Vuto: Malire a Tebulo
Martingale ya $10 pa tebulo la $500. Kodi imasweka kangati, imataya zingati ikasweka, ndipo kodi kukweza malire kumathandiza?
Kuluza kasanu ndi kamodzi motsatizana kumaiswa: 1.8% pa cycle iliyonse, pafupifupi 60% ya magawo a kuzungulira 100. Kusweka kumadula $630. Kukweza malire kufika $5,000 kumapangitsa kusweka kukhala kosowa (0.25% pa cycle) ndi kwakukulu ($5,110). Kutayika koyembekezeka pa dola iliyonse yobetchedwa ndi 2.70% pa malire aliwonse.
Vuto
Wosewera abetcha $10 pa zofiirabetchaZofiiraBetcha la even-money pa manambala 18 ofiira. Mu Chifalansa: rouge.Werengani yonse → ndipo awirikiza pambuyo pa kuluza kulikonse, nabwerera poyambira pambuyo popambana. Malire apamwamba a tebulo ndi $500. (a) Kodi ndi kuluza kangati motsatizana kumene kumaswa progressionnjiraProgressionLamulo lililonse limene limasintha ndalama zobetcha potengera zotsatira zakale. Maprogression olakwika amazikweza pambuyo poluza, abwino pambuyo popambana.Werengani yonse →? (b) Kodi kuthekeramasamuKuthekeraMwayi wa zotsatira, kuchokera 0 mpaka 1 kapena 0% mpaka 100%. Nambala imodzi: 1/37 = 2.70%.Werengani yonse → pa cycle iliyonse ndi kotani? (c) Kodi chimatayika n’chiyani pa kusweka? (d) Kodi malire a $5,000 amasintha bwanji mayankho? (e) Kodi pali malire aliwonse amene amapangitsa dongosolo kupindula?
Mayankho (a)–(c)
Ndalama zobetcha: 10, 20, 40, 80, 160, 320. Yachisanu ndi chiwiri ikanakhala 640 > 500, choncho kuluza kasanu ndi kamodzi kumaiswa. (b) p(kuluza) = 19/37 pa zofiira; (19/37)⁶ = 0.0183, pafupifupi 1.8% pa cycle iliyonse. Cycle imakhalitsa pafupifupi kuzungulira kawiri pa avareji, choncho gawo la kuzungulira 100 lili ndi pafupifupi ma cycle 50 ndipo p(kusweka kamodzi pang’ono) ≈ 1 − 0.9817⁵⁰ ≈ 60%. (c) 10 + 20 + 40 + 80 + 160 + 320 = $630, zimene ndi ma unitndalamaUnitNdalama zobetcha zoyambira zimene dongosolo kapena wosewera amagwiritsa ntchito. Maprogression amafotokozedwa mu ma unit kuti agwire ntchito pa tebulo lililonse.Werengani yonse → a maziko 63, poyerekeza ndi $10 imene cycle inali kuyesa kupambana.
Yankho (d)
Pa $5,000: ndalama zobetcha mpaka 2,560 zimaloledwa; ndalama zobetcha zachikhumi, 5,120, zimakanidwa. Kuluza kasanu ndi kanayi kumaiswa: (19/37)⁹ ≈ 0.25% pa cycle iliyonse, pafupifupi 11% ya magawo a kuzungulira 100. Kutaya pa kusweka: 10 + 20 + … + 2,560 = $5,110. Wosewera wagula tsoka losowa pa mtengo wa tsoka lalikulu. Pa magawo ambiri mtengo woyembekezeka wa kusweka ndi p × kutaya ≈ 0.0183 × 630 = $11.5 pa cycle iliyonse pa malire a $500 ndi 0.0025 × 5,110 = $12.8 pa $5,000; ndi nambala imodzimodzi kupatula kuzungulitsa, ndipo ndi kutayika koyembekezekamasamuKutayika koyembekezekaMtengo woyembekezeka kuchulukitsa ndi ndalama zonse zobetchedwa; kuchuluka kwapakati kwa ndalama zotayika mu gawo la masewera kapena nthawi inayake.Werengani yonse → kwa cycle kuphatikiza $10 imene ma cycle opambana amapeza.
Yankho (e)
Ayi. Kutayika koyembekezeka pa cycle = (ndalama zonse zobetcha zoyembekezeka mu cycle) / 37, pa malire aliwonse, chifukwa betcha lililonse ndi −1/37 ya ilo lokha. Malire amangosankha mmene kutayika kumagawidwira pakati pa kupambana kwazing’ono kochuluka ndi kutaya kwakukulu kochepa. Popanda malire ndi ndalama zosewererandalamaNdalama zosewereraNdalama zonse zimene mwazisiyira masewera. Kusamalira ndalama zosewerera ndiko kusankha kuchuluka kwake komwe mungaike pachiopsezo pa betcha lililonse ndi pa gawo lililonse la masewera.Werengani yonse → zopanda malire progression ikanati “igwire ntchito”, m’lingaliro lakuti sikanasweka konse, ndipo ikanabetchanso ndalama zopanda malire ndi kutayika koyembekezeka kwa 2.70% ya ndalama zopanda malire zimenezo. Malire a tebulotebuloMalire a tebuloBetcha lochepa kwambiri ndi lalikulu kwambiri lololedwa. Malire apamwamba ndiwo amaimitsa maprogression owirikiza.Werengani yonse → si amene amaletsa MartingalenjiraMartingaleProgression yowirikiza betcha pambuyo poluza kulikonse. Onani gawo la Njira kuti mudziwe zimene imachita ndi zimene siimachita.Werengani yonse → kugwira ntchito. Masamu ndiwo amaletsa.
Matebulo awiri enieni
Chitsanzo cha Thorp ndi tebulo la $1 lokhala ndi malire apamwamba a $1,000, pamene wosewera akuyembekeza kupambana $30 ya chakudya chamadzulo dola imodzi nthawi iliyonse. Ndalama zobetcha 1, 2, 4 … 512 zimalola mabetcha khumi, choncho kuluza kakhumi motsatizana kumaswa progression: kamodzi pa ma cycle 785 pa gudumu la ku Ulaya (kamodzi pa 613 pa la ku America), pa mtengo wa $1,023. Ma cycle makumi atatu onse amapambana 96.2% ya nthawi. Ena 3.8% amataya pafupifupi $1,000, ndipo zotsatira za avareji za madzulo ndi −$9.17, zimene ndi ndendende 1/37 ya $339 imene ma cycle makumi atatu amabetcha pa avareji. Tebulo la $5 lokhala ndi malire apamwamba a $2,000 si losiyana: ndalama zobetcha mpaka $1,280 zimalola mabetcha asanu ndi anayi, ndipo kusweka kumabwera kamodzi pa ma cycle 403 pa gudumu la ku Ulaya (kamodzi pa 323 pa la ku America) ndipo kumadula $2,555.
Wosewera wolemera
Patsani progression ndalama zosewerera zochuluka m’malo mwa malire otsika: ma unit 1,000, maziko a unit imodzi ndi kuzungulira 1,000 pa zofiira, kuyambanso pa unit imodzi nthawi iliyonse pamene kuwirikiza kotsatira kuli kopitirira zotsala. Tinayerekeza madzulo otere miliyoni imodzi. Pa gudumