Lmaziyya n lkazinu deg rulit
Amur n yal rrehn i teṭṭef lkazinu s ulemmas.
Rulit tawrupit: 2,70% ɣef yal rrehn amagnu, acku lexlaṣ yettwaḥsab am wakken llant 36 n texxamin, maca llant 37.
Asuffeɣ
Assaɣ n lḥeqq i yiwen wuṭṭunrrehnYiwen wuṭṭunYiwen wuṭṭun kan, ixelleṣ 35:1.Ɣer akk → ad yili 36 ɣef 1, acku llan 36 n yiberdan n lexsara i yal abrid n rrbeḥ. Lkazinu txelleṣ 35 ɣef 1. AferdisidrimenAferdisRrehn agejdan s wacu i yettxeddem unagraw neɣ amurar. Inagrawen n usnerni ttwaglamen s yiferdisen akken ad ilin i yal ṭṭabla.Ɣer akk → ixuṣṣen, yettwabḍan ɣef 37 n yigmaḍ s yiwet n taprubabilit, d 1/37 = 2,70% n udrim n rrehn i yal tuzzya. Lexṣaṣ-a yettban-d deg yal lexlaṣidrimenLexlaṣAyen i d-yettak rrehn i yerbḥen, yettwanna «X ɣef 1» nnig rrehn i d-yettuɣalen.Ɣer akk → acku yal lexlaṣ yesseqdac alugen 36/n − 1: sin wuṭṭunenrrehnSin wuṭṭunenSin wuṭṭunen yemyuḍanen, ixelleṣ 17:1.Ɣer akk → xellṣen 17 deg umkan n 17,5, ddzinarrehnDdzina1–12, 13–24 neɣ 25–36, ixelleṣ 2:1.Ɣer akk → 2 deg umkan n 2,083, azeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk → 1 deg umkan n 1,056. Lexṣaṣ d 1/n n yiferdisen yal tikkelt i yal rrbeḥ, d n/37 n yirbaḥen i tuzzya, ihi yal tikkelt 1/37 i tuzzya.
Lmaziyya mgal ayen i d-teṭṭef lkazinu
Lmaziyya d lexsara yettwaṛǧantusnaktLexsara yettwaṛǧanAzal yettwaṛǧan seg tmerna n yidrimen yettwarhen; d alemmas n wayen yettwaxsar deg yiwet n tɣimit neɣ deg yiwen wakud.Ɣer akk → i yal aferdis yettwarehnen: 2,70% i tuzzya. Ayen i d-teṭṭef lkazinuidrimenAyen i d-teṭṭef lkazinu (hold)Aḥric seg yidrimen i d-ttawin yimuraren ɣer ṭṭabla i teṭṭef lkazinu s tidet. Yugar lmaziyya n lkazinu acku rrbeḥ yettuɣal yettwarhen.Ɣer akk → d ayen i teṭṭef s tidet lkazinu seg yedrimen i d-tewwim ɣer ṭṭabla, yerna yugar aṭas acku tɛawdem tettrehnem irbaḥen-nwen. Asɣi n yijiṭunenṭṭablaAsɣi n yijiṭunenAsenfel n yidrimen s yijiṭunen ɣef ṭṭabla. Yettili gar snat n tuzzyiwin, idrimen ttwasersen ɣef tfelwit, ur ttwafkan ara deg ufus n ukrupi.Ɣer akk → n $100 yettwarehnen $10 yal tikkelt deg 200 n tuzzyiwin yewweḍ amḍan n rrhun meṛṛa n $2 000, ixelleṣ qrib $54 n lmaziyya; ayen i d-teṭṭef lkazinu seg usɣi-nni d 54%. Lkazinu ttmeslayent ɣef wayen i d-ṭṭfent; imuraren ilaq ad xemmen s lmaziyya.
