Te Rautaki Rūreti Fibonacci
I te rautaki rūreti Fibonacci, ka whai ngā moni peti i te 1, 1, 2, 3, 5, 8, 13… Kotahi te hīkoi whakamua i muri i te hinga, e rua whakamuri i muri i te toa.
Kāore e hinga i a ia te wīra; kāore he mahere moni peti e pērā ana. He ngāwari ake i te Martingale, nā reira ka ora roa ake i ngā raupapa hinga i mua i te taenga ki te tepe, ā, he pōturi ake te whakaora. Ko te ngaronga tūmanako he 2.70% tonu o te tapeke petimoniTapeke petiTe tapeke o te moni kua petihia i roto i te wā tākaro, i tētahi wā rānei, tae atu ki ngā moni toa kua petihia anō. Arā anō: handle, action.Pānuitia katoatia →.
Te hanganga o te raupapa
Ko ia tau te tapeke o ngā tau e rua i mua i a ia.
Nō reira, i muri i te 8 me te 13 ko te 21.
Tuhia ia tau hei tapawhā, ā, ka tōtika te noho tahi o ngā tapawhā: he ōrite te roa o ia tapawhā hou ki ngā mea e rua i mua i a ia ina whakatakotoria taha ki te taha. Ka hono ngā hauwhā porowhita puta noa i ia tapawhā hei kōiri.
Hīkoitia te raupapa
Ka neke te hinga kotahi te hīkoi ki te matau. Ka neke te toa e rua ngā hīkoi whakamuri.
Ko ngā moni peti me ngā hua he wae o te peti taketake.
Ka pēhea te mahi a te pūnaha rūreti Fibonacci?
Tuhia ngā tau FibonaccirautakiFibonacciHe kauneke e whai ana i te raupapa 1, 1, 2, 3, 5, 8, 13…: kotahi te hīkoi whakamua i muri i te hinga, e rua ngā hīkoi whakamuri i muri i te toa.Pānuitia katoatia →: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. Ko ia tau te tapeke o ngā tau e rua i mua i a ia. Tīmata i te tuatahi, ā, petihia taua maha o ngā waemoniWaeTe moni peti taketake e mahi ai tētahi pūnaha, tētahi kaitākaro rānei. Ka whakaahuatia ngā kauneke ki ngā wae kia hāngai ai ki ia tēpu.Pānuitia katoatia →. Ki te hinga, ka neke koe kotahi te hīkoi ki matau. Ki te toa, ka neke koe e rua ngā hīkoi ki mauī, ki te tīmatanga rānei mēnā kāore he wāhi. Koinā te pūnaha katoa. E whakaatu ana te tūtohi i te utu o ia hīkoi: ko te raupapa hinga ka poroa e te tepe tēputēpuTepe tēpuTe peti iti rawa me te peti nui rawa ka whakaaetia. Ko te tepe nui te mea e aukati ana i ngā kauneke whakarua.Pānuitia katoatia →, e tō pūtea tākaromoniPūtea tākaroTe katoa o te moni kua wehea mō te tākaro. Ko te whakahaere pūtea tākaro te whakatau i te nui e tūraru ai i ia peti, i ia wā tākaro.Pānuitia katoatia → rānei, ka ngaro te tapeke o ngā mea katoa kua petihia i taua wā.
He pēhea te āhua o tētahi wā tākaro?
Tangohia he $10 taketake me ngā hurihanga e waru: H H T H H H T T (H = hinga, T = toa). Ko ngā moni peti: 10, 10, 20 (toa, hoki e rua, ki te hīkoi 1), 10, 10, 20, 30 (toa, hoki e rua, ki te hīkoi 2), 10 (toa, hoki ki te tīmatanga). Kua ngaro: 10 + 10 + 10 + 10 + 20 = 60. Kua riro: 20 + 30 + 10 = 60. E rima ngā hinga, e toru ngā toa, ā, kua ōrite koe. Koinā te kukume o te pūnaha. Kei taua rārangi anō te utu: e $120 ngā peti i hiahiatia kia tae ki reira, ā, ka mau ia tāra i petihia i te painga o te wharepāngarauPainga o te whareTe wāhanga o ia moni peti ka puritia e te whare petipeti i te toharite: 2.70% i te rūreti Ūropi.Pānuitia katoatia →.
He aha e hoki ai e rua ngā hīkoi, kaua ko te kotahi?
