Abunus, leɛruḍ d tuɣalin n lexsara deg rulit
Ibunusen n rulit am tkarḍiwin matchplay, ijiṭunen ur nettbeddil ara ɣer yedrimen d tuɣalin n lexsara ssmuttin cwiṭ n yedrimen seg lkazinu ɣer umurar. Mi ara ttwaḥesben akken iwata, kra seg-sen sɛan azal ugar n wayen yettawi uḍebsi.
Takarḍa i yessnernayen s sin lexlaṣ imsawi tesɛa azal n qrib 46% n rrehn ɣef uḍebsi awrupi. Ajiṭun n lɛerḍ n yiwet n tikkelt yesɛa azal n (36 − n)/37 n wazal-is ɣef rrehn i yeṭṭfen n n wuṭṭunen: 95% ɣef yiwen wuṭṭun, 49% ɣef uzeggaɣ. Tuɣalin n wazgen n lexsara-nwen tačurant terra taɣimit tawezlant ɣef uzeggaɣ tesɛa azal. Ula d yiwet ur tbeddel aḍebsi; tbeddel win ara yexellṣen.
Ayɣer lɛerḍ yezmer ad yeɣleb lmaziyya
Lmaziyya n lkazinutusnaktLmaziyya n lkazinuAḥric n yal rrehn i teṭṭef lkazinu s ulemmas: 2,70% deg rulit tawrupit.Ɣer akk → d ssuma i yal aferdisidrimenAferdisRrehn agejdan s wacu i yettxeddem unagraw neɣ amurar. Inagrawen n usnerni ttwaglamen s yiferdisen akken ad ilin i yal ṭṭabla.Ɣer akk → yettwarehnen: 2,70% ɣef uḍebsi awrupi. Abunus n rulit yettarnu idrimen ɣer yiwet n tama n rrehn, yerna ma yerna ugar n 2,70% n udrim, rrehn-nni sennig n yilem alamma yekfa lɛerḍ. Lkazinu ttakent-ten akken yebɣu yili acku ttwaḥeddden: yiwet n tkarḍa i yal tirza, ijiṭunenidrimenAjiṭunTamatart i d-yemmalen azal yettwasbedden, yettwasersen ɣef tfelwit akken ad yili rrehn. Daɣen: check.Ɣer akk → i yezmren ad ttwarehnen maca ur ttbeddilen ara ɣer yedrimen, tuɣalin kan i yimuraren i yexsren idrimen imeqqranen. Leḥsab d yiwen am deg yal amkan deg usmel-a: taprubabilit sgut lexlaṣidrimenLexlaṣAyen i d-yettak rrehn i yerbḥen, yettwanna «X ɣef 1» nnig rrehn i d-yettuɣalen.Ɣer akk →, yettwasmernin ɣef yigmaḍ.
Tikarḍiwin matchplay
Takarḍa matchplay teqqim ɣer tama n rrehn s yedrimen, tessnernay s sin ayen ixelleṣ rrehn ma yerbeḥ; ama yerbeḥ ama yexser, lkazinu teṭṭef takarḍa. Bollman (2024) yeḥseb azal n tkarḍa n Las Vegas n 2022 i yessnernayen alamma d $50 ɣef rrehn s lexlaṣ imsawirrehnRrehn s lexlaṣ imsawiAzeggaɣ/aberkan, aryan/uyug, afellay/adday. 18 n wuṭṭunen, ixelleṣ 1:1.Ɣer akk →. Ɣef uḍebsi awrupi, $50 ɣef uzeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk → s tkarḍa yettarbaḥ $100 s taprubabilit n 18/37, yettxesser $50 s taprubabilit n 19/37: +$22,97 yettwaṛǧan, neɣ 45,9% n rrehn. Ɣef uḍebsi amarikani d +$21,05, 42,1%. Ɣef yiwen wuṭṭunrrehnYiwen wuṭṭunYiwen wuṭṭun kan, ixelleṣ 35:1.Ɣer akk →, yiwet n tkarḍa tili tesɛa azal s sin, d ayɣer tikarḍiwin ttwaḥeddadent i rrhun s lexlaṣ imsawi.
