Iselkimen n rulit
Amek i yettaktazal uselkim takurt, anwa i yebnan imezwura, d acḥal n telqayt i yesra.
Aselkim n rulit yettaktazal takurt d uqerru deg tsinin timezwura n tuzzya u yessemmay amur n uḍebsi anda ilaq ad teɣli tkurt. Edward Thorp d Claude Shannon bnan amezwaru deg 1961, u Eudaemons bnan iselkimen umḍinen seg 1976. Tarrayt tesra rrhun yettwaqeblen deffir uḍeqqer: istudyuten srid tura mdlen rrhun deg uḍeqqer, u Nevada tegdel ibenkan am wigi seg 1985.
Amek i yettwabna unagraw amezwaru n uselkim n rulit
Tikti tusa-d ɣer Edward Thorp deg tefsut n 1955, mi yella d anelmad n tfizikt deg UCLA: aḍebsi yettwaxedmen akken iwata armi ur yesɛi ara amyal ilaq ad yessezzi takurtibenkanTakurtTakurt tamecṭuḥt i yettwaḍeqqren deg ubrid mgal aqerru yettezzin. Tikurin n tura d ivorine neɣ d Teflon, 18–21 mm.Ɣer akk → s wudem yettwassnen uqbel am yiwet n tmeẓla. Yesuddem aḍebsi n uzgen n teɣzi ur nesqam ara s tmrilt n usiḍen deg tugna, u yufa-t ur yemṣada ara akken ad yettwassen uqbel, u tikli ɣer Nevada deg Dujembeṛ 1958 tesken-as belli iḍebsiyen n lkazinu ttezzin s lemṣada, war amuddu. Syin blackjack yeṭṭef amkan. Deg Nunembeṛ 1960, deg MIT, yessuter i Claude Shannon ad yazen amagrad-is ɣef usiḍen n tkarḍiwin i National Academy of Sciences; deg taggara n umyager Shannon yesteqsa-t ɣef wayen nniḍen ɣef i yettxeddem, u asenfar n rulit yuɣal ɣer tzeqqa n ddaw n wexxam n Shannon. Uɣen aḍebsi alugan seg Reno s $1 500, sersen-t ɣef ṭṭabla taqdimt n bilyaṛ n uẓru, u ktazlen takurt s tafat n strobe d tamrilt yettɣaran ar timiḍi n tsint. S usileɣ, tuccḍiwin-nsen deg uktazal nqent seg wazal n 0,03 ɣer 0,01 n tsint. Deg Yunyu 1961, aselkim yesɛa tnac n yitransistuṛen u tiddi-s am tbwaṭ n cigaṛu: taqeffalt deg usebbaḍ, yettwaxdam s uḍad ameqqran n uḍar, tettaktazal aqerru yettezzinibenkanAqerru yettezzin (rotor)Aḥric n uḍebsi yettezzin i yeṭṭfen tixxamin.Ɣer akk → d tkurt, u taɣect deg yiwet n tmeẓẓuɣt tessemmay yiwet seg tam n tgezminaḍebsiTagzemtAḥric n texxamin yemmeḍfaren ɣef uḍebsi, mačči d tagrumma ɣef tfelwit.Ɣer akk → n uḍebsi. Deg Las Vegas deg unebdu-nni, Shannon yettaktazal ɣer uḍebsi u yettaru uṭṭunen am yal amurar n unagraw, mi ara yettrehhen Thorp s yiṣurdiyen imecṭaḥ deg taggara n ṭṭabla. Tussna uqbel teṭṭef, maca ifilen irqaqen am wazar ɣer umeslaw ttrẓen yal tikkelt, u yiwet n tikkelt tameṭṭut yellan rrif n Thorp temmuqel s tugdi ɣer umeslaw i d-yeffɣen seg tmeẓẓuɣt-is. Werǧin rehnen s tidet. Thorp yesbeggen anagraw n uselkim n rulit deg 1966 u yessuffeɣ talqayt deg 1979 d 1984.
