Enteekateeka ya Fibonacci mu Roulette
Mu nteekateeka ya zzaala eya Fibonacci mu roulette, ssente za zzaala zigoberera 1, 1, 2, 3, 5, 8, 13… Genda mu maaso omutendera gumu oluvannyuma lw'okufiirwa, ddayo emabega emitendera ebiri oluvannyuma lw'okuwangula.
Tewangula nnamuziga; tewali ntegeka ya ssente za zzaala ekikola. Teyanguwa nga Martingale, n'olwekyo egumira ennyiriri z'okufiirwa empanvu nga tennatuuka ku kkomo, era eddamu okuwona mpola. Okufiirwa okusuubirwa kwe kumu, 2.70% ku mugatte gwa zzaalassenteOmugatte gwa zzaalaOmugatte gwa ssente zonna ezisibiddwa mu kiseera ky'okuzannya oba mu bbanga, nga mw'otwalidde n'amagoba agaddamu okusibwa. Era guyitibwa: handle, action.Soma byonna →.
Engeri olunyiriri gye luzimbibwamu
Buli nnamba ye mugatte gw'ennamba ebbiri eziri emabega waayo.
N'olwekyo oluvannyuma lwa 8 ne 13 wajja 21.
Wandiika buli nnamba ng'ekisanduuko ekyenkanankana enjuyi, ebisanduuko bikwatagana: buli kipya kiwanvu ng'ebibiri ebikisooka nga biteekeddwa wamu ku mabbali. Ekitundu ky'enkulungo ekiri mu buli kisanduuko kiyungibwa ne kifuuka enzinga.
Tambula mu lunyiriri
Okufiirwa kukusembeza omutendera gumu ku ddyo. Okuwangula kukuzza emabega emitendera ebiri.
Ssente za zzaala n'ebivuddemu biri mu yuniti za zzaala ey'omusingi.
Enkola ya Fibonacci mu roulette ekola etya?
Wandiika ennamba za FibonaccienteekateekaFibonacciOkulinnyisa zzaala okugoberera olunyiriri 1, 1, 2, 3, 5, 8, 13…: eddaala limu mu maaso oluvannyuma lw'okufiirwa, amadaala abiri emabega oluvannyuma lw'okuwangula.Soma byonna →: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. Buli emu gwe mugatte gw'ebbiri ezigikulembera. Tandikira ku esooka osibe yunitissenteYunitiSsente za zzaala ez'entandikwa enkola oba omuzannyi z'akozesa. Okulinnyisa zzaala kunnyonnyolwa mu yuniti kusobole okukola ku mmeeza yonna.Soma byonna → ezenkana awo. Bw'ofiirwa, ogenda omutendera gumu ku ddyo. Bw'owangula, oddayo emitendera ebiri ku kkono, oba ku ntandikwa singa tewali bbanga. Eyo y'enkola yonna. Emmeeza eraga buli mutendera ky'egula: olunyiriri lw'okufiirwa olukomezebwa ekkomo ly'emmeezaemmeezaEkkomo ly'emmeezaZzaala esinga obutono n'esinga obunene ekkirizibwa. Ekkomo ery'waggulu lye liyimiriza enkola ez'okukubisaamu bbiri.Soma byonna → oba ssente z'okuzannyisassenteSsente z'okuzannyisaOmugatte gwa ssente ezaawulibwa ku lw'okuzannya. Okuddukanya ssente z'okuzannyisa kwe kusalawo omuwendo gw'oteeka mu kabi ku buli zzaala ne mu buli kiseera ky'okuzannya.Soma byonna → zo lufiiriza omugatte gwa byonna ebisibiddwa okutuusa awo.
Ekiseera ky'okuzannya kiba kitya?