Ijiṭunen ur nettbeddil ara ɣer yedrimen
Ijiṭunen n lɛerḍ, i wumi qqaren daɣen ijiṭunen ur nettwazenzan ara, zemren ad ttwarehnen maca ur ttbeddilen ara s yedrimen. Alugen yettwassnen d yiwet n tikkelt: rrehn i yerbḥen yettwaxelleṣ s yijiṭunen n yal ass, ajiṭun n lɛerḍ yettwakkes; win yexsren yettwakkes daɣen. Ajiṭun n $100 ɣef rrehn i yeṭṭfen n n wuṭṭunen yettarbaḥ (36 − n)/n × $100 s taprubabilit n/37, ihi yesɛa azal n (36 − n)/37 n wazal-is. Azal n ujiṭun s yiman-is werǧin yettuɣal, d irbaḥen kan, yerna rrehn i yettarbaḥen qlil maca ixelleṣ aṭas d win yettxesren drus akk akka: $94,59 ɣef yiwen wuṭṭun, $48,65 ɣef uzeggaɣ. Anda ajiṭun yezmer ad yeqqim ɣef tfelwit n rrhunibenkanTafelwit n rrhunAẓeṭṭa n rrhun yettwarun ɣef ṭṭabla. Daɣen: ṭṭabla, tajellabt, aceṭṭiḍ.Ɣer akk → alamma yexser, rrehn s lexlaṣ imsawi yesɛa azal n 18/19 n wazal-is ɣef uḍebsi awrupi d 9/10 ɣef umarikani (Bollman, 2024).
Abeddel n yijiṭunen ɣer yedrimen
Azal d alemmas; amurar i yebɣan idrimen s tidet yezmer ad ten-yaɣ s usenqes n lxeṭṛ. Amedya n Bollman d win n lkazinu taqburt Vegas World: $1 000 n yijiṭunen n yiwet n tikkelt ɣef uḍebsi amarikani, $500 ɣef uzeggaɣ d $500 ɣef uberkanrrehnAberkanRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen iberkanen. S tefransist: noir.Ɣer akk →, s $20 n yedrimen ɣef yal yiwen seg 0 d 00. Azeggaɣ neɣ aberkan yettarbaḥ $500, yettxesser $40 n yedrimen: +$460. 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 → yexser sin yijiṭunen, ixelleṣ $700 ɣef yedrimen: +$680. Amurar yesmad ma drus $460, yerna alemmas, $471,58, d 99,6% n wazal n yijiṭunen ɣef uzeggaɣ weḥd-s. Anda ilugan sirigen ijiṭunen ɣef yiwen wuṭṭun, aḍebsi awrupi yettak asenqes n lxeṭṛ yifen: ijiṭunen n $25 ɣef 36 n wuṭṭunen akk ($900) d $25 n yedrimen ɣef yilem. Yal uṭṭun i d-yeffɣen ixelleṣ $875, idrimen ɣef yilem xesren ala ma yeffeɣ-d yilem s yiman-is, ihi amurar yeṭṭef ma drus $850, 94% n wazal n yijiṭunen, war ula d lxeṭṛ.
Tuɣalin n lexsara
Imuraren s rrhun imeqqranen s waṭas ttwafkan-asen tuɣalin n lexsara: amur seg lexsara-nsen tačurant yettuɣal-d deg taggara n teɣimit yettwaqeblen. Tuɣalin txelleṣ kan mi ara texsrem, ihi tesɛa azal ugar mi ara ttbeddilen yigmaḍ aṭas, taɣimit d tawezlant akken lmaziyya mazal ur teɣleb. Epstein (2013) yeḥseb taluft i uḍebsi amarikani; imḍanen-nneɣ i uḍebsi awrupi ttḍafaren. S wazgen n lexsara tačurant yettuɣalen, rrehn ur nettbeddil s lexlaṣ imsawi yesɛa azal alamma d 103 n tuzzyiwin, ifaz deg 25, s wazal n +0,51 n yidrimen n rrehn s ulemmas. Ɣef yiwen wuṭṭun, ibeddilen meqqren aṭas akken taɣimit teqqim sennig n yilem qrib 3 600 n tuzzyiwin, tifazt deg 882, s wazal n +17,25 n yidrimen n rrehn. S tuɣalin n 10% yettwassnen ugar, lexlaṣ imsawi sennig n yilem kan i yiwet n tuzzya, ma d yiwen wuṭṭun ifaz deg 20 n tuzzyiwin, s wazal n +0,62 n yidrimen n rrehn.