Iselkimen umḍinen imezwura
Tamacint n Thorp d Shannon d tanalugit: tazagant-is d ahil-is, u abeddel n tarrayt yebɣa ad ttwabeddlen yifilen. Amikruproseṣur yekkes talast-a. Alan Lewis, anelmad deg Caltech, yewwi aselkim umḍin i yebna s yiman-is deg tbwaṭ n tkamiṛat ɣer Circus Circus deg Las Vegas deg 1972, yettaktazal iḍebsiyen seg ubalkun sennig n ṭṭablat u yettazen ayen yettwasiḍen uqbel s tradyut i umeddakel-is ddaw. Yedda, u ur d-yewwi idrimen; yeẓra deffir akken belli yeǧǧa akennu n uḍebsi. Seg 1976, tagrumma n yinelmaden n tfizikt deg Santa Cruz, Eudaemons, xedmen axeddim s telqayt. Uɣen aḍebsi n lkazinu, ktazlen takurt, aqerru, akennu d uneggez, u uran tigdaliwin s semmus n yiɣewwaren i yesseggam umurar i yal aḍebsi s usiti ɣef tqeffalin n uḍad azal n ɛecrin n tesdatin send ad yerhen. Aselkim-nsen yessemmay yiwet seg tam n tgezmin deg kra n tsinin seg tazwara n tuzzya. Ɣef ṭṭabla n tidet deg Yennayer 1978 yefka-d lmaziyya i ḥesben 25%; ibenkan, yettwaqqnen ɣer tfekka syin ttwabnan deg yisebbaḍen, ccḍen ugar aṭas n tfizikt (walit Eudaemons).
Acuɣer rrhun deffir wakud sɛan azal
Lkazinu tezmer ad teḥbes tifin uqbel meṛṛa ma tegdel rrhun mi ara tettwaḍeqqer tkurt. Thorp yufa belli ttaqrib ula d yiwet ur txeddem aya: deg Reno, Las Vegas, London, Monte Carlo, Nice, Venice d Puerto Rico, lɛada d asiwel n «ulac rrhun nniḍentikliUlac rrhun nniḍenAsiwel n ukrupi (neɣ tazmilt ɣef ugdil) i yemdelen rrhun. Ijiṭunen ur zmiren ad ttwasersen, ad mbiwlen neɣ ad ttwakksen.Ɣer akk →» yiwet neɣ snat n tuzzyiwin send ad teɣli tkurt. Akud-a d ayen i yesra yal anagraw n tifin uqbel seg wass-nni, seg Eudaemons ar yisawalen deffir wakud n terbaɛt n Ritz ɣef racetrackṭṭablaRacetrackAɣerdu aqerqur ɣef tfelwiyin srid d tid n tmacinin i d-yesskanen uṭṭunen s umyizwer n uḍebsi, yettwasqedcen i users n rrhun n lǧiran d tegzemt s yiwen usiti.Ɣer akk →. Nevada tegdel ibenkan n tifin uqbel deg Mayyu 1985, u istudyuten srid tura mdlen rrhun deg uḍeqqer.
Amek i mmegrent lkazinu
Deg yiseggasen anda rrhun mazal ttwaqeblen deffir uḍeqqer, lkazinu mmegrent imuraren yesɛan ccekk s ukrupi. Tiqsiḍin ɣef yimuraren n unagraw n Norman Leigh deg Nice deg 1966 d tirbaɛ n tifin uqbel d-yusan deffir-s glament akrupiimdanenAkrupiBab n ṭṭabla n rulit, i yettsellifen urar.Ɣer akk → amaynut yal tuzzya, takurt tettwabeddel, tuzzyiwin tiwezlanin neɣ tizrib, ṭṭabla teččur s yemdanen n lkazinu, u taggara ṭṭabla tettwamdel. Tiqsiḍin-a d-kkant-d seg tama n yimuraren u weɛrent i usenqed (Goldman, 2007). Tiḥila-nni sɛant lmeɛna ɣas akken: tuzzya tawezlant neɣ tazrit ur tezmir ara ad tawi takurt s lebɣi ɣer texxamtibenkanTaxxamtYiwet seg 37 n texxamin s wuṭṭunen ɣef uqerru yettezzin. Daɣen: slot, cup.Ɣer akk →, maca tessexlaḍ akud i yettaktazal uselkim n tifin uqbel.
