Tastratijit Fibonacci
Deg tstratijit Fibonacci n rulit, idrimen n rrehn ḍefren 1, 1, 2, 3, 5, 8, 13… Ddut yiwet n tseddart ɣer zdat deffir lexsara, snat ɣer deffir deffir rrbeḥ.
Ur tettɣellib ara aḍebsi; ulac ahil n rrhun i t-yeɣlben. D tin yugaren Martingale deg leɛqel, ihi tettqawem azrar n lexsarat aɣezfan uqbel ad tawweḍ ɣer talast, u tettuɣal s leɛqel ugar. Lexsara yettwaṛǧan d yiwet: 2,70% 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 →.
Amek yettwabna umyizwer
Yal uṭṭun d amatu n sin i t-yezwaren.
Ihi deffir 8 d 13 ad d-yas 21.
Sunɣet yal uṭṭun d amkuẓ, ad walim imkuẓen ttemlilen: yal amaynut yeɣzif am sin i t-yezwaren yettwasersen yiwen ɣer tama n wayeḍ. Rbeɛ n twinest ɣef yal amkuẓ ttemlilen, d tanezzayt.
Ḍfer amyizwer
Lexsara tesseddu yiwet n tseddart ɣer yeffus. Rrbeḥ yessuɣal snat n tseddarin ɣer deffir.
Rrhun d yigmaḍ s yiferdisen n rrehn n tazwara.
Amek yeddu unagraw Fibonacci n rulit?
Arut uṭṭunen n FibonaccitastratijitFibonacciAnagraw n usnerni i yeḍfaren umuɣ 1, 1, 2, 3, 5, 8, 13…: yiwen usurif ɣer zdat deffir lexsara, sin ɣer deffir deffir rrbeḥ.Ɣer akk →: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. Yal yiwen d amatu n sin i t-yezwaren. Bdut seg umezwaru u rhent amḍan-nni n yiferdisenidrimenAferdisRrehn agejdan s wacu i yettxeddem unagraw neɣ amurar. Inagrawen n usnerni ttwaglamen s yiferdisen akken ad ilin i yal ṭṭabla.Ɣer akk →. Ma texsrem, ad tedum yiwet n tseddart ɣer yeffus. Ma trebḥem, ad tedum snat n tseddarin ɣer zelmeḍ, neɣ ɣer tazwara ma ulac amkan. D wa i d anagraw meṛṛa. Tafelwit tesskan-d acḥal tettkellif yal taseddart: azrar n lexsarat i yeḥbes talast n ṭṭablaṭṭablaTalast n ṭṭablaRrehn adday d rrehn afellay i yettwasirgen. Talast tafellayt d ayen i yeḥebsen inagrawen n usnegmu.Ɣer akk → 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 yexser amatu n wayen meṛṛa yettwarehnen ar tura.
Amek tettban taɣimit?
Ṭṭfet lsas n $10 d tam n tuzzyiwin: X X R X X X R R. Idrimen n rrehn ddan 10, 10, 20 (rbeḥ, snat ɣer deffir, ɣer tseddart 1), 10, 10, 20, 30 (rbeḥ, snat ɣer deffir, ɣer tseddart 2), 10 (rbeḥ, ɣer tazwara). Ayen yexsren: 10 + 10 + 10 + 10 + 20 = 60. Ayen yerbḥen: 20 + 30 + 10 = 60. Semmus n lexsarat, kraḍ n rrbeḥ, u ulac rrbeḥ ulac lexsara. D wa i yesseɛǧaben deg unagraw. Ssuma tella deg yiwen ujerriḍ-nni: yewwi $120 n rrhun akken ad tawwḍem ɣer dinna, u yal dular yettwarehnen yesɛa lmaziyya n lkazinutusnaktLmaziyya n lkazinuAḥric n yal rrehn i teṭṭef lkazinu s ulemmas: 2,70% deg rulit tawrupit.Ɣer akk →.
Acuɣer snat n tseddarin ɣer deffir, mačči yiwet?
Acku yiwen n rrbeḥ ixelleṣ snat n lexsarat, ur yugar ur yenqis. Yal uṭṭun d amatu n sin i t-yezwaren, ihi rrbeḥ ɣef 5 n yiferdisen yettarra-d 2 d 3 yexsren uqbel. Xemmet ɣef tseddarin: yiwet ɣer ufella i yal lexsara, snat ɣer wadda i yal rrbeḥ. Taseddart ɣef tbeddem d ttrusi-nwen. Deg tseddart 5 txesrem 7 n yiferdisen, deg tseddart 8 txesrem 33, u mi ara tuɣalem ɣer tseddart tamezwarut ulac rrbeḥ ulac lexsara ula s yiwen uferdis. Rrbeḥ yettas-d kan seg rrbeḥ ɣef tseddart tamezwarut, yiwen uferdis yal tikkelt.