Twala $10 ku ntandikwa n'okwetooloola munaana: F F W F F F W W (F = okufiirwa, W = okuwangula). Ssente za zzaala zigenda 10, 10, 20 (owangula, odda emabega ebiri, ku mutendera 1), 10, 10, 20, 30 (owangula, odda emabega ebiri, ku mutendera 2), 10 (owangula, odda ku ntandikwa). Ebyafiirwa: 10 + 10 + 10 + 10 + 20 = 60. Ebyawangulwa: 20 + 30 + 10 = 60. Okufiirwa kutaano, okuwangula kusatu, era oli ku kyenkanyi. Ekyo kye kisikiriza mu nkola eno. Ensaasaanya eri ku lunyiriri lwe lumu: kyetaagisizza zzaala za $120 okutuuka awo, era buli doola esibiddwa erina enkizo ya kaasinookubalaEnkizo ya kaasinoEkitundu kya buli ssente za zzaala kaasino ky'ekuuma ku kigero: 2.70% mu roulette ya Bulaaya.Soma byonna →.
Lwaki odda emabega ebiri, so si emu?
Kubanga okuwangula kumu kusasulira okufiirwa kubiri kwokka. Buli nnamba gwe mugatte gw'ebbiri ezigikulembera, n'olwekyo okuwangula ku yuniti 5 kuzzaawo 2 ne 3 ezaakafiirwa. Lowooza ku madaala: eddaala limu waggulu ku buli kufiirwa, amadaala abiri wansi ku buli kuwangula. Eddaala ly'oyimiriddeko lye bbanja lyo. Ku mutendera 5 oli wansi yuniti 7, ku mutendera 8 oli wansi 33, ate ng'oddeyo ku ddaala erisooka oli ku kyenkanyi ddala. Amagoba gava ku kuwangula ku ddaala erisooka kwokka, yuniti emu omulundi gumu.
Ng'okuwangula kunaatera okwenkana okufiirwa, amadaala abiri ku limu kiwulikika ng'ekirungi, era emirundi egisinga amadaala gakuzzaayo wansi ddala. Ekizibu kiri nti amadaala geeyongera obuwanvu gy'okoma okulinnya. Okuwangula kumi ku ddaala erisooka kuleeta yuniti 10. Okufiirwa kusatu ku mitendera 6, 7 ne 8 kufiiriza 8 + 13 + 21 = 42.
- p10 −$500
- p25 −$500
- wakati −$500
- p75 +$250
- p90 +$920
Enkola ya Fibonacci ekola?
Nedda. Si ng'engeri y'okumaliriza ng'oli waggulu. Okubala kwe kumu nga ku buli nkola: buli zzaala efiirwa 1/37 ku ssente zaayo ku kigero, n'olwekyo olunyiriri lwonna lufiirwa 1/37 ku byonna ebisibiddwa. Okukozesa olunyiriri lwa Fibonacci mu roulette tekukyusa ekyo, kubanga nnamuziga asasula emikisa gye gimu ne bwe cipussenteCipuAkabonero akakiikirira omuwendo ogutakyuka, akateekebwa ku mmeeza ya zzaala okusiba zzaala. Era kayitibwa: check.Soma byonna → eba ya bunene ki. Ssente za zzaala eza Fibonacci zirinnya mpola, n'olwekyo esiba ssente nnyingi buli kwetooloola okusinga zzaala ey'omuwendo gumuenteekateekaZzaala ey'omuwendo gumuOkusiba ssente ze zimu buli kwetooloola. Kye kipimo buli kulinnyisa zzaala kwe kugeraageranyizibwako.Soma byonna →, era okufiirwa okusuubirwaokubalaOkufiirwa okusuubirwaOmuwendo ogusuubirwa nga gukubisiddwamu ssente zonna ezisibiddwa; ssente ez'okufiirwa ku kigero mu kiseera ky'okuzannya oba mu kiseera ekimu.Soma byonna → kwayo buli kiseera ky'okuzannya kusingako. MartingaleenteekateekaMartingaleOkulinnyisa zzaala okukubisaamu zzaala bbiri oluvannyuma lwa buli kufiirwa. Laba ekitundu ky'Enteekateeka za Zzaala okumanya ky'ekola ne ky'etakola.Soma byonna → esiba ssente nnyingi n'okusingawo, era efiirwa nnyingi.