Nā te mea ka utua e te toa kotahi ngā hinga e rua tonu. Ko ia tau te tapeke o ngā tau e rua i mua i a ia, nā reira ko te toa i te 5 wae ka whakahoki i te 2 me te 3 i ngaro i mua tata. Whakaarohia he arawhata: kotahi te hīkoi whakarunga mō ia hinga, e rua ngā hīkoi whakararo mō ia toa. Ko te hīkoi e tū ana koe ko tō nama. I te hīkoi 5, kua heke koe e 7 wae; i te hīkoi 8, kua heke e 33; ā, ina hoki ki te hīkoi tuatahi, kua ōrite tonu koe. Ka puta te huamoni i ngā toa i te hīkoi tuatahi anake, kotahi te wae i ia wā.
I te mea he tata ōrite te maha o ngā toa me ngā hinga, ko ngā hīkoi e rua mō te kotahi he āhua utu pai, ā, i te nuinga o te wā ka arahina koe e te arawhata ki raro anō. Ko te mahanga, ka teitei ake ngā hīkoi i a koe e piki ana. Ko ngā toa tekau i te hīkoi tuatahi ka whiwhi 10 wae. Ko ngā hinga e toru i ngā hīkoi 6, 7 me 8 ka utu 8 + 13 + 21 = 42.
- p10 −$500
- p25 −$500
- tau waenga −$500
- p75 +$250
- p90 +$920
Ka whai hua rānei te pūnaha Fibonacci?
Kāo. Ehara i te huarahi kia puta me te huamoni. He ōrite te tātai ki tō ia pūnaha: ka ngaro i ia peti te 1/37 o tōna moni peti i te toharite, nā reira ka ngaro i te raupapa katoa te 1/37 o ngā moni katoa i petihia. Ko te whakamahi i te raupapa Fibonacci i te rūreti kāore e huri i tēnā, nā te mea he ōrite ngā tūpono ka utua e te wīra ahakoa te rahi o te maramaramoniMaramaraHe tohu e tohu ana i tētahi moni pūmau, ka whakatakotoria ki te mahere peti hei peti. Arā anō: check.Pānuitia katoatia →. Ka nuku whakarunga ngā moni peti Fibonacci, nā reira he nui ake tāna e peti ana ia hurihanga i tō te peti papatahirautakiPeti papatahiTe peti i te moni ōrite i ia hurihanga. Koia te paerewa e whakatairitea ai ia kauneke.Pānuitia katoatia →, ā, he nui ake tōna ngaronga tūmanakopāngarauNgaronga tūmanakoTe uara tūmanako whakareatia ki te tapeke o te moni kua petihia; te moni toharite ka ngaro i roto i te wā tākaro, i tētahi wā rānei.Pānuitia katoatia → ia wā tākaro. He nui ake anō tā te MartingalerautakiMartingaleHe kauneke e whakarua ana i te peti i muri i ia hinga. Tirohia te wāhanga Rautaki mō ōna mahi me ngā mea kāore e mahia e ia.Pānuitia katoatia → e peti ana, ā, he nui ake tāna e ngaro ana.
He haumaru ake rānei i te Martingale?
He pōturi ake, ehara i te mea ōrite. Ka tupu ngā moni peti Fibonacci kia 1.6× pea ia hīkoi, kaua ko te 2×, nā reira ka taea te tepe $500 i muri i ngā hinga karapīpiti tekau pea mai i te $10 taketake, kaua ko te ono. Nā tēnā ka onge ake te pari: ko ngā hinga utu ōrite tekau karapīpiti he (19/37)¹⁰ ≈ 0.13%, ki te (19/37)⁶ ≈ 1.8% mō te ono. Engari he teitei ake anō te pari, nā te mea he nui ake kua petihia i te ara ki reira, ā, kāore te toa kotahi e whakakore i a ia.
I ahu mai ngā tau i hea?
Mai i tētahi panga mō ngā rāpeti. Nā Leonardo o Pisa, i tapaina i muri mai ko Fibonacci, i whakatakoto i tōna Liber Abaci o 1202: tīmata ki te takirua kotahi, waiho kia whakaputa ia takirua i tētahi takirua hou ia marama mai i tōna marama tuarua, ā, tatauria ngā takirua. Ko te whakautu 1, 2, 3, 5, 8, 13. Ehara ko ia te tuatahi i kite i te ture. Kua tuhia kētia e ngā tohunga Īnia o te manawataki ruri: e whai ana a Singh (1985) i a ia ki a Virahanka, i waenga i te 600 me te 800, kātahi ki a Gopala me Hemachandra.
Kāore he wīra i ō rātou whakaaro. Kāore ngā puna i whakamahia i konei e kī ana nā wai i peti tuatahi i te moni mā te raupapa. Ko tā rātou e whakaatu ana, kāore te tātai o te raupapa me te tātai o te rūreti e tūtaki: ko tētahi e kī ana me pēhea te tupu o ngā moni peti, ko tētahi atu e kī ana he aha tā ia moni peti e whakahoki ana.