S qrib amḍan n rrbeḥ am win n lexsarat, snat n tseddarin i yiwet yettban d lfayda, u s waṭas n tikkal tiseddarin rrant-awen-d ɣer wadda. Ugur d belli tiseddarin ttimɣurent mi ara tettalim. Mraw n rrbeḥ ɣef tseddart tamezwarut ttawin-d 10 n yiferdisen. Kraḍ n lexsarat deg tseddarin 6, 7 d 8 ttkellifent 8 + 13 + 21 = 42.
- p10 −$500
- p25 −$500
- azal n tlemmast −$500
- p75 +$250
- p90 +$920
Anagraw Fibonacci yeddu?
Ala. Mačči d abrid n tuffɣa s rrbeḥ. Leḥsab d yiwen i yal anagraw: yal rrehn yexser 1/37 n udrim-is s ulemmas, ihi amtawal meṛṛa yexser 1/37 n wayen meṛṛa yettwarehnen. Aseqdec n umtawal n Fibonacci deg rulit ur ibeddel ara aya, acku aḍebsi ixelleṣ yiwen n ussaɣ akken yebɣu yili wazal n ujiṭunidrimenAjiṭunTamatart i d-yemmalen azal yettwasbedden, yettwasersen ɣef tfelwit akken ad yili rrehn. Daɣen: check.Ɣer akk →. Idrimen n rrehn n Fibonacci ttalin cwiṭ s cwiṭ, ihi yessers ugar i yal tuzzya n rrehn ur nettbeddiltastratijitRrehn ur nettbeddilRrehn n yiwen wazal deg yal tuzzya. D aswir ɣer wacu i yettwaserwas yal anagraw n usnerni.Ɣer akk →, u lexsara yettwaṛǧantusnaktLexsara yettwaṛǧanAzal yettwaṛǧan seg tmerna n yidrimen yettwarhen; d alemmas n wayen yettwaxsar deg yiwet n tɣimit neɣ deg yiwen wakud.Ɣer akk →-is i yal taɣimit tugar. MartingaletastratijitMartingaleAnagraw n usnerni i yessneggmen rrehn deffir yal lexsara. Walit taggayt n tstratijit i wayen i yettxemmem d wayen ur yettxemmim ara.Ɣer akk → yessers ugar, u yexser ugar.
Ur yesɛi ara lxeṭṛ am Martingale?
D win yugaren s leɛqel, mačči d yiwet n tɣawsa. Idrimen n rrehn n Fibonacci ttimɣuren azal n 1,6× i yal taseddart deg wadeg n 2×, ihi talast n $500 tettwaweḍ deffir azal n mraw n lexsarat yemmeḍfaren seg lsas n $10 mačči sḍis. Aya yerra iɣzer drus ugar: mraw n lexsarat s lexlaṣ imsawi yemmeḍfaren d (19/37)¹⁰ ≈ 0,13%, mgal (19/37)⁶ ≈ 1,8% i sḍis. Maca iɣzer yugar deg tɣuzi, acku ttwarehnen ugar deg ubrid, u yiwen n rrbeḥ ur t-yessefsax ara.
Ansi i d-kkan wuṭṭunen?
Seg ugur ɣef yiwtal. Leonardo n Pisa, i d-yettusemman ticki Fibonacci, yura-t deg Liber Abaci-ines n 1202: bdut s yiwet n tyugit, ǧǧet yal tayugit ad d-tefk tayugit tamaynut yal ayyur seg wayyur-is wis sin, u ḥesbet tiyugiwin. Tiririt tedda 1, 2, 3, 5, 8, 13. Mačči d netta i d amezwaru i yufan alugen. Imusnawen n Lhend n uẓawan n tmedyazt uran-t-id uqbel: Singh (1985) yerra-t ɣer Virahanka, gar 600 d 800, syin ɣer Gopala d Hemachandra.
Ulac yiwen deg-sen i yesɛan aḍebsi deg uqerru-s. Iɣbula i yettwasseqdacen da ur d-nnin ara anwa i yezwaren ad yerhen idrimen s umtawal. Ayen i d-sskanen d belli leḥsab-is d leḥsab n rulit ur mlalen ara: yiwen yenna-d amek ttimɣuren yedrimen n rrehn, wayeḍ yenna-d acu i d-yettarra yal adrim n rrehn.
Acḥal i yexsren deffir azrar n lexsarat?