Terimu kabi kanene okusinga Martingale?
Egenda mpola, ekitali kye kimu. Ssente za zzaala eza Fibonacci zeeyongera nga emirundi 1.6× buli mutendera mu kifo kya 2×, n'olwekyo ekkomo lya $500 lituukibwako oluvannyuma lw'okufiirwa nga kumi omuddiriŋŋanwa okuva ku $10, mu kifo ky'omukaaga. Ekyo kifuula olwazi okubaawo emirundi mitono: okufiirwa zzaala za emu ku emu kumi omuddiriŋŋanwa kuba (19/37)¹⁰ ≈ 0.13%, ate omukaaga (19/37)⁶ ≈ 1.8%. Naye olwazi era luwanvuwa, kubanga ssente nnyingi ziba zisibiddwa mu kkubo okutuuka awo, era okuwangula kumu tekukuzzaawo.
Ennamba zino zaava wa?
Mu kikokko ku bayaayaana. Leonardo ow'e Pisa, oluvannyuma eyatuumibwa Fibonacci, yakissa mu kitabo kye Liber Abaci mu 1202: tandika n'abayaayaana babiri, leka buli babiri bazaale babiri abapya buli mwezi okuva ku mwezi gwabwe ogw'okubiri, obale emigogo. Okuddamu kugenda 1, 2, 3, 5, 8, 13. Si ye yasooka okuzuula etteeka lino. Abayivu b'e Buyindi abaasoma ennyimba z'ebitontome baali baliwandiise edda: Singh (1985) alizza ku Virahanka, wakati wa 600 ne 800, n'oluvannyuma ku Gopala ne Hemachandra.
Tewali n'omu ku bo yali alowooza ku nnamuziga. Ensonda ezikozesebwa wano teziyogera ani eyasooka okusiba ssente ng'agoberera olunyiriri luno. Kye ziraga kiri nti okubala kwalwo n'okubala kwa roulette tebisisinkana: okumu kulaga ssente za zzaala bwe zeeyongera, okulala kulaga buli zzaala ky'ezzaayo.
Ssente mmeka ezifiirwa oluvannyuma lw'olunyiriri lw'okufiirwa?
Amateeka abiri gafuula emmeeza waggulu ennyangu okukebera. Oluvannyuma lw'okufiirwa n omuddiriŋŋanwa, ebifiiriddwa byonna ye nnamba ya Fibonacci ey'ekifo (n + 2) ng'oggyeko 1, ekiwa 1, 2, 4, 7, 12, 20 n'ebirala, ate ssente za zzaala eziddako ye nnamba ya Fibonacci ey'ekifo (n + 1). Bollman (2021) akakasa ekivaamu kye kimu ng'akozesa induction ku lunyiriri olutandika 1, 2, 3, ekisengula buli nnamba ekifo kimu. Ku kkomo lya yuniti 500 ng'otandikira ku yuniti 1, Martingale tesobola kusiba zzaala yaayo ey'e 10, yuniti 512. Fibonacci esobola okusiba ey'e 14, yuniti 377, naye si ey'e 15, 610.
Kiki ekikyuka ku dazeni oba ku mpagi?
Ku dazenizzaalaDazeni1–12, 13–24 oba 25–36, esasula 2:1.Soma byonna → oba ku mpagizzaalaEmpagiEnnamba kkumi na bbiri mu mpagi emu eyimiridde ku mmeeza ya zzaala, esasula 2:1.Soma byonna →, esasula 2 ku 1, okudda emabega tekwetaagisa. Okuwangula ku ssente za zzaala F kusasula 2F, ekisinga bulijjo byonna ebyafiirwa emabega, n'olwekyo buli kuwangula kumaliriza olunyiriri ng'oli waggulu. Omuwendo gwe kino kigula guli nti dazeni ewangula emirundi 12 gyokka ku 37, n'olwekyo ennyiriri z'okufiirwa empanvu zibaawo nnyo nnyini: okufiirwa ku dazeni kkumi na nnya omuddiriŋŋanwa kubaawo nga omulundi gumu ku kugezaako 242, ate ku mmyufuzzaalaEmmyufuZzaala ya emu ku emu ku nnamba 18 emmyufu. Mu Lufalansa: rouge.Soma byonna → nga omulundi gumu ku 11,000.