E hia kua ngaro i muri i tētahi raupapa hinga?
E rua ngā tuakiri e ngāwari ai te arotake i te tūtohi i runga. I muri i ngā hinga n karapīpiti, ko te tapeke kua ngaro ko te tau Fibonacci tua-(n + 2) tango 1, ka puta ko 1, 2, 4, 7, 12, 20 me ērā atu, ā, ko te moni peti e whai ake ana ko te tau Fibonacci tua-(n + 1). Ka whakamatau a Bollman (2021) i taua hua anō mā te whakauru mō tētahi raupapa ka tīmata ki te 1, 2, 3, e neke ana i ia tau kia kotahi te wāhi. I te tepe 500 wae mai i te tīmatanga 1 wae, e kore e taea e te Martingale te tuku i tōna peti tua-10, 512 wae. Ka taea e te Fibonacci te tuku i tōna peti tua-14, 377 wae, engari kāore i tōna tua-15, 610.
He aha ka huri i runga i te tatini, i te tīwae rānei?
I runga i te tatinipetiTatini1–12, 13–24, 25–36 rānei, ko te utunga 2:1.Pānuitia katoatia →, i te tīwaepetiTīwaeNgā tau tekau mā rua i tētahi tīwae poutū o te mahere peti, ko te utunga 2:1.Pānuitia katoatia → rānei, e utu ana i te 2 ki te 1, kāore e hiahiatia te hoki whakamuri. Ko te toa i te moni peti F ka utu i te 2F, ā, he nui ake i ngā mea katoa i ngaro i mua, nā reira ka mutu te raupapa me te huamoni i ia toa. Ko te utu, 12 noa ngā wā i te 37 ka toa te tatini, nā reira he auau ake ngā raupapa hinga roa: ko ngā hinga tatini tekau mā whā karapīpiti ka puta kotahi pea i ia 242 whakamātau, ki te kotahi pea i ia 11,000 mō te wheropetiWheroHe peti utu ōrite ki ngā tau whero e 18. Wīwī: rouge.Pānuitia katoatia →.
Ka pēhea ki te mutu koe i muri anake i ngā toa e rua karapīpiti?
Ka neke tētahi atu momo kotahi te hīkoi whakamua i muri i ia hurihanga, ahakoa toa, hinga rānei, ā, ka mutu i muri anake i ngā toa e rua karapīpiti. Mēnā e n ngā hinga i mua i ngā toa e rua, ko te huamoni ko te tau Fibonacci tua-(n + 1) tāpiri 1: he iti ina wawe mai ngā toa, he nui ake ina tōmuri mai, ā, ka riro i runga i ngā moni peti kua tupu kia rite. Ko te takirua toa wawe ka puta i ngā moni peti iti i ngā wā katoa; ko te takirua tōmuri ka hiahia pea i tētahi peti nui i te wā tonu kua tino kino te wā tākaro.
Taputapu whaihanga · Fibonacci
2,000 wā tākaro o ngā peti utu ōrite mai i te pūtea tākaro $1,000.
Peti taketake $10 · tepe tēpu $500 · 100 hurihanga ia wā tākaro
Kia hia te auau o te raupapa hinga
Ka hinga te peti utu ōrite i te wīra kore kotahi i ngā hurihanga 19 o ia 37. Ko ia rārangi te tūpono ka hinga katoa tētahi raupapa hurihanga, me te nui kua ngaro i taua wā i te kaitākaro Fibonacci, e neke ana kotahi te hīkoi i te raupapa i muri i ia hinga.
| ngā hinga raupapa | tūpono | tata ki te 1 i ia | kua ngaro tae noa ki nāianei | peti e whai ake ana |
|---|---|---|---|---|
| 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 |
Ko te tūpono, ko te 19/37 kua whakareatia ki a ia anō kotahi te wā mō ia hinga, ka tatauria mai i tētahi hurihanga kua tohua. He maha ngā hurihanga i te wā tākaro roa e tīmata ai pea taua raupapa, nō reira i te pō katoa he nui ake rawa tōna tūpono i tā te rārangi kotahi e whakaatu ana.
Ngā pātai
Āe: whakamua i muri i te toa, whakamuri i muri i te hinga. He rite tōna whanonga ki te ParolirautakiParoliHe kauneke whakarunga i te toa: whakaruatia i muri i te toa, tīmata anō i muri i te hinga, i muri rānei i ngā toa e toru i te raupapa kotahi. Arā anō: Martingale kōaro.Pānuitia katoatia → pōturi ake.
