbeddil s texxamtibenkanTaxxamtYiwet seg 37 n texxamin s wuṭṭunen ɣef uqerru yettezzin. Daɣen: slot, cup.Ɣer akk →. Yal yiwen yeqqim −2,70% n udrim akk n rrehn, acku azalen yettwaṛǧan ttwarnan. Asebter yesskan leḥsab i semmus-nni akk.

rrhun s wawal
5 imagnuten
ijiṭunen
4 ɣer 9
EV i yal ajiṭun
−1/37
lexlaṣ yettbeddil s texxamt
ih

Ayɣer ttbanen mgaraden

Yiwen wuṭṭunrrehnYiwen wuṭṭunYiwen wuṭṭun kan, ixelleṣ 35:1.Ɣer akk → yesɛa yiwen ugmuḍ i ixelleṣen. Voisins du zéroFR · tagzemtVoisins du zéro«Lǧiran n yilem»: sbeɛṭac n wuṭṭunen seg 22 ɣer 25 ɣef uḍebsi, s tẓa n yijiṭunen.Ɣer akk → yesɛa kraḍ n lexlaṣidrimenLexlaṣAyen i d-yettak rrehn i yerbḥen, yettwanna «X ɣef 1» nnig rrehn i d-yettuɣalen.Ɣer akk → yemgaraden ɣef leḥsab ma teɣli tkurtibenkanTakurtTakurt tamecṭuḥt i yettwaḍeqqren deg ubrid mgal aqerru yettezzin. Tikurin n tura d ivorine neɣ d Teflon, 18–21 mm.Ɣer akk → deg yizirigrrehnIzirigKraḍ n wuṭṭunen deg yiwen ujerriḍ n tfelwit, ixelleṣ 11:1. S tefransist: transversale.Ɣer akk → s snat n tẓayin, deg tɣemertrrehnTiɣmertUkkuẓ n wuṭṭunen yesɛan yiwet n tɣemert tamcerkt ɣef tfelwit, ixelleṣ 8:1.Ɣer akk → s snat n tẓayin neɣ deg yiwen n sin wuṭṭunenrrehnSin wuṭṭunenSin wuṭṭunen yemyuḍanen, ixelleṣ 17:1.Ɣer akk →. Tanawit-a teffer ayen ur nettbeddil: yal ajiṭunidrimenAjiṭunTamatart i d-yemmalen azal yettwasbedden, yettwasersen ɣef tfelwit akken ad yili rrehn. Daɣen: check.Ɣer akk → deg rrehn d rrehn am wiyaḍ s EV n −1/37 n yiman-is, yerna ayen akk d timernit.

Voisins du zéro (9 n yijiṭunen, 17 n wuṭṭunen)

2 ɣef 0-2-3 (izirig, ixelleṣ 11), 2 ɣef 25-26-28-29 (tiɣmert, txelleṣ 8), 1 ɣef yal yiwen seg sin wuṭṭunen 4-7, 12-15, 18-21, 19-22, 32-35 (xellṣen 17). Tuṭṭfa deg yizirig: +22 − 7 = +15. Tuṭṭfa deg tɣemert: +16 − 7 = +9. Tuṭṭfa ɣef sin wuṭṭunen: +17 − 8 = +9. Ulac tuṭṭfa: −9. EV = (3 × 15 + 4 × 9 + 10 × 9 − 20 × 9)/37 = (45 + 36 + 90 − 180)/37 = −9/37. Tẓa n yijiṭunen, −9/37: −1/37 i yal ajiṭun.

rrehn s wawalijiṭunenyeṭṭefigmaḍ (iferdisen ačuranen, tixxamin)EV (iferdisen)
Voisins du zéro917+15 × 3 · +9 × 14 · −9 × 20−9/37
Tiers du cylindre612+12 × 12 · −6 × 25−6/37
Orphelins (en cheval)58+31 × 2 · +13 × 6 · −5 × 29−5/37
Lǧiran (5)55+31 × 5 · −5 × 32−5/37
Jeu zéro47+32 × 1 · +14 × 6 · −4 × 30−4/37
Kraḍ n tgezmin akk yid-sent2037+15/+9/+12/+31/+13 s texxamt; werǧin ulac tuṭṭfa−20/37
Bḍut EV ɣef yijiṭunen, yal ajerriḍ d −1/37.

Tiers du cylindre (6 n yijiṭunen, 12 n wuṭṭunen)

Sḍis n rrhun ɣef sin wuṭṭunen, yal yiwen ixelleṣ 17. Yal tuṭṭfa: +17 − 5 = +12. Ulac tuṭṭfa: −6. EV = (12 × 12 − 25 × 6)/37 = (144 − 150)/37 = −6/37. Rrehn s wawalṭṭablaRrehn s wawalRrehn i yettwanan i ukrupi deg wadeg ad yettwasers s ufus, s umata d rrehn ɣef tegzemt n uḍebsi am voisins neɣ tiers. Daɣen «announced bet».Ɣer akk → yettɣimin akk: yiwen lexlaṣ, yiwet n lexsara.