Ayɣer yal rrehn yesɛa yiwet n lmaziyya
D afran n tɣessa, mačči d tagnit. Alugen 36/n − 1 yettwasbedd deg lqern wis 18, ilem wis sintawsitSin yilmawenTaxxamt 00 n uḍebsi amarikani. Mi ara tili, lmaziyya n lkazinu tettali seg 2,70% ɣer 5,26%.Ɣer akk → yettwakkes sakin war ma ttwannalen lexlaṣ. Lukan lexlaṣ yella s lḥeqq i 37 n texxaminibenkanTaxxamtYiwet seg 37 n texxamin s wuṭṭunen ɣef uqerru yettezzin. Daɣen: slot, cup.Ɣer akk →, yiwen wuṭṭun ad ixelleṣ 36 ɣef 1, lkazinu ur tettili ɣur-s ula d rrbeḥ. Lmaziyya yettwasewḥden tesshal leḥsab: ulac rrehn n rulit d «rrehn n uɣyul» mgal wayeḍ, ala rrehn amarikani ɣef semmus n wuṭṭunen s 7,89%.
Ayen ur nelli d lmaziyya n rulit
Mačči d 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 lexsara n teɣimit; tugget n tɣimiyin tiwezlanin d tavaryanstusnaktTavaryansAktazal n wamek i d-ttwazzaren igmaḍ i tama n wazal yettwaṛǧan. Meqqret i rrehn ɣef yiwen wuṭṭun, meẓẓiyet i rrhun s lexlaṣ imsawi.Ɣer akk → i tent-yefran, yerna qrib 42% n tɣimiyin n 100 n tuzzyiwin s lexlaṣ imsawi ttfakkent s rrbeḥ. Mačči d ssuma i yal taɣimit; tettali d 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 →, ihi anagraw n usnernitastratijitAnagraw 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 → i yettrehinen ugar ixelleṣ ugar. Mačči d ayen tezmer ad tessfes tmudemt n rrhun, acku lmaziyyat n rrhun yellan deg yiwet n tikkelt ttwarnant s ufmiḍi n yedrimen-nsen.
S yedrimen
I yal $1 000 yettwarehnen, lexsara yettwaṛǧan d $27,03 deg rulit tawrupittawsitRulit tawrupitAḍebsi s yiwen yilem, 37 n texxamin, lmaziyya n lkazinu 2,70%. D tamudemt tagejdant n usmel-a.Ɣer akk →, $52,63 deg tmarikanit, $13,51 ɣef rrhun s lexlaṣ imsawirrehnRrehn s lexlaṣ imsawiAzeggaɣ/aberkan, aryan/uyug, afellay/adday. 18 n wuṭṭunen, ixelleṣ 1:1.Ɣer akk → s la partagealugenLa partageAlugen afransis: mi ara d-yeffeɣ yilem, azgen n rrehn s lexlaṣ imsawi yettuɣal-d. Yessenqas lmaziyya n lkazinu ɣef rrhun-a ɣer uzgen, d 1,35%.Ɣer akk →. Amurar n yal ass i yettrehinen $500 i tmeddit, snat n tikkal deg ddurt, i useggas, yewweḍ amḍan n rrhun meṛṛa n $52 000, ixelleṣ qrib $1 400 n lmaziyya ɣef uḍebsi awrupi. Amḍan-a d amecṭuḥ i yal tuzzya, ur yettḥebbis ara i yal aseggas.
