Asurif s usurif: taɣimit Martingale
Mraw n yidularen ɣef uzeggaɣ, s sin deffir yal lexsara, ɣef ṭṭabla n $500. Tuzzya s tuzzya, ula d tuzzya i tt-ifukken.
Taɣimit Martingale yettwasimulin seg ugerruj n $1 000. Waḥed u ṛebɛin n yirbaḥen imecṭaḥ, sakin sḍis n lexsarat yeṭṭafaren d rrehn wis sebɛa yettwagin. Taɣimit tekfa s lexsara n $220 deffir mi tella deg +$410, d ayen i yettxedim unagraw.
Aɣawas
Rhent $10 ɣef uzeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk →. Deffir lexsara, snernit s sin. Deffir rrbeḥ, uɣalet ɣer $10. Talast n ṭṭablaṭṭablaTalast n ṭṭablaRrehn adday d rrehn afellay i yettwasirgen. Talast tafellayt d ayen i yeḥebsen inagrawen n usnegmu.Ɣer akk → $500, ihi rrhun d 10, 20, 40, 80, 160, 320, sakin rrehn n $640 ara tagi ṭṭabla. Sḍis n lexsarat yeṭṭafaren rrẓent anagraw; yal aneɛruḍ yesɛa (19/37)⁶ ≈ 1,8% akken ad yeḍru waya, yerna taɣimit n 100 n tuzzyiwin tesɛa qrib 50 n yineɛruḍen. Ayen yettwaṛǧan: qrib 60% n taprubabilit n uṛeẓ deg 100 n tuzzyiwin, d lexsara n $630 mi ara yeḍru.
Tuzzyiwin 1–30
MartingaletastratijitMartingaleAnagraw n usnerni i yessneggmen rrehn deffir yal lexsara. Walit taggayt n tstratijit i wayen i yettxemmem d wayen ur yettxemmim ara.Ɣer akk → am yal ass: izrar n yiwet ɣer kraḍ n lexsarat, yal yiwen yekfa s rrbeḥ i d-yettaken +$10. Deg tuzzya 30 nesɛa 17 n yirbaḥen, yal yiwen yessekfa tunnḍa, nerbeḥ $170. Rrehn ameqqran akk alamma d tura d $80 deffir kraḍ n lexsarat. Yettban am tmacint i yettarun tiwriqin n $10.
Tuzzyiwin 31–60
Kif kif, s yiwet n tunnḍa n ukkuẓ n lexsarat (rrhun alamma d $160, sakin rrbeḥ) i yesrusen $310 ɣef ṭṭabla i kra n wakud, yerna tettban d tabɣest. Deffir 60 n tuzzyiwin: 41 n tunnḍiwin fukkent, rrbeḥ n $410, aswir adday akk n ugerrujidrimenAgerrujAkk idrimen yettwaǧǧan i wurar. Asefrek n ugerruj d tagrut: acḥal seg-s ara tesrem i yal rrehn d yal taɣimit.Ɣer akk → seg tuzzya 30 yella $1 040. Ahistugram n yal taɣimit Martingale yettban akka deg tugget n teɣzi-s.
Tuzzyiwin 61–66
X X X X X X. Rrhun 10, 20, 40, 80, 160, 320: $630 xesren. Rrehn d-iteddun ad yili $640; talast d $500. Anagraw yerreẓ. Nezmer ad nrehn $500 (ma yerbeḥ, ad neqqim s lexsara n $130 deg tunnḍa) neɣ ad nuɣal ɣer $10 ad neqbel lexsara. Sḍis n uberkanrrehnAberkanRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen iberkanen. S tefransist: noir.Ɣer akk → neɣ n 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 → yeṭṭafaren sɛan 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 1,8% i yal tunnḍa. Nexdem qrib 45 n tunnḍiwin. Taprubabilit n wawaḍ ɣer da deg kra n umkan deg 45 n tunnḍiwin tella qrib 55%. Mačči d zzher n diri; d azal n tlemmast.
- p10 −$1 000
- p25 −$1 000
- azal n tlemmast −$1 000
- p75 +$790
- p90 +$1 690
Leḥsabat
Rrbeḥ n $410 deffir 60 n tuzzyiwin, lexsara n $220 deffir 66. Amḍan n rrhun meṛṛa: qrib $2 100 deg 66 n tuzzyiwin, mgal $660 i umurar s $10 ur nettbeddil. Lexsara yettwaṛǧantusnaktLexsara yettwaṛǧanAzal yettwaṛǧan seg tmerna n yidrimen yettwarhen; d alemmas n wayen yettwaxsar deg yiwet n tɣimit neɣ deg yiwen wakud.Ɣer akk → ɣef $2 100 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 → d $57; −$220-nneɣ n tidet qrib tulut n ubeɛɛed alugantusnaktAbeɛɛed aluganAẓar amkuẓ n tavaryans; ameccaq n umata gar ugmuḍ d wazal yettwaṛǧan.Ɣer akk → ddaw-s, ayen ur nesweḥcen ara i unagraw ideg abeṭṭu yesɛa ajeḥnuḍ aɣezfan ɣer zelmeḍ. Lukan nḥebs deg tuzzya 60 s talast n rrbeḥtastratijitTalast n rrbeḥIswi n rrbeḥ yettwasbedden send, anda ara tfakkem taɣimit.Ɣer akk → n $400, nili neffeɣ s rrbeḥ n $410, yerna taɣimit d-iteddun tili tesɛa yiwet n 1,8% i yal tunnḍa.