Orphelins (5 n yijiṭunen, 8 n wuṭṭunen)

1 n yiwen wuṭṭun ɣef 1 (ixelleṣ 35), sin wuṭṭunen 6-9, 14-17, 17-20, 31-34 (xellṣen 17). Tuṭṭfa ɣef 1: +35 − 4 = +31. Tuṭṭfa ɣef 17 (sin n rrhun ɣef sin wuṭṭunen): +34 − 3 = +31. Tuṭṭfa ɣef 6, 9, 14, 20, 31, 34: +17 − 4 = +13. Ulac tuṭṭfa: −5. EV = (31 + 31 + 6 × 13 − 29 × 5)/37 = (62 + 78 − 145)/37 = −5/37.

Lǧiran d jeu zéro

LǧiranrrehnLǧiranYiwen wuṭṭun d snat n texxamin ɣef yal tama-s ɣef uḍebsi, semmus n yijiṭunen ɣef yiwen wuṭṭun.Ɣer akk →: semmus n rrhun ɣef yiwen wuṭṭun; yal tuṭṭfa +35 − 4 = +31; EV = (5 × 31 − 32 × 5)/37 = (155 − 160)/37 = −5/37. Jeu zéroFR · tagzemtJeu zéro«Urar n yilem»: sa n wuṭṭunen iqerben ugar ɣer yilem (12, 35, 3, 26, 0, 32, 15), s ukkuẓ n yijiṭunen.Ɣer akk →: sin wuṭṭunen 0-3, 12-15, 32-35 d yiwen wuṭṭun ɣef 26; tuṭṭfa ɣef 26: +35 − 3 = +32; tuṭṭfa ɣef sin wuṭṭunen: +17 − 3 = +14; EV = (32 + 6 × 14 − 30 × 4)/37 = (32 + 84 − 120)/37 = −4/37.

Taprubabilit n yal tuṭṭfa, rrhun s wawal% n tuzzyiwin
Jeu zéro (7)
18,9%
Lǧiran (5)
13,5%
Orphelins (8)
21,6%
Tiers (12)
32,4%
Voisins (17)
45,9%
Kraḍ akk (37)
100%
% n tuzzyiwin
050100%
Tuṭṭfa n kullec s 20 n yijiṭunen teḍmen agmuḍ gar −2 d +16 n yiferdisen d EV n −20/37. Aḍman-a yettkellif 2,70% am kullec.

Rrehn Jeu Zéro

Ɣef uḍebsi aliktruni

Roulette Evolution n IGT, akken i t-yeglem Bollman (2021), tettak rrhun-a s wawal ɣef uḍebsi aliktruni s yiwen yilemaḍebsiIlemTaxxamt 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 →. Leḥsab ur ibeddel ara: yal yiwen yeqqim −1/37 i yal ajiṭun. Ayen ibeddlen d ssebba kan i d-ttaken yimuraren i rrhun n tegzemtaḍebsiTagzemtAḥric n texxamin yemmeḍfaren ɣef uḍebsi, mačči d tagrumma ɣef tfelwit.Ɣer akk →. Ɣef ṭṭabla n tidet kra ttamnen belli zemren ad ɣren lɛadat n ukrupi d tazrit n tuzzya akken ad ɣilen tamnaḍt anda ara teɣli tkurt, ayen i wumi qqaren aktazal n uḍebsi, yerna rrehn s wawal d abrid agamay n urhen ɣef tmnaḍt. Aḍebsi aliktruni ulac ɣur-s akrupi ara teɣrem, yerna ssebba-nni, ur nǧhid ara ula ɣef ṭṭabla n tidet, iruḥ.

Ɣef uḍebsi aliktruni ulac akrupi ara teɣrem, yerna ssebba n urhen ɣef tmnaḍt n uḍebsi iruḥ yid-s.

Timacinin n rulit

Tasirt

Rrhun s wawal d asishel, mačči d tusnakt. D abrid yettɣawalen akk i urhen ɣef tegzemt n uḍebsi, d abrid kan i t-yexdmen s yiwen n wawal. Azal-nsen yettwaṛǧantusnaktAzal yettwaṛǧanAlemmas n ugmuḍ n yal rrehn deg uɣawas aɣezfan. −1/37 n rrehn i yal rrehn amagnu awrupi.Ɣer akk → d yiwen i yal ajiṭun am rrehn ɣef yiwen wuṭṭun amagnu akk, yerna tanawit n lexlaṣ d leḥsab kan, mačči d lmaziyya.

