Tastratijit D'Alembert
Tastratijit D’Alembert n rulit ternu yiwen uferdis deffir lexsara u tekkes yiwen deffir rrbeḥ.
Ur tettɣellib ara aḍebsi. D 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 → yettwassnen akk yeṣfan: idrimen n rrehn ttalin s leɛqel, aɣelluy n ugerruj d alemmas, u lmaziyya ur tettwannal ara.
Ḍfer anagraw
Lexsara tessali yiwet n tseddart. Rrbeḥ yessuɣal yiwet n tseddart ɣer deffir.
Rrhun d yigmaḍ s yiferdisen n rrehn n tazwara.
Anagraw D’Alembert n rulit, asurif s usurif
Rhent yiwen uferdisidrimenAferdisRrehn agejdan s wacu i yettxeddem unagraw neɣ amurar. Inagrawen n usnerni ttwaglamen s yiferdisen akken ad ilin i yal ṭṭabla.Ɣer akk →. Ma texsrem, rrehn i d-iteddun yugar s yiwen uferdis. Ma trebḥem, yeddaw s yiwen uferdis, ur yettɣelli ara ddaw yiwen. D aya kan. Xemmet ɣef tmizant: yal lexsara tessali adrim n rrehn s yiwet n tseddart u yal rrbeḥ tessenqas-it. Tamuɣli i yellan ddaw-s d belli rrbeḥ d lexsara ad mṣadan, ihi adrim n rrehn ad d-yuɣal ɣer lsas. Ayen i yesseɛǧaben d belli yal tayugit n yiwen n rrbeḥ d yiwet n lexsara s yedrimen yemmeḍfaren tettak +1 uferdis ačuran: xser 3, rbeḥ 4, ačuran +1.
Amek tettban taɣimit?
Taɣimit s leɛqel, s udrim n rrehn yettali cwiṭ s cwiṭ. Imi lexsarat ugarent rrbeḥ s 19 ɣef 18 ɣef lexlaṣ imsawi, adrim n rrehn yettali deg tɣimit taɣezfant. Acku adrim n rrehn yugar mi ara tilim tettxesrem, u yeddaw mi ara tettrebḥem, alemmas n udrim deg tallit n lexsara yugar alemmas deg tallit n rrbeḥ. Tiɣimiyin ṣfant ugar 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 →, s uɣelluy n ugerrujidrimenAɣelluy n ugerrujAɣelluy seg uqerru n ugerruj ɣer uswir adday i d-iteddun deg yiwet n tɣimit. Aɣelluy ameqqran d win akk yugaren.Ɣer akk → alemmas u war iɣzer, u xesrent cwiṭ ugar n rrehn ur nettbeddiltastratijitRrehn ur nettbeddilRrehn n yiwen wazal deg yal tuzzya. D aswir ɣer wacu i yettwaserwas yal anagraw n usnerni.Ɣer akk → s ulemmas acku alemmas n udrim n rrehn yugar.
- p10 −$500
- p25 −$500
- azal n tlemmast −$500
- p75 −$500
- p90 −$500
Anagraw D’Alembert yeddu?
Ala. Taɣimit yemṣadan tettrebḥ, u tiɣimiyin ur qqiment ara mṣadant. Deffir w n rrbeḥ d l n lexsarat s yedrimen yemmeḍfaren, agmuḍ ačuran d w − l n yiferdisen d useɣti almend n wanda tellam deg tseddarin. Ma yella w = l, agmuḍ d +w n yiferdisen, ur yugar ur yenqis, ayen yettbanen d rrbeḥ yettwaḍemnen. Ugur d belli w = l mačči d tagnit yettwaṛǧan: deg 37 n tuzzyiwin, tettṛaǧum 18 n rrbeḥ d 19 n lexsarat. Yiwet n lexsara nniḍen s udrim n rrehn i yulin ar, ad nini, 8 n yiferdisen tettkellif ugar n tam n tyugiwin n +1 i d-yettunefken. Ayen yettwaṛǧan yettak-d −1/37 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 →, akken ilaq.
Acuɣer tiɣimiyin tiwezlanin s waṭas ttrebḥent?
Tagnit yemṣadan d aḥric n yiwen n ulugen i yeṭṭfen yal taɣimit. Ad nsemmi D amḍan n lexsarat kkes amḍan n rrbeḥ. Taɣimit n N n tuzzyiwin i yebdan s yiwen uferdis tettfakk ɣef (N − D²)/2 − D n yiferdisen, ma yella ulac rrehn n yiwen uferdis i yerbḥen (deffir rrbeḥ am wa, adrim n rrehn ur yesɛi anida ara yeɣli). S D = 0, d +N/2, +w n uḥric i yellan nnig. Yal lexsara nniḍen tettwaḥsab s umkuẓ: deffir 100 n tuzzyiwin, D n 4 yeǧǧa-d +38 n yiferdisen, D n 8 yeǧǧa-d +10, u D n 10 yeǧǧa-d −10. Zzher weḥd-s yessewseɛ D ar wazal n √N, mraw deffir 100 n tuzzyiwin, u deg urar war 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 →, rrbeḥ n waṭas n tɣimiyin yemṣadan d lexsarat n kra n tɣimiyin yemyelan ttemḥuḍent armi ur d-yeqqim kra. Ilem yerna-d yiwet n lexsara nniḍen yal 37 n tuzzyiwin s ulemmas, u acku D yettwasget s yiman-is, ssuma-s tettimɣur s tazzla ugar n tɣimit. Ugar n tɣimiyin ar 100 n tuzzyiwin ttfakkent s rrbeḥ; alemmas ur yettili ara akk akka, u deffir kra n tmeḍwin n tuzzyiwin ugar n tɣimiyin ttxesrent daɣen.