I tuzzya neɣ i rrehn yettwafran
Qrib yal rrehn n rulit yettwafran s yiwet n tuzzya, ihi lmaziyya-s i tuzzya d lmaziyya-s i rrehn d yiwen umḍan. Rrehn i yezmren ad yili ur yerbiḥ ur yexsir, ad yeqqim ɣef tfelwit n rrhunibenkanTafelwit n rrhunAẓeṭṭa n rrhun yettwarun ɣef ṭṭabla. Daɣen: ṭṭabla, tajellabt, aceṭṭiḍ.Ɣer akk →, yesɛa sin. Rrehn azegzaw n Riverboat Roulette yeṭṭef 3 n wuṭṭunen n uḍebsi amarikani, yettarbaḥ s 2 ɣef 1 ma yella yiwen seg-sen yeffeɣ-d uqbel yiwen seg 8 n wuṭṭunen imellalen, ur yerbiḥ ur yexsir deg wayen nniḍen. I yal rrehn yettwafran yexser 2/11 n udrim n rrehn, 18,18%. I tuzzya yexser 2/38, 5,26%, acku s ulemmas rrehn yeqqim 38/11 n tuzzyiwin, qrib 3,5. Sin yimḍanen d tidet. Amḍan i tuzzya yesserwas rrehn d ṭṭabla akk, yesbadu ssuma n tsaɛett; amḍan i rrehn yettwafran yeqqar acḥal seg yal adrim n rrehn ara d-yuɣalen mi ara yettwafru rrehn ɣer taggara.
Mi ara tɣelleḍ lkazinu deg ssuma
Yal lmaziyya deg usebter-a d-tettas seg leḥsab i txeddem lkazinu s umata akken iwata. Tikwal, ala. Deg tuber 1994, Grand Casino deg Biloxi, Mississippi, tefka 80 ɣef 1 i kraḍ n zzhaṛ s tmernit n 4, kif kif i 17. Kraḍ n zzhaṛ ɣellin s 216 n yiberdan, 3 kan seg-sen i d-yettaken 4, ihi rrehn yerra-d 81 × 3/216 = 1,125 i yal aferdis yettwarehnen: lmaziyya n 12,5% i umurar. Imuraren walan-tt. Lkazinu texser qrib $180 000 deg yiwen wass, tmedel rrehn, tɛawed telli-t s 60 ɣef 1, ayen yettarran 3 n tegniwin-nni seg 216 d lmaziyya n 15,3% i lkazinu. Hunacek (2025), s ubder n Bollman, yeḥka-d taqsiḍt. Lexlaṣ amagnu n rulit d afessas aṭas akken ad yettwaɣlet akka; rrhun n tamarrehnRrehn n tamaRrehn nniḍen s lebɣi yeqqnen ɣer wurar agejdan, s umata ɣef yizrar, ɣef tedyant n ubunus neɣ ɣef jackpot. Qrib yal tikkelt ɣlay ugar n rrhun imagnuten.Ɣer akk →-ines ur nettwassen ara d anida yelha usenqed n leḥsab.
Rrhun n tama deg wuraren nniḍen n ṭṭabla
Bollman (2021) yessers rrhun igejdanen n blackjack, baccarat, craps d rulit ɣer tama n rrhun n tama yettwassnen ɣef yiwet n ṭṭabla. Deg kraḍ n wuraren imezwura, rrehn n tama yettkellif ugar n rrehn agejdan, s waṭas aṭas n tikkal ugar. Ayen yeffɣen i ulugen d urar aneggaru deg tfelwit: lmaziyya n rulit tamarikanittawsitRulit tamarikanitAḍebsi s 0 d 00, 38 n texxamin, lmaziyya n lkazinu 5,26%. Mačči d tamudemt tamezwarut n usmel-a.Ɣer akk → d 5,26% ɣef rrhun igejdanen, d tameqqrant akken rrehn n tama am Colors neɣ WINGO yezmer ad yerxes ugar.
Tasemselt
Isteqsiyen
Ala. D 2,70% n wayen i terehnem. Mi ara tɛawdem ad terhnem idrimen-nni, ad ttwarehnen tikkelt nniḍen.
Ala. D afmiḍi. Lexsara yettwaṛǧan s yidularen tettali d udrim n rrehn.
S lmaziyya, akk rrhun imagnuten iwrupiyen msawan; mgaraden kan deg acḥal i ttarbaḥen d wacḥal i xellṣen. S la partage, rrhun s lexlaṣ imsawi d azgen n wiyaḍ.