Ilugan n leɛruḍ n rulit: ayen ɣef tettkel lkazinu
Yal lɛerḍ yesɛa talast, yerna talast teḥrez lkazinu: yiwet n tkarḍa i tirza, ijiṭunen s wazal yettwasbedden, tuɣalin yettwaqeblen kan d yimuraren ideg lexsara yettwaṛǧan deg yiwen usikel tugar aṭas tuɣalin. Amurar i yesseqdacen takarḍa sakin yeqqim tameddit s rrhun n $50 ɣef uzeggaɣ yettarra $22,97 deg 17 n tuzzyiwin, s $1,35 i tuzzya. Azal d tidet i umurar i tt-yeṭṭfen yerna yeffeɣ, neɣ i win ara yuraren aya akken yebɣu yili.
Tasemselt
Isteqsiyen
I yiwen n rrehn i wumi teqqen, ih. Yal rrehn nniḍen yettkellif 2,70% n udrim.
Drus n yimuraren i ɣef d-yettmektin, ijiṭunen ttwaḥeddden, yerna lkazinu teḥseb yakan lɛerḍ am lexbar n usenzi.
Qlil. D tawtilt n yimuraren imeqqranen, s umata tettwaqbal d unebgi n lkazinu, tettwaxelleṣ ɣef lexsara tačurant n yiwen usikel.
Urar s tusnakt
Ɛerḍet-tent s yiman-nwen qbel. Yal tifrat tettwaffer; ldit-tt mi ara tilim twejdem.
Ttunefkem ajiṭunidrimenAjiṭunTamatart i d-yemmalen azal yettwasbedden, yettwasersen ɣef tfelwit akken ad yili rrehn. Daɣen: check.Ɣer akk → n usnerni n $25 ara yettwakksen deffir yiwen n rrehn, s rrbeḥ neɣ s lexsara. Anda ara t-tsersem: ɣef uzeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk →, ɣef ddzinarrehnDdzina1–12, 13–24 neɣ 25–36, ixelleṣ 2:1.Ɣer akk → neɣ ɣef yiwen wuṭṭun?
Sken-d tifrat
Tiririt Ɣef yiwen wuṭṭun. Dinna yesɛa azal n $23,65 s ulemmas; ɣef ddzina $16,22 u ɣef uzeggaɣ $12,16.
Ajiṭun s yiman-is werǧin ad d-yuɣal, ala ayen i yerbeḥ. Ɣef uzeggaɣ yerbeḥ $25 s tprubabilit n 18/37: $12,16. Ɣef ddzina yerbeḥ $50 s tprubabilit n 12/37: $16,22. Ɣef yiwen wuṭṭun yerbeḥ $875 s tprubabilit n 1/37: $23,65.
S umata, rrehn ɣef n n wuṭṭunen yesɛa azal n (36 − n)/37 n ujiṭun, ihi ma drus wuṭṭunen, yif. S ujiṭun amagnu ulac amgired, acku rrehn yettuɣal-d s yal rrbeḥ u yal rrehn yesɛa azal n 36/37-ines. Tukksa n rrehn tḍurr rrhun i yettrebḥen aṭas n tikkal u qrib ur tennal ara rrehn i yettrebḥen yiwet n tikkelt deg 37.
Lkazinu ad awen-d-terr azgen n lexsara-nwen tačurant deffir yiwet n tuzzya kan. $100 ɣef uzeggaɣ yesɛa azal? D $100 ɣef yiwen wuṭṭun?
Sken-d tifrat
Tiririt I sin: qrib +$22,97 ɣef uzeggaɣ d +$45,95 ɣef wuṭṭun.
Ɣef uzeggaɣ terbḥem $100 s tprubabilit n 18/37 u, deffir tuɣalin, texsrem $50 s tprubabilit n 19/37: (1 800 − 950)/37 = +$22,97.
Ɣef yiwen wuṭṭun terbḥem $3 500 s tprubabilit n 1/37 u texsrem $50 s tprubabilit n 36/37: (3 500 − 1 800)/37 = +$45,95.