Ma tettuɣalem-t s tnila nniḍen?
Contra-D’Alembert, i d-yettusemman daɣen D’Alembert amettiw, yettarnu aferdis deffir rrbeḥ u yekkes yiwen deffir lexsara. D lemri n uneṣli, war amgired. Ma yella ulac rrehn n yiwen uferdis i yexsren, taɣimit n N n tuzzyiwin tettfakk ɣef (D² − N)/2 + D n yiferdisen, anda D tura d rrbeḥ kkes lexsarat. Taɣimit yemṣadan txessar azgen n uferdis i yal tuzzya, u d azrar kan n rrbeḥ i yugaren s waṭas lexsarat i d-yettawin rrbeḥ. Ihi ugar n tɣimiyin xesrent cwiṭ u kra rebḥent aṭas, d tamettiwt n talɣa n uneṣli, u alemmas d yiwen 2,70%-nni n yedrimen yettwarehnen.
Anwa i d d’Alembert?
Jean le Rond d’Alembert, amussnaw n tusnakt u amaẓrag-amɛawen n Encyclopédie, yenna-d deg umagrad n 1754 belli deffir azrar n uqerru, taɛrurt tettuɣal d tin i d-yettasen ugar. Ur yesɛi ara lḥeqq, u tuccḍa i yeṭṭfen isem-is d yiwet n talɣa n tuccḍa n umqemmer. Anagraw D’Alembert deg rulit yettusemma ɣef yisem-is ticki, sɣur imqemmren i yesɛan yiwet n tikti-nni. Mačči d netta i t-yesnulfan, u ahat ur t-yettqebbil ara.
Llant tiwsatin nniḍen?
Contra-D’Alembert, i d-nenna nnig, yetteddu am ParolitastratijitParoliAsnerni deffir rrbeḥ: snegmu deffir rrbeḥ, wennez deffir lexsara neɣ deffir kraḍ n rrbeḥ yemmeḍfaren. Daɣen: Martingale tamettiwt.Ɣer akk → s leɛqel. Kra n yimuraren rennun sin yiferdisen deffir lexsara u kksen yiwen deffir rrbeḥ, ayen yessulin tiseddarin ɣer tmurt n Martingale. Tiwsatin akk sɛant yiwet n 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.
Asimulatur · D'Alembert
2 000 n tɣimiyin n rrhun s lexlaṣ imsawi, s ugerruj n $1 000.
Rrehn n tazwara $10 · talast n ṭṭabla $500 · 100 n tuzzyiwin i yal taɣimit
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 D’Alembert, i yettrennun yiwen n rrehn n tazwara 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 | $3 |
| 3 | 13,5% | 7 | $6 | $4 |
| 4 | 7,0% | 14 | $10 | $5 |
| 5 | 3,6% | 28 | $15 | $6 |
| 6 | 1,8% | 55 | $21 | $7 |
| 7 | 0,94% | 106 | $28 | $8 |
| 8 | 0,48% | 207 | $36 | $9 |
| 9 | 0,25% | 403 | $45 | $10 |
| 10 | 0,13% | 784 | $55 | $11 |
| 11 | 0,065% | 1527 | $66 | $12 |
| 12 | 0,034% | 2974 | $78 | $13 |
| 13 | 0,017% | 5792 | $91 | $14 |
| 14 | 0,0089% | 11279 | $105 | $15 |
| 15 | 0,0046% | 21965 | $120 | $16 |
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
Ur yesɛi ara iɣzer, ayen i t-yerran d anagraw n usnerni deffir lexsara akk s leɛqel. Ur yerxis ara ugar n rrehn ur nettbeddil; yeɣla cwiṭ ugar.
D talast n ṭṭablaṭṭablaTalast n ṭṭablaRrehn adday d rrehn afellay i yettwasirgen. Talast tafellayt d ayen i yeḥebsen inagrawen n usnegmu.Ɣer akk → kan neɣ agerrujidrimenAgerrujAkk idrimen yettwaǧǧan i wurar. Asefrek n ugerruj d tagrut: acḥal seg-s ara tesrem i yal rrehn d yal taɣimit.Ɣer akk →-nwen. Deg tɣimit taɣezfant n lexsara, yettali war aḥbas.