Urar s tusnakt
Ɛerḍet-tent s yiman-nwen qbel. Yal tifrat tettwaffer; ldit-tt mi ara tilim twejdem.
Ɣef uḍebsi awrupi, rrehn ɣef yiwen wuṭṭunrrehnYiwen wuṭṭunYiwen wuṭṭun kan, ixelleṣ 35:1.Ɣer akk → d rrehn ɣef uzeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk → tteklifen i sin 2,70%, ɣas yiwen iḍebber yiwen wuṭṭun, wayeḍ tmanyaṭac. Acuɣer yal rrehn yesɛa yiwet n lmaziyya n lkazinutusnaktLmaziyya n lkazinuAḥric n yal rrehn i teṭṭef lkazinu s ulemmas: 2,70% deg rulit tawrupit.Ɣer akk →?
Sken-d tifrat
Tiririt Yal lexlaṣidrimenLexlaṣAyen i d-yettak rrehn i yerbḥen, yettwanna «X ɣef 1» nnig rrehn i d-yettuɣalen.Ɣer akk → yettwasbedd am akken ilemaḍebsiIlemTaxxamt 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-it, ihi yal rrehn yexser yiwen uferdisidrimenAferdisRrehn agejdan s wacu i yettxeddem unagraw neɣ amurar. Inagrawen n usnerni ttwaglamen s yiferdisen akken ad ilin i yal ṭṭabla.Ɣer akk → deg 37 n tuzzyiwin, akken yebɣu yili wayen i yeḍebber.
Ṭṭfet rrehn ɣef n n wuṭṭunen. Ixelleṣ (36 − n)/n ɣef 1. Deg 37 n tuzzyiwin yerbeḥ, s ulemmas, n n tikkal, yexser 37 − n n tikkal.
Rrbeḥ yettawi-d n × (36 − n)/n = 36 − n n yiferdisen. Lexsara tetteklif 37 − n n yiferdisen. Amgired d −1 n uferdis deg yal 37 n tuzzyiwin, u n yettwakkes: agmuḍ d yiwen i yiwen wuṭṭun, i tɣemertrrehnTiɣmertUkkuẓ n wuṭṭunen yesɛan yiwet n tɣemert tamcerkt ɣef tfelwit, ixelleṣ 8:1.Ɣer akk → neɣ i ddzinarrehnDdzina1–12, 13–24 neɣ 25–36, ixelleṣ 2:1.Ɣer akk →. Yiwen uferdis yexsren deg 37 d 2,70%.
Ɣef uḍebsi s N n texxaminibenkanTaxxamtYiwet seg 37 n texxamin s wuṭṭunen ɣef uqerru yettezzin. Daɣen: slot, cup.Ɣer akk →, amatu-nni yettak-d (36 − N)/N, ihi −2/38 = 5,26% ɣef uḍebsi amarikani. Yiwen n rrehn kan i yerrẓen alugen-a d rrehn amarikani ɣef semmus n wuṭṭunen: alugen yenna ilaq ad ixelleṣ 6,2 ɣef 1, ixelleṣ 6, yetteklif 7,89%.
Keno, urar am lluṭu, yettaṭṭaf 25% neɣ ugar n wayen yettwarehnen. Ma yella lkazinu terna-d ilmawen i uḍebsi n rulit u teǧǧa lexlaṣ akken yella, acḥal n yilmawen ara yilin akken ad tuɣal rulit tɣella am keno?
Sken-d tifrat
Tiririt Tnac n yilmawen: aḍebsi s 48 n texxamin.
S z n yilmawen, aḍebsi yesɛa 36 + z n texxamin, ma d lexlaṣ mazal yebna ɣef 36. S walugen n tmsalt nnig-a, yal rrehn yexser z n yiferdisen deg 36 + z n tuzzyiwin, ihi lmaziyya n lkazinu d z/(36 + z).
Ma nerra-tt d rbeɛ: 4z = 36 + z, ihi z = 12. Tnac n yilmawen ɣef uḍebsi s 48 n texxamin ad tteklifen 25%.