Acḥal ilaq ad telhu tifin uqbel
Thorp (1984) yessuffeɣ azal n tifin uqbel mi ara tuccḍa-s tḍeffer taznagt n uqelwac: deg tuzzya tamagnut, taxxamt i yettwaṛǧan tbeɛɛed s σ n texxamin ɣer yiwet n tama neɣ ɣer tayeḍ. Rhent ɣef wuṭṭun i yettwaṛǧan iman-is, neɣ fell-as d sin n lǧiranrrehnLǧiranYiwen wuṭṭun d snat n texxamin ɣef yal tama-s ɣef uḍebsi, semmus n yijiṭunen ɣef yiwen wuṭṭun.Ɣer akk → ɣef yal tama, u lmaziyya teqqen ɣer σ kan. Tussna uqbel tummidt ad terbeḥ yal rrehn ɣef yiwen wuṭṭunrrehnYiwen wuṭṭunYiwen wuṭṭun kan, ixelleṣ 35:1.Ɣer akk →. S σ = 10 n texxamin, talqayt i wwḍen Thorp d Shannon, rrehn ɣef yiwen wuṭṭun yettarra-d azal n +44%, azal i d-yefka Thorp i yibenk-nsen; aḥkay-is n 1998 yerra-t ɣef umur wis tam n uḍebsi yettwafernen ugar. Lmaziyya tettenqis s tazrit mi ara tali tuccḍa u truḥ ɣer 17 n texxamin ɣef uḍebsi awrupi d 16 ɣef umarikani, mi ara yecceḍ usiḍen qrib s uzgen n uḍebsi. Asiḍen n tuccḍiwin n Thorp s yiman-is yesskan acuɣer talast-a tqerreb: tuccḍiwin yemgaraden n 1,4 d 5,5 n texxamin seg uktazal n uqerru d tkurt, 7 seg uɣelli n tkurt ɣef yimsenfalenibenkanAmsenfalYiwen seg yiɣunab n wuzzal ɣef tama yeknan i yesseḍrayen takurt mi ara teɣli. Daɣen: canoe, diamond, pin.Ɣer akk → d 6 seg uneggez deg texxamin sdukklen ɣer wazal n 10,8.
Isteqsiyen
Ala. Ulac takurt. Uṭṭun yettwafren s useɣzan send asmussu.
Ad ilint ur ṭṭifent ara zdat uktazal, d ayen i yettaǧǧan ula d yiwet ur tetteddu akka.
Urar s tusnakt
Ɛerḍet-tent s yiman-nwen qbel. Yal tifrat tettwaffer; ldit-tt mi ara tilim twejdem.
Rrehn s wawal ɣef lǧiranrrehnLǧiranYiwen wuṭṭun d snat n texxamin ɣef yal tama-s ɣef uḍebsi, semmus n yijiṭunen ɣef yiwen wuṭṭun.Ɣer akk → yessers yiwen ujiṭunidrimenAjiṭunTamatart i d-yemmalen azal yettwasbedden, yettwasersen ɣef tfelwit akken ad yili rrehn. Daɣen: check.Ɣer akk → ɣef wuṭṭun d snat n texxaminibenkanTaxxamtYiwet seg 37 n texxamin s wuṭṭunen ɣef uqerru yettezzin. Daɣen: slot, cup.Ɣer akk → ɣef yal tama-s ɣef uḍebsi: semmus n yijiṭunen. Acḥal n tikkal ilaq ad teṣḥeḥ tifin uqbel deg semmus-nni n texxamin akken ur yettrebḥ ur yettexsar, d acu i yettawi ma tṣeḥḥa yiwet n tikkelt deg semmus?
Sken-d tifrat
Tiririt Ur yettrebḥ ur yettexsar ɣer 5 deg 36, 13,9%, mgal 13,5% s zzher kan. Ma tṣeḥḥa yiwet n tikkelt deg semmus, yerra-d 44% ugar n wayen yettwarehnen.