Snat n tegdawalin rrant tafelwit i yellan nnig fessus i usenqed. Deffir n n lexsarat yemmeḍfaren, amatu yexsren d uṭṭun wis (n + 2) n Fibonacci kkes 1, ayen i d-yettaken 1, 2, 4, 7, 12, 20 atg., u rrehn i d-iteddun d uṭṭun wis (n + 1) n Fibonacci. Bollman (2021) yessefhem-d yiwen ugmuḍ-nni s usuddem i umtawal i yebdan s 1, 2, 3, ayen yessenqalen yal uṭṭun s yiwen umkan. S talast n 500 n yiferdisen seg tazwara n 1 uferdis, Martingale ur yezmir ara ad isers rrehn-is wis 10, 512 n yiferdisen. Fibonacci yezmer ad isers wis 14, 377 n yiferdisen, maca mačči wis 15, 610.
Acu ibeddlen ɣef ddzina neɣ tagejdit?
Ɣef ddzinarrehnDdzina1–12, 13–24 neɣ 25–36, ixelleṣ 2:1.Ɣer akk → neɣ tagejditrrehnTagejditTnac n wuṭṭunen deg yiwet n tgejdit tubdidt n tfelwit, ixelleṣ 2:1.Ɣer akk →, i yettxelliṣen 2 ɣef 1, tuɣalin ɣer deffir ur tesɛi ara azal. Rrbeḥ s udrim F ixelleṣ 2F, i yugaren yal tikkelt ayen meṛṛa yexsren uqbel-is, ihi yal rrbeḥ yettfakk amtawal s rrbeḥ. Ssuma-s d belli ddzina tettrebḥ kan 12 n tikkal seg 37, ihi izrar iɣezfanen n lexsarat ttilin s waṭas ugar: ṛbeɛṭac n lexsarat ɣef ddzina yemmeḍfaren ttilin azal n yiwet n tikkelt seg 242 n yineɛruḍen, mgal azal n yiwet n tikkelt seg 11 000 i uzeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk →.
Ma teḥbsem kan deffir sin n rrbeḥ yemmeḍfaren?
Tawsit nniḍen tetteddu yiwet n tseddart ɣer zdat deffir yal tuzzya, rbeḥ neɣ xser, u tettḥbis kan deffir sin n rrbeḥ yemmeḍfaren. S n n lexsarat uqbel sin n rrbeḥ, rrbeḥ d uṭṭun wis (n + 1) n Fibonacci rnu 1: amecṭuḥ mi ara d-asen rrbeḥ zik, ameqqran mi ara d-asen ticki, u yettwarbeḥ ɣef yedrimen n rrehn i yimɣuren s waya. Tayugit n rrbeḥ i d-yusan zik tettas-d yal tikkelt s yedrimen imecṭaḥ; tin i d-yusan ticki tezmer ad tesra rrehn ameqqran deg tallit anda taɣimit tewweḍ ɣer diri-ines.
Asimulatur · Fibonacci
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 Fibonacci, i yettedduyen yiwet n tseddart deg umyizwer deffir yal lexsara.
| lexsarat ṭṭafarent | taprubabilit | qrib 1 seg | lexsara ar tura | rrehn d-iteddun |
|---|---|---|---|---|
| 1 | 51,4% | 2 | $1 | $1 |
| 2 | 26,4% | 4 | $2 | $2 |
| 3 | 13,5% | 7 | $4 | $3 |
| 4 | 7,0% | 14 | $7 | $5 |
| 5 | 3,6% | 28 | $12 | $8 |
| 6 | 1,8% | 55 | $20 | $13 |
| 7 | 0,94% | 106 | $33 | $21 |
| 8 | 0,48% | 207 | $54 | $34 |
| 9 | 0,25% | 403 | $88 | $55 |
| 10 | 0,13% | 784 | $143 | $89 |
| 11 | 0,065% | 1527 | $232 | $144 |
| 12 | 0,034% | 2974 | $376 | $233 |
| 13 | 0,017% | 5792 | $609 | $377 |
| 14 | 0,0089% | 11279 | $986 | $610 |
| 15 | 0,0046% | 21965 | $1 596 | $987 |
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
Ih: ɣer zdat deffir rrbeḥ, ɣer deffir deffir lexsara. Yetteddu am ParolitastratijitParoliAsnerni deffir rrbeḥ: snegmu deffir rrbeḥ, wennez deffir lexsara neɣ deffir kraḍ n rrbeḥ yemmeḍfaren. Daɣen: Martingale tamettiwt.Ɣer akk → i yetteddun s ttawil ugar.