Tasemselt

EV(rrehn s wawal) = Σ EV(ijiṭunen) = −(ijiṭunen)/37
ačuran ma yeṭṭef = lexlaṣ ɣef yijiṭun(en) i yerbḥen − ijiṭunen yexsren

Isteqsiyen

Yella rrehn s wawal yifen wiyaḍ?

Ala. Yal yiwen d −1/37 i yal ajiṭun. Mgaraden deg tuṭṭfa d udem n lexlaṣ.

Ayɣer orphelins ixelleṣ +31 ɣef 17?

Sin n rrhun ɣef sin wuṭṭunen sɛan 17, ihi tuṭṭfa txelleṣ 17 s sin, texser kraḍ kan n yijiṭunen.

Ma rehneɣ voisins s 2 n yijiṭunen i yal amkan?

18 n yijiṭunen, yal lexlaṣ s sin, EV −18/37. Asnerni n teskala ur ibeddel acemma.

Urar s tusnakt

Ɛerḍet-tent s yiman-nwen qbel. Yal tifrat tettwaffer; ldit-tt mi ara tilim twejdem.

  1. Aḍebsi aliktruni yettak-d rrhun s wawalṭṭablaRrehn s wawalRrehn i yettwanan i ukrupi deg wadeg ad yettwasers s ufus, s umata d rrehn ɣef tegzemt n uḍebsi am voisins neɣ tiers. Daɣen «announced bet».Ɣer akk → ifransisen: tiers (6 n yijiṭunenidrimenAjiṭunTamatart i d-yemmalen azal yettwasbedden, yettwasersen ɣef tfelwit akken ad yili rrehn. Daɣen: check.Ɣer akk →), jeu zéroFR · tagzemtJeu zéro«Urar n yilem»: sa n wuṭṭunen iqerben ugar ɣer yilem (12, 35, 3, 26, 0, 32, 15), s ukkuẓ n yijiṭunen.Ɣer akk → (4), orphelinsFR · tagzemtOrphelins«Igujilen»: tam n wuṭṭunen i d-yeqqimen deffir voisins d tiers: 17, 34, 6 d 1, 20, 14, 31, 9.Ɣer akk → (5), voisins (9) d lǧiranrrehnLǧiranYiwen wuṭṭun d snat n texxamin ɣef yal tama-s ɣef uḍebsi, semmus n yijiṭunen ɣef yiwen wuṭṭun.Ɣer akk → (5). I yal yiwen, acḥal n tikkal i yettrebḥ kra, d acḥal i yetteklif?

    Sken-d tifrat

    Tiririt Yal yiwen yetteklif 2,70%. Rebḥen kra deg 12, 7, 8, 17 d 5 n tuzzyiwin seg 37.

    Ssuma d-tettak seg walugen n usebter-a: yal ajiṭun d rrehn amagnu yexsren 1/37 n yiman-is, u azal yettwaṛǧantusnaktAzal yettwaṛǧanAlemmas n ugmuḍ n yal rrehn deg uɣawas aɣezfan. −1/37 n rrehn i yal rrehn amagnu awrupi.Ɣer akk → yettemrennu.

    Taprubabilit n rrbeḥ n kra d amḍan n texxaminibenkanTaxxamtYiwet seg 37 n texxamin s wuṭṭunen ɣef uqerru yettezzin. Daɣen: slot, cup.Ɣer akk → i yeḍebber rrehn, seg 37. Tiers yeḍebber 12, jeu zéro 7, orphelins 8 d voisins 17. Lǧiran ḍebbren uṭṭun d snat n texxamin ɣef yal tama-s ɣef uḍebsi: 5.

    Bollman (2021) yeglem-d jeu zéro s ukkuẓ n yijiṭunen ɣef 26 deg wadeg n yiwen. Ayagi yerra-t d rrehn n 7 n yijiṭunen u ibeddel lexlaṣidrimenLexlaṣAyen i d-yettak rrehn i yerbḥen, yettwanna «X ɣef 1» nnig rrehn i d-yettuɣalen.Ɣer akk →-is, mačči ssuma-s: mazal 2,70%.

    rrehnijiṭunentixxamin yettwaḍebrenyerbeḥ kralmaziyya n lkazinu
    tiers61232,4%2,70%
    jeu zéro4718,9%2,70%
    orphelins5821,6%2,70%
    voisins91745,9%2,70%
    lǧiran5513,5%2,70%

Taḍsa i usgunfu

Tẓa n yijiṭunen, tẓa n tsebɛa u tlatin. Leḥsab d ijiṭunen.

Tẓa n yijiṭunen, tẓa n tsebɛa u tlatin. Leḥsab d ijiṭunen.

Iɣbula

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Ixef 13, rulit.
  2. Wykes, A. The Complete Illustrated Guide to Gambling. Doubleday, 1964.
  3. Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette. CRC Press, 2021. Ixef 2, rulit.
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