Urar s tusnakt
Ɛerḍet-tent s yiman-nwen qbel. Yal tifrat tettwaffer; ldit-tt mi ara tilim twejdem.
Turarem D’Alembert ɣef uzeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk → deg 50 n tuzzyiwin, s tazwara n yiwen uferdisidrimenAferdisRrehn agejdan s wacu i yettxeddem unagraw neɣ amurar. Inagrawen n usnerni ttwaglamen s yiferdisen akken ad ilin i yal ṭṭabla.Ɣer akk →, u werǧin terbḥem rrehn n yiwen n uferdis (deffir rrbeḥ am wa, rrehn ur yesɛi ara anda ara d-iɣli ugar). Tekfam s 27 n lexsarat d 23 n rrbeḥ. Acḥal n yiferdisen i terbḥem neɣ i texsrem? U s 29 n lexsarat d 21 n rrbeḥ?
Sken-d tifrat
Tiririt +13 n yiferdisen s 27 n lexsarat, −15 n yiferdisen s 29. Snat n tuzzyiwin seg xemsin yuɣen abrid nniḍen tteklifent 28 n yiferdisen.
Semmet D lexsarat ma nekkes rrbeḥ. Agmuḍ d (N − D²)/2 − D i N n tuzzyiwin. S 27 n lexsarat d 23 n rrbeḥ, D = 4: (50 − 16)/2 − 4 = 17 − 4 = +13. S 29 d 21, D = 8: (50 − 64)/2 − 8 = −7 − 8 = −15.
Acuɣer yeṭṭef walugen: rrehn yal tikkelt d yiwen n uferdis yernan lexsarat ar tura ma nekkes rrbeḥ ar tura. Yal lexsara i yessefsex yiwen n rrbeḥ deffir-s terra tayuga, lexsara s s, syin rrbeḥ s s + 1, i d-yettawin +1 n uferdis, akken i d-tesskan tfelwit nnig-a. Deg N n tuzzyiwin, (N − D)/2 n tyugiwin am tigi ttilint, s wazal n +(N − D)/2. D-nni n lexsarat yeqqimen ttwasersen s rrhun 1, 2 … D deg ubrid n usawen u werǧin ttwasefsxen; tteklifent 1 + 2 + … + D = D(D + 1)/2. Akk: (N − D)/2 − D(D + 1)/2 = (N − D²)/2 − D.
Amkuẓ d tamacahut meṛṛa. Taɣimit yemsawan txelleṣ azgen n uferdis i yal tuzzya, u yal tasurift ibeɛden ɣef umsawi tetteklif ugar n tin i tt-yezwaren.
Turarem D’Alembert amettiw ɣef uzeggaɣ deg 100 n tuzzyiwin, s tazwara n yiwen n uferdis, u werǧin yexser yiwen n rrehn n yiwen n uferdis. Tekfam s 52 n rrbeḥ d 48 n lexsarat. Anda tellam? U s 60 n rrbeḥ d 40 n lexsarat?
Sken-d tifrat
Tiririt −38 n yiferdisen s 52 n rrbeḥ, +170 s 60. Ma yugar rrbeḥ lexsarat s drus, mazal d lexsara; ala ma yugar-itent s waṭas i yettxelliṣ.
Semmet D rrbeḥ ma nekkes lexsarat. Agmuḍ d (D² − N)/2 + D i N n tuzzyiwin.
52 n rrbeḥ d 48 n lexsarat: D = 4, ihi (16 − 100)/2 + 4 = −42 + 4 = −38.
60 n rrbeḥ d 40 n lexsarat: D = 20, ihi (400 − 100)/2 + 20 = 150 + 20 = +170.
Acuɣer: yal rrbeḥ i yessefsex lexsara deffir-s yerra tayuga, rrbeḥ s s, syin lexsara s s + 1, i d-yettawin −1. D-nni n rrbeḥ yeqqimen ttwasersen s rrhun 1, 2 … D deg ubrid n usawen u werǧin ttwasefsxen; ttawin-d D(D + 1)/2. Deg N n tuzzyiwin, (N − D)/2 n tyugiwin ttilint, ihi amatu d D(D + 1)/2 − (N − D)/2 = (D² − N)/2 + D.
D alugen n D’Alembert n tazwara s yiskilen yettwaqelben: dinna, amsawi yerbeḥ azgen n uferdis i yal tuzzya u ur nemsawa ara yettwaɛaqeb; dagi, amsawi yetteklif azgen n uferdis i yal tuzzya u ur nemsawa ara yettwaxelleṣ.
Taḍsa i usgunfu
Yettusemma ɣef umussnaw n tusnakt i yeɣlḍen deg uṣurdi.
Iɣbula
- RouletteDoc. Aglam n tstratijit d yimedyaten.
- Roulette77. Aglam n tstratijit d yimedyaten.
- d’Alembert, J. “Croix ou pile.”
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.