Ate bw'okoma oluvannyuma lw'okuwangula emirundi ebiri omuddiriŋŋanwa kyokka?
Engeri endala egenda omutendera gumu mu maaso oluvannyuma lwa buli kwetooloola, ng'owangudde oba ofiiriddwa, era ekoma oluvannyuma lw'okuwangula emirundi ebiri omuddiriŋŋanwa kyokka. Ng'olina okufiirwa n nga okuwangula okubiri tekunnaba, amagoba ye nnamba ya Fibonacci ey'ekifo (n + 1) ng'ogasseeko 1: matono okuwangula bwe kujja mangu, mangi bwe kujja ekikeerezi, era gawangulwa ku ssente za zzaala ezikuze okugenderako. Okuwangula okubiri okujja mangu bulijjo kujja ku ssente za zzaala entono; okujja ekikeerezi kuyinza okwetaaga zzaala ennene ddala mu kiseera ekyo ekiseera ky'okuzannya we kisinga okuba ekibi.
Ekyokugezesa · Fibonacci
Ebiseera by'okuzannya 2,000 ebya zzaala ya emu ku emu, nga otandika ne ssente z'okuzannyisa $1,000.
Zzaala ey'omusingi $10 · ekkomo ly'emmeeza $500 · okwetooloola 100 mu buli kiseera
Okufiirwa okuddiriŋŋana kujja emirundi emeka
Zzaala ya emu ku emu ku nnamuziga wa zeero emu efiirwa okwetooloola 19 ku 37. Buli lunyiriri bwe busoboka nti okwetooloola okuddiriŋŋana kwonna kufiirwa, n'ebyo omuzannyi wa Fibonacci, atambula omutendera gumu mu lunyiriri oluvannyuma lwa buli kufiirwa, by'abeera afiiriddwa olwo.
| okufiirwa okuddiriŋŋana | obusoboka | nga 1 ku | ebifiiriddwa okutuusa kati | zzaala eddako |
|---|---|---|---|---|
| 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 |
Obusoboka buba 19/37 nga bukubisibwamu bwokka omulundi gumu ku buli kufiirwa, nga bubalibwa okuva ku kwetooloola kumu okumanyiddwa. Ekiseera ky'okuzannya ekiwanvu kirimu okwetooloola kungi awayinza okutandikira okufiirwa okw'engeri eyo, kale mu kiro kimu kisoboka nnyo okusinga olunyiriri olumu bwe lulaga.
Ebibuuzo
Weewaawo: mu maaso oluvannyuma lw'okuwangula, emabega oluvannyuma lw'okufiirwa. Ekola nga ParolienteekateekaParoliOkulinnyisa oluvannyuma lw'okuwangula: kubisaamu emirundi ebiri ng'owangudde, ddayo ku ntandikwa ng'ofiiriddwa oba ng'owangudde emirundi esatu egiddiriŋŋana. Era eyitibwa: Martingale ey'ekifuulannenge.Soma byonna → egenda mpola.
Okwesanyusa n'Okubala
Gezaako bino ggwe kennyini okusooka. Buli kugonjoola kuzingiddwa; kuggulewo ng'oli mwetegefu.
Zannya enkola ekyusa endala etambula eddaala limu ku lunyiriri oluvannyuma lwa buli kwetooloola, ng'owangudde oba ng'ofiiriddwa, era ekoma oluvannyuma lw'okuwangula kubiri nga kuddiriŋŋana: ssente za zzaala 1, 1, 2, 3, 5, 8 n'ebirala. Ebivaamu kkumi na bina ebisooka biri W F W F F F W F F F W F F W (W = okuwangula, F = okufiirwa). Oyimiridde wa, era zzaala eddako y'eruwa?