Ma yeffeɣ-d rrehn s wawal, yiwen ujiṭun yerbeḥ 35 ɣef 1 u yuɣal-d s rrbeḥ-is, 36 n yijiṭunen, u ukkuẓ nniḍen xesren. Ihi tuɣli terra-d 36 i 5 yettwarehnen, u rrehn s wawal ur yettrebḥ ur yettexsar ma yeffeɣ-d 5 n tikkal deg 36, 13,9%. S zzher yeffeɣ 5 n tikkal deg 37, 13,5%. Amgired-a amecṭuḥ, ddaw n wezgen n tenqiḍt, d ansi d-tekka 2,70% meṛṛa.
S yiwet n tuɣli deg semmus, 0,2 × 36 = 7,2 n yijiṭunen ttuɣalen-d i yal 5 yettwarehnen, +44%. S yiwet deg ukkuẓ, +80%.
D ayagi i yerran asali amecṭuḥ deg tseddi yesɛa azal meqqren, d acuɣer lkazinu ttemdalent rrhun s wawalṭṭablaRrehn s wawalRrehn i yettwanan i ukrupi deg wadeg ad yettwasers s ufus, s umata d rrehn ɣef tegzemt n uḍebsi am voisins neɣ tiers. Daɣen «announced bet».Ɣer akk → zik s rrhun imeqqranen: amgired-a amecṭuḥ d lmaziyya meṛṛa n lkazinu. Imuraren n Ritz n 2004, akken qqaren, rehnen akka.
Thorp yura-d ukkuẓ n tuccḍiwin timanayin deg tifin-is zik, s texxamin: 1,4 seg uktazal n wakud n uqerru yettezzinibenkanAqerru yettezzin (rotor)Aḥric n uḍebsi yettezzin i yeṭṭfen tixxamin.Ɣer akk →, 5,5 seg uktazal n wakud n tkurtibenkanTakurtTakurt tamecṭuḥt i yettwaḍeqqren deg ubrid mgal aqerru yettezzin. Tikurin n tura d ivorine neɣ d Teflon, 18–21 mm.Ɣer akk →, 7 seg uɣelluy n tkurt ɣef yimsenfalenibenkanAmsenfalYiwen seg yiɣunab n wuzzal ɣef tama yeknan i yesseḍrayen takurt mi ara teɣli. Daɣen: canoe, diamond, pin.Ɣer akk → d 6 seg tunṭiḍt deg texxamin. Acḥal i d amatu, d acḥal i rennunt snat n tuccḍiwin n wakud?
Sken-d tifrat
Tiririt Qrib 10,8 n texxamin s umata. War tuccḍiwin n wakud yili d 9,2, ihi snat n tuccḍiwin n wakud rennunt 1,6 kan.
Tuccḍiwin timanayin ur ttemrennunt ara srid; d imkuẓen-nsent i yettemrennun. Tiddi tamagnut n umatu d aẓar amkuẓ n umatu n yimkuẓen: 1,4² + 5,5² + 7² + 6² = 1,96 + 30,25 + 49 + 36 = 117,2, u √117,2 ≈ 10,8.
War snat n tuccḍiwin n wakud: √(49 + 36) = √85 ≈ 9,2.
Amatu n 10,8 n texxamin yella daxel n talast n 17 n texxamin deg tfelwit n usebter-a u yesɛa azal n qrib +34% ɣef yiwen wuṭṭun. Tamsirt i d-yessufeɣ Thorp: mi ara yili uɣelluy ɣef yimsenfalen d tuccḍa tameqqrant akk, aktazal yelhan n wakud ur d-yettawi ara aṭas.
Taḍsa i usgunfu
Tafizikt tetteddu. Akud n rrhun yemdel.
Iɣbula
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Thorp, E. O. “The invention of the first wearable computer.”
- Bass, T. A. The Eudaemonic Pie.
- Small, M. & Tse, C. K. “Predicting the outcome of roulette.”
- Goldman, N. Great Gambling Scams.
- Nevada Revised Statutes, ixef 465.