Urar s tusnakt
Ɛerḍet-tent s yiman-nwen qbel. Yal tifrat tettwaffer; ldit-tt mi ara tilim twejdem.
Urart s lqem i yettedduyen yiwet n tseddart deg umyizwer deffir yal tuzzya, s rrbeḥ neɣ s lexsara, u yettḥebbis deffir snat n rrbeḥ ṭṭafarent: rrhun 1, 1, 2, 3, 5, 8 d wiyaḍ. Rbeɛṭac n yigmaḍ imezwura d R X R X X X R X X X R X X R. Anda tellam, d acu i d rrehn d-iteddun?
Sken-d tifrat
Tiririt Texsrem 22 n yiferdisenidrimenAferdisRrehn agejdan s wacu i yettxeddem unagraw neɣ amurar. Inagrawen n usnerni ttwaglamen s yiferdisen akken ad ilin i yal ṭṭabla.Ɣer akk →. Rrehn d-iteddun d 610 n yiferdisen, u rrbeḥ ad yessekfu taɣimit s 588 n rrbeḥ.
Rrhun d rbeɛṭac n wuṭṭunen imezwura n FibonaccitastratijitFibonacciAnagraw n usnerni i yeḍfaren umuɣ 1, 1, 2, 3, 5, 8, 13…: yiwen usurif ɣer zdat deffir lexsara, sin ɣer deffir deffir rrbeḥ.Ɣer akk →: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 d 377. Rnut rrbeḥ u kkset lexsarat: +1 −1 +2 −3 −5 −8 +13 −21 −34 −55 +89 −144 −233 +377 = −22.
Agmuḍ aneggaru d rrbeḥ, ihi yiwen n rrbeḥ nniḍen ad tt-yessekfu. Rrehn d-iteddun d 610: rrbeḥ ad yeǧǧ +588, lexsara ad teǧǧ −632 d rrehn d-iteddun n 987.
Lqem-a yettfakka yal tikkelt s rrbeḥ, maca dagi yesra rrehn n 610 n yiferdisen akken ad t-yaweḍ. S yilugan imagnuten, snat n tseddarin ɣer deffir deffir rrbeḥ, rbeɛṭac-nni n yigmaḍ ad ǧǧen kan lexsara n 1 n uferdis s rrehn d-iteddun n 2. Bollman (2021), i yebdan amyizwer s 1, 2, 3, yufa-d lexsara n 1 d rrehn d-iteddun n 3. Ilugan imagnuten xesren drus dagi acku yal rrbeḥ yessenqas rrhun.
tuzzyaadrim n rrehnagmuḍamatu ar tura11R+121X032R+243X−155X−668X−14713R−1821X−22934X−561055X−1111189R−2212144X−16613233X−39914377R−22Deg lqem-nni yiwen, acuɣer n n lexsarat sdeffir-sent snat n rrbeḥ ttaǧǧant yal tikkelt rrbeḥ yemṣadan d wuṭṭun wis (n + 1) n Fibonacci yernan 1?
Sken-d tifrat
Tiririt Lexsarat-nni n n ttemrennunt d uṭṭun wis (n + 2) n Fibonacci ma nekkes 1, u snat-nni n rrbeḥ d sin wuṭṭunen d-iteddun, i yugaren ayagi s wuṭṭun wis (n + 1) yernan 1.
Arut F₁, F₂, F₃ … i 1, 1, 2, 3, 5 … Yal uṭṭun d amatu n sin i t-yezwaren.
Lexsarat: F₁ + F₂ + … + Fₙ. Rnut 1 ɣer umatu-a, s talɣa n F₂, ad yettwasdukkel s yiwet s yiwet: F₂ + F₁ = F₃, syin F₃ + F₂ = F₄, akka ar ad yuɣal umatu meṛṛa d Fₙ₊₂. Ihi lexsarat ttemrennunt d Fₙ₊₂ − 1.
Rrbeḥ d sin n rrhun d-iteddun, Fₙ₊₁ d Fₙ₊₂. Rrbeḥ ačuran: Fₙ₊₁ + Fₙ₊₂ − (Fₙ₊₂ − 1) = Fₙ₊₁ + 1. S ukkuẓ n lexsarat, d F₅ + 1 = 6 n yiferdisen.
Taḍsa i usgunfu
Assaɣ n ureɣ yemlal d tfelwit n rrehn ameqqran.
Iɣbula
- RouletteDoc. Aglam n tstratijit d yimedyaten.
- Roulette77. Aglam n tstratijit d yimedyaten.
- 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.
- Sigler, L. E. Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation.
- Singh, P. The so-called Fibonacci numbers in ancient and medieval India.