Aḍebsi s kraḍ yilmawen n Strip n Las Vegas, rulit yugaren akk deg ssuma i ara mlilen tuget n yimuraren, yesɛa rbeɛ n umḍan-a.
ilmawentixxaminlmaziyya n lkazinu1372,70%2385,26%3397,69%44010,00%124825,00%Massachusetts Lottery tessekcem deg 2023 aḍebsi s 36 n wuṭṭunen war ilem. Yiwen wuṭṭun ixelleṣ 25 i 1, u azeggaɣ, aberkanrrehnAberkanRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen iberkanen. S tefransist: noir.Ɣer akk →, aryan neɣ uyug xelṣen 3 i 2. Imi ulac ilem, yerxes ugar n rulit?
Sken-d tifrat
Tiririt Ala, yugar aṭas deg ssuma: 30,56% ɣef wuṭṭun d 25% ɣef uzeggaɣ neɣ ɣef uberkan, mgal 2,70% ɣef uḍebsi awrupi.
«I» yesɛa rrehn daxel-is. Rrehn n $1 ɣef wuṭṭun yerra-d $25 yiwet n tikkelt deg 36 n tuzzyiwin s ulemmas: $25 yuɣal-d i $36 yettwarehnen, lexsara n $11 deg 36, 30,56%.
Rrehn n $2 ɣef uzeggaɣ yerra-d $3 azgen n wakud: $3 yuɣal-d i yal $4 yettwarehnen, lexsara n 25%.
Ilem d yiwet kan seg tarrayin n usbadu n ssuma. Rulit txelleṣ am akken llant 36 n texxamin u terna-d tis 37; aḍebsi-a yesɛa 36 n texxamin u ixelleṣ drus kan. Bollman (2024) yefka-t d tawuri.
Lkazinu tebɣa rrehn amaynut ɣef ḥdaṛac n wuṭṭunen imenzatusnaktAmḍan amenzuAmḍan ummid nnig 1 i yebḍan kan ɣef 1 d yiman-is: 2, 3, 5, 7, 11, 13 d wiyaḍ.Ɣer akk → seg 1 ar 36: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 d 31. Acḥal ara ixelleṣ akken ad yetteklif 2,70%-nni am yal rrehn nniḍen ɣef uḍebsi awrupi? Acḥal ara yetteklif s 2 ɣef 1?
Sken-d tifrat
Tiririt 25 ɣef 11, qrib 2,27 ɣef 1. S 2 ɣef 1 ad yetteklif 10,81%.
Seqdecet alugen n tmsalt tamezwarut: rrehn ɣef n n wuṭṭunen ixelleṣ (36 − n)/n ɣef 1. S n = 11, d 25/11 ɣef 1, d lexlaṣ yuɛren, imi ajiṭunidrimenAjiṭunTamatart i d-yemmalen azal yettwasbedden, yettwasersen ɣef tfelwit akken ad yili rrehn. Daɣen: check.Ɣer akk → n $10 ad yerbeḥ $22,73.
S 2 ɣef 1, rrehn n $1 yerbeḥ $2 deg 11 n tuzzyiwin seg 37, yexser $1 deg 26 nniḍen: 22 − 26 = −4 n yiferdisen deg yal 37 n tuzzyiwin, 10,81%.
D ayagi i yerran rulit tettak rrhun ɣef 1, 2, 3, 4, 6, 12 d 18 n wuṭṭunen: 36 yettwabḍa ɣef yal yiwen seg-sen, ihi lexlaṣ n lḥeqq d amḍan ummid. Taylor (2021) yefka tawuri-ya s mraw n wuṭṭunen imenza; llan ḥdaṛac.
Taḍsa i usgunfu
1/37 n yal adrim n rrehn, ɣef yal rrehn, deg yal tuzzya.
Iɣbula
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Hunacek, M. Quantitative Literacy Through Games and Gambling.