D imḍanen n matchplay tikkelt nniḍen. Rrehn n $100 i yettexsaren $50 kan yettrebḥ $100 neɣ yettexsar $50, am rrehn n $50 s ukupun i yessnernayen s snat rrbeḥ-is. Deg teɣimit taɣezfant ugar, tuɣalin tettwaxelleṣ ɣef ugmuḍ ačuran kan, rrbeḥ d lexsara ttemsefsaxen qbel ad tettwaxelleṣ, u azal yettenqas; i uzeggaɣ s wezgen yettuɣalen, 25 n tuzzyiwin d teɣzi yelhan akk.
Lkazinu ad awen-d-terr azgen n lexsara-nwen tačurant deffir amḍan yettwasbedden n rrhun n $100 ɣef uzeggaɣ, yettwafernen zik: 1, 2 neɣ 3 n tuzzyiwin. Anta i yesɛan azal ameqqran akk?
Sken-d tifrat
Tiririt Kraḍ n tuzzyiwin: qrib +$31,45. Yiwet n tuzzya tesɛa azal n +$22,97, snat kan +$20,96.
Yiwet n tuzzya: rrbeḥ n $100 s tprubabilit n 18/37, neɣ lexsara n $100 d tuɣalin n $50 s tprubabilit n 19/37: +$22,97, am deg tewuri nnig-a.
Snat n tuzzyiwin: rebḥent i snat (324 n tikkal deg 1 369), +$200. Yiwet d yiwet (684 n tikkal), $0, ulac ayen ara d-yuɣalen. Xesrent i snat (361 n tikkal), −$200, −$100 deffir tuɣalin. Alemmas: (200 × 324 − 100 × 361)/1 369 = +$20,96. Tuɣalin txelleṣ ɣef lexsara kan, u snat n tuzzyiwin rrant aṭas n lexsarat n yiwet n tuzzya d amsawi.
Kraḍ n tuzzyiwin werǧin ttaǧǧant amsawi. Kraḍ n rrbeḥ (5 832 n tikkal deg 50 653): +$300. Sin n rrbeḥ (18 468): +$100. Yiwen n rrbeḥ (19 494): −$100, yettuɣal −$50. Ulac (6 859): −$300, yettuɣal −$150. Alemmas: +$31,45.
Tuɣalin tesɛa azal ugar ma yali umḍan n tuzzyiwin i tefrenem zik, ma d lmaziyya tetteklif $2,70 kan i yal tuzzya, ihi azal yettali ar qrib +$51 ɣer 25 n tuzzyiwin (walit tafelwit nnig-a), u amḍan aryan n tuzzyiwin yugar yal tikkelt amḍan uyug i d-iteddun deffir-s.
Yiwet n lkazinu n Las Vegas tefka yiwet n tikkelt akupun: rhent $5 ɣef 00 u, ma yerbeḥ, ad tettwaxelṣem $250 deg wadeg n $175 yettwassnen. Acḥal i d azal n rrehn n $5 s ukupun, am tesgunt n rrehn, ɣef uḍebsi-ines 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 →?
Sken-d tifrat
Tiririt Qrib +34%: rrehn yesɛa azal n +$1,71 s ulemmas. Ma yella $250 yesɛa daxel-is $5 yettuɣalen, d +31,6%.
00 yerbeḥ yiwet n tikkelt deg 38 n tuzzyiwin. S ukupun: +$250 yiwet n tikkelt, −$5 deg 37 n tikkal nniḍen. Alemmas: (250 − 37 × 5)/38 = 65/38 = +$1,71, d 34,2% n $5. War akupun: (175 − 185)/38 = −$0,26, −5,26%-nni yettwassnen.
Ma yella $250 d amatu yettuɣalen, rrbeḥ d $245 u alemmas d (245 − 185)/38 = +$1,58, neɣ 31,6%.
Bollman (2024) yefka akupun-a, seg lkazinu Lady Luck (tura d Downtown Grand), d tawuri; tiririt i d-yefka yid-s, 7,89%, ur temṣada ara d yiwet seg tɣuriwin-a. Am ukupun n matchplay, yesɛa azal yiwet n tikkelt: urart-t u ḥebset.
Taḍsa i usgunfu
Lɛerḍ yesɛa azal ugar i umurar i t-yeṭṭfen yuɣal s axxam.
Iɣbula
- Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.