Laga okugonjoola
Eky'okuddamu Ofiiriddwa yunitissenteYunitiSsente za zzaala ez'entandikwa enkola oba omuzannyi z'akozesa. Okulinnyisa zzaala kunnyonnyolwa mu yuniti kusobole okukola ku mmeeza yonna.Soma byonna → 22. Zzaala eddako ya yuniti 610, era okuwangula kwandikomezza ekiseera ky'okuzannya ng'oli waggulu ne 588.
Ssente za zzaala ze nnamba kkumi na nnya ezisooka eza FibonaccienteekateekaFibonacciOkulinnyisa zzaala okugoberera olunyiriri 1, 1, 2, 3, 5, 8, 13…: eddaala limu mu maaso oluvannyuma lw'okufiirwa, amadaala abiri emabega oluvannyuma lw'okuwangula.Soma byonna →: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ne 377. Gatta okuwangula oggyeemu okufiirwa: +1 −1 +2 −3 −5 −8 +13 −21 −34 −55 +89 −144 −233 +377 = −22.
Ekivuddemu ekisembayo kwali kuwangula, n'olwekyo okuwangula okumu okulala kukikomya. Ssente za zzaala eziddako ze 610: okuwangula kulekawo +588, okufiirwa kulekawo −632 ne zzaala eddako eya 987.
Enkola eno bulijjo ekoma ng'oli waggulu, naye wano eyetaaga zzaala ya yuniti 610 okukikola. Wansi w'amateeka aga bulijjo, amadaala abiri okudda emabega oluvannyuma lw'okuwangula, ebivaamu ebyo kkumi na bina bikulekawo ng'ofiiriddwa yuniti 1 yokka ne zzaala eddako eya 2. Bollman (2021), atandika olunyiriri ku 1, 2, 3, afuna okufiirwa 1 ne zzaala eddako eya 3. Amateeka aga bulijjo gafiirwa kitono wano kubanga buli kuwangula kukkakkanya ssente za zzaala.
okwetooloolassente za zzaalaekivuddemuomugatte ogugenda11W+121F032W+243F−155F−668F−14713W−1821F−22934F−561055F−1111189W−2212144F−16613233F−39914377W−22Mu nkola eyo y'emu, lwaki okufiirwa n nga kuddiriddwa okuwangula kubiri bulijjo kulekawo amagoba ga nnamba ya Fibonacci ey'(n + 1) n'ogattako 1?
Laga okugonjoola
Eky'okuddamu Okufiirwa n kugattibwa ne kufuuka ennamba ya Fibonacci ey'(n + 2) ng'oggyeeko 1, era okuwangula kubiri ze nnamba ebbiri eziddako, ezigisinga awamu n'ennamba ey'(n + 1) n'ogattako 1.
Wandiika F₁, F₂, F₃ … ku 1, 1, 2, 3, 5 … Buli nnamba gwe mugatte gw'ebbiri ezigikulembera.
Okufiirwa: F₁ + F₂ + … + Fₙ. Gattako 1 ku mugatte ogwo, ewandiikiddwa nga F₂, era gukendeera: F₂ + F₁ = F₃, olwo F₃ + F₂ = F₄, n'ebirala, okutuusa omugatte gwonna lwe guba Fₙ₊₂. N'olwekyo okufiirwa kwonna kuli Fₙ₊₂ − 1.
Okuwangula ze ssente za zzaala ebbiri eziddako, Fₙ₊₁ ne Fₙ₊₂. Amagoba: Fₙ₊₁ + Fₙ₊₂ − (Fₙ₊₂ − 1) = Fₙ₊₁ + 1. N'okufiirwa kuna, ekyo kye F₅ + 1 = yuniti 6.
Eky'okusesa
Omugerageranyo ogwa zaabu gusisinkana ekipande kya zzaala esinga obunene.
Ensibuko
- RouletteDoc. Ennyinnyonnyola y'enteekateeka ya zzaala n'ebyokulabirako.
- Roulette77. Ennyinnyonnyola y'enteekateeka ya zzaala n'ebyokulabirako.
- 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.