Ayen i d-tesken teɣimit
Martingale tettbeddil rrehn n 48,65% ɣer wazrar n rrhun i yettarbaḥen 98% n tunnḍiwin-is, yettxesser 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 → deg 2% nniḍen. Ur tbeddel ara lexsara yettwaṛǧan i yal adular; tessgutut idularen. Amurar s rrehn ur nettbeddil i yellan ɣer tama-nneɣ yerhen tulut kan, yexser, s ulemmas, tulut kan. Amurar ara yesseqdacen anagraw-a aseggas ad yerbeḥ tugget n tmeddiyin, ad yexser aseggas.
Acḥal n tikkal i d-yettas uzrar n lexsara
Rrehn s lexlaṣ imsawi ɣef uḍebsi s yiwen yilem yettexsar 19 n tuzzyiwin seg 37. Yal ajerriḍ d taprubabilit ara xesrent akk tuzzyiwin n yiwen uzrar, d wayen yexser ar tura umurar n Martingale, i yessnernayen rrehn s snat deffir yal lexsara.
| lexsarat ṭṭafarent | taprubabilit | qrib 1 seg | lexsara ar tura | rrehn d-iteddun |
|---|---|---|---|---|
| 1 | 51,4% | 2 | $1 | $2 |
| 2 | 26,4% | 4 | $3 | $4 |
| 3 | 13,5% | 7 | $7 | $8 |
| 4 | 7,0% | 14 | $15 | $16 |
| 5 | 3,6% | 28 | $31 | $32 |
| 6 | 1,8% | 55 | $63 | $64 |
| 7 | 0,94% | 106 | $127 | $128 |
| 8 | 0,48% | 207 | $255 | $256 |
| 9 | 0,25% | 403 | $511 | $512 |
| 10 | 0,13% | 784 | $1 023 | $1 024 |
| 11 | 0,065% | 1527 | $2 047 | $2 048 |
| 12 | 0,034% | 2974 | $4 095 | $4 096 |
| 13 | 0,017% | 5792 | $8 191 | $8 192 |
| 14 | 0,0089% | 11279 | $16 383 | $16 384 |
| 15 | 0,0046% | 21965 | $32 767 | $32 768 |
Taprubabilit d 19/37 yettwasgeten s yiman-is yiwet n tikkelt i yal lexsara, seg yiwet n tuzzya yettwafernen. Taɣimit taɣezfant tesɛa aṭas n tuzzyiwin anda yezmer ad yebdu wazrar am wa, ihi deg yiwet n tmeddit taprubabilit-is tugar aṭas ayen i d-yesskan yiwen ujerriḍ.
Isteqsiyen
Tẓa n lexsarat i t-yerrẓen deg umkan n sḍis: 0,25% i yal tunnḍa, d $5 110 i yexsren mi ara yeḍru. Aɣelluy d qlil ugar, d ameqqran ugar, yiwet n −2,70%.
Ad yerbeḥ 48,65% n wakud, ad yeǧǧ tunnḍa deg −$130 akken yebɣu yili. Ulac tikli yelhan deffir Martingale yerrẓen; yella kan udrim n rrehn ara tfernem sakin.
Ih, i teɣimit-nni. Mačči i ulemmas n tɣimiyin meṛṛa.
Urar s tusnakt
Ɛerḍet-tent s yiman-nwen qbel. Yal tifrat tettwaffer; ldit-tt mi ara tilim twejdem.
Ɣef ṭṭabla n $1 ar $500, amurar 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 → yebda s $1 ɣef uzeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk → ɣef uḍebsi 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 →. Acḥal n lexsarat ṭṭafarent i yeḥbsen asnerni s snat, acḥal i yexsren ar tura, d acḥal n tikkal i d-yettḍuru?
Sken-d tifrat
Tiririt Tẓa n lexsarat: $511 yexsren, u rrehn d-iteddun yili d $512. Yettḍuru yiwet n tikkelt deg qrib 403 n yimyizwaren.
Rrhun d 1, 2, 4, 8, 16, 32, 64, 128 d 256: s umata $511. Wis mraw yili d $512, nnig talast. Rrehn n $500 i yerbḥen mazal yeǧǧa amurar s lexsara n $11; win yexsren yeǧǧa-t s lexsara n $1 011.
Azeggaɣ yexser s tprubabilit n 19/37, ihi tẓa n lexsarat ṭṭafarent sɛant taprubabilit n (19/37)⁹ ≈ 0,25%, yiwet n tikkelt deg qrib 403 n yimyizwaren. Yal amyizwer i yekfan yerbeḥ $1, ihi amurar yettṛaǧu qrib $402 n rrbeḥ amecṭuḥ qbel yiwet n lexsara n $511, u 2,70% n wayen meṛṛa yettwarehnen mazal yexser s ulemmas.
Ɣef uḍebsi s sin yilmawen taprubabilit d (20/38)⁹, yiwet n tikkelt deg qrib 323. Bollman (2021) yura «qrib 1 seg 833», d (18/38)⁹, taprubabilit n tẓa n rrbeḥ ṭṭafaren.
Taḍsa i usgunfu
Waḥed u ṛebɛin n yirbaḥen imecṭaḥ d yiwet n lexsara tameqqrant. D wagi i d anagraw akk.
Iɣbula
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”