He Pārekareka te Pāngarau
Me whakamātau koe i ēnei i te tuatahi. Kua kōpakina ia otinga; whakatuwherahia ina rite koe.
Tākarohia te momo ka neke kotahi te kaupae i te raupapa i muri i ia hurihanga, ahakoa toa, ahakoa hinga, ā, ka mutu i muri i ngā toa e rua karapīpiti: ngā moni peti 1, 1, 2, 3, 5, 8, aha atu. Ko ngā hua tuatahi tekau mā whā, ko T H T H H H T H H H T H H T (T = toa, H = hinga). Kei hea koe e tū ana, ā, he aha te peti e whai ake nei?
Whakaaturia te otinga
Whakautu Kua heke 22 waemoniWaeTe moni peti taketake e mahi ai tētahi pūnaha, tētahi kaitākaro rānei. Ka whakaahuatia ngā kauneke ki ngā wae kia hāngai ai ki ia tēpu.Pānuitia katoatia →. Ko te peti e whai ake nei, 610 wae, ā, ki te toa, ka mutu te wā tākaro me te 588 ki runga.
Ko ngā moni peti, ko ngā tau FibonaccirautakiFibonacciHe kauneke e whai ana i te raupapa 1, 1, 2, 3, 5, 8, 13…: kotahi te hīkoi whakamua i muri i te hinga, e rua ngā hīkoi whakamuri i muri i te toa.Pānuitia katoatia → tuatahi tekau mā whā: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 me te 377. Tāpirihia ngā toa, tangohia ngā hinga: +1 −1 +2 −3 −5 −8 +13 −21 −34 −55 +89 −144 −233 +377 = −22.
He toa te hua whakamutunga, nā reira kotahi anō te toa ka mutu. Ko te moni peti e whai ake nei, 610: ki te toa, ka toe te +588, ki te hinga, ka toe te −632 me te moni peti e whai ake nei 987.
Ka mutu tonu te momo nei me te huamoni, engari i konei me peti 610-wae kia pērā ai. I raro i ngā ture noa, e rua ngā kaupae whakamuri i muri i te toa, ka waiho e aua hua tekau mā whā anō koe kia kotahi noa te wae kua heke, me te peti e whai ake nei 2. Ko Bollman (2021), ka tīmata i te raupapa i te 1, 2, 3, ka puta te 1 kua heke me te peti e whai ake nei 3. He iti iho te ngaronga i raro i ngā ture noa i konei, nā te mea ka tōia whakararo anō ngā moni peti e ia toa.
hurihangamoni petihuatapeke haere11T+121H032T+243H−155H−668H−14713T−1821H−22934H−561055H−1111189T−2212144H−16613233H−39914377T−22I taua momo anō, he aha ka waiho tonu ai e ngā hinga n, ka whai ko ngā toa e rua, he huamoni ōrite ki te tau Fibonacci tua-(n + 1) tāpiri 1?
Whakaaturia te otinga
Whakautu Ko te tapeke o ngā hinga n, ko te tau Fibonacci tua-(n + 2) tango 1, ā, ko ngā toa e rua, ko ngā tau e rua e whai ake nei, ā, ka hipa rāua i tērā, ka whakakotahia, i te tau tua-(n + 1) tāpiri 1.
Tuhia te F₁, F₂, F₃ … mō te 1, 1, 2, 3, 5 … Ko ia tau, ko te tapeke o ngā tau e rua i mua i a ia.
Ngā hinga: F₁ + F₂ + … + Fₙ. Tāpirihia te 1 ki taua tapeke, ka tuhia hei F₂, ā, ka hinga tahi: F₂ + F₁ = F₃, kātahi F₃ + F₂ = F₄, aha atu, kia riro te tapeke katoa hei Fₙ₊₂. Nā reira ko te tapeke o ngā hinga, ko Fₙ₊₂ − 1.
Ko ngā toa, ko ngā moni peti e rua e whai ake nei, ko Fₙ₊₁ me Fₙ₊₂. Huamoni: Fₙ₊₁ + Fₙ₊₂ − (Fₙ₊₂ − 1) = Fₙ₊₁ + 1. Mēnā e whā ngā hinga, ko te F₅ + 1 = 6 wae tērā.
He katakata iti
Ka tūtaki te ōwehenga koura ki te tohu peti nui rawa.
Ngā Puna
- RouletteDoc. Whakamārama rautaki me ngā tauira.
- Roulette77. Whakamārama rautaki me ngā tauira.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, putanga 2.
- 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.