Tusnakt n rulit · Ugur n tusnakt · 7 tsd

Ugur: snat n ddzinat d yiwen ujiṭun

Snat n ddzinat ṭṭfent 24 n wuṭṭunen. Rnut ajiṭun ɣef yilem, ad teṭṭfem 25. Leḍman-nni yettarbaḥ?

Tiririt tawezlant

Ala. Yal aḥric d −2,70% n udrim-is, ihi asemlili d −2,70% n wayen akk. Ugur yessefhem ayɣer, yeḥseb abeṭṭu s tidet, yesskan ayen ibeddlen (udem) d wayen ur nbeddel ara (ssuma).

snat n ddzinat
24/37 · ačuran +1 neɣ −2
rnu ilem
25/37 ttwaṭṭfen
EV i uferdis
−1/37 akken yebɣu yili
tamsirt
EV ttwarnan

Ugur

Tettrehinem $10 ɣef ddzinarrehnDdzina1–12, 13–24 neɣ 25–36, ixelleṣ 2:1.Ɣer akk → tamezwarut, $10 ɣef ddzina tis snat d $1 ɣef 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 →. (a) D acu i d igmaḍ yezmren d tiprubabiliyin-nsen? (b) D acu i d azal yettwaṛǧantusnaktAzal yettwaṛǧanAlemmas n ugmuḍ n yal rrehn deg uɣawas aɣezfan. −1/37 n rrehn i yal rrehn amagnu awrupi.Ɣer akk →? (c) AjiṭunidrimenAjiṭunTamatart i d-yemmalen azal yettwasbedden, yettwasersen ɣef tfelwit akken ad yili rrehn. Daɣen: check.Ɣer akk → n yilem yesselhay rrehn?

Tifrat (a) d (b)

Igmaḍ: takurtibenkanTakurtTakurt tamecṭuḥt i yettwaḍeqqren deg ubrid mgal aqerru yettezzin. Tikurin n tura d ivorine neɣ d Teflon, 18–21 mm.Ɣer akk → deg 1–24 (24 n texxaminibenkanTaxxamtYiwet seg 37 n texxamin s wuṭṭunen ɣef uqerru yettezzin. Daɣen: slot, cup.Ɣer akk →): yiwet n ddzina txelleṣ $20, tayeḍ texser $10, ilem yexser $1: ačuran +$9. Takurt deg 25–36 (12 n texxamin): snat n ddzinat xesrent, ilem yexser: −$21. Takurt ɣef yilem (1 n texxamt): ddzinat xesrent $20, ilem ixelleṣ $35: +$15. EV = (24 × 9 + 1 × 15 − 12 × 21)/37 = (216 + 15 − 252)/37 = −21/37 ≈ −$0,57 i tuzzya ɣef $21 yettwarehnen: 2,70%.

agmuḍtixxamintaprubabilitagmuḍ
1–242464,9%+$9
25–361232,4%−$21
012,7%+$15
yettwaṛǧan−$0,57 = 2,70% n $21

Tifrat (c)

War ajiṭun n yilem: (24 × 10 − 13 × 20)/37 = (240 − 260)/37 = −20/37 ≈ −$0,54 ɣef $20 yettwarehnen, daɣen 2,70%. Ajiṭun n yilem yerra agmuḍ n yilem n −$20 d +$15 (asnerni n $35 yiwet n tikkelt seg 37, s wazal n $0,95 i tuzzya) yekellef $1 deg 36 n tuzzyiwin nniḍen (s wazal n $0,97 i tuzzya). Abeddel ačuran: −$0,03 i tuzzya, d 2,70% n udular amernan. Leḍman yesɛa ssuma am kullec.

Ayɣer yettwasnas ɣef kullec

Azalen yettwaṛǧan ttwarnan. Yal agraw n rrhun deg yiwet n tikkelt yesɛa EV yegdan timernit n EV n yiḥricen, yal yiwen d −1/37 n udrim-is. Ihi yal asemlili d −1/37 n udrim akk n rrehn. Ulac aseggem n yijiṭunen ɣef tfelwit n rrhunibenkanTafelwit n rrhunAẓeṭṭa n rrhun yettwarun ɣef ṭṭabla. Daɣen: ṭṭabla, tajellabt, aceṭṭiḍ.Ɣer akk →, akken yebɣu yili umḍan-nsen, i yeffɣen i waya; afecku «Abennay n rrhun» ad t-yesbegen i yal agraw i tzemrem ad tessersem. Ayen ttbeddilen yisemlilen d abeṭṭu: acḥal i terebḥem, acḥal, d wacḥal n diri i yella wayen n diri akk.

Yiwen $21 s kraḍ n yiberdan: taprubabilit n rrbeḥ d wayen n diri akk
$21 ɣef uzeggaɣ: p(rrbeḥ)
48,6% · n diri akk −$21
snat n ddzinat + ilem: p(rrbeḥ)
67,6% · n diri akk −$21
$21 ɣef 17: p(rrbeḥ)
2,7% · n diri akk −$21
033,8067,6% · n diri akk −$21
Kraḍ yid-sen sɛan EV n −$0,57 i tuzzya. Mgaraden kan deg udem.

Ugur nniḍen iwɛer ugar

Afet-d asemlili n rrhun imagnuten i yeṭṭfen akk 37 n wuṭṭunen. Kraḍ n ddzinat ($10 yal yiwet) rnu $1 ɣef yilem: yal yiwen seg 1–36 yettak −$1 (yiwet n ddzina txelleṣ $20, snat nniḍen xesrent $20, ilem yexser $1), ilem yettak +$35 − $30 = +$5. EV = (36 × (−1) + 5)/37 = −31/37 ɣef $31 yettwarehnen: 2,70%. Tzemrem ad teḍmnem belli werǧin ad tweḥḥcem, maca ad txelṣem yiwet n ssuma ɣef lferḥ-a.

Tasemselt

EV(asemlili) = Σ EV(iḥricen) = −(adrim akk)/37

Isteqsiyen

Yella usemlili n rrhun s lmaziyya tamecṭuḥt ugar?

Ala, ɣef ṭṭabla tawrupit. Ɣef ṭṭabla tafransist, rrhun s lexlaṣ imsawirrehnRrehn s lexlaṣ imsawiAzeggaɣ/aberkan, aryan/uyug, afellay/adday. 18 n wuṭṭunen, ixelleṣ 1:1.Ɣer akk → weḥd-sen d 1,35%; asemlili s wayen nniḍen yessali lmaziyya yemxelḍen.

Ma d arhen ɣef uzeggaɣ d uberkan s tikkelt?

Yexser $1 i yal $1 ɣef yilem kan, ur yettarbaḥ acemma deg wayen nniḍen. EV −2,70% war ula d yiwen n lfayda: d asemlili yiwen kan ur nesɛi lmeɛna akk.

Ihi ayɣer ad nesdukkel rrhun?

Akken ad tfernem udem n teɣimit i tḥemmlem. D sebba yeṣḥan, d yiwet kan.

Taḍsa i usgunfu

Leḍman ɣef ṭṭabla n rulit yettkellif ayen i d-yessellek, ur yugar ur yenqis.

Leḍman ɣef ṭṭabla n rulit yettkellif ayen i d-yessellek, ur yugar ur yenqis.

Iɣbula

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Ixef 13, rulit.
yettwasenqed 2026-09-28tamudemt: tawrupit, yiwen yilemtarrayt ↗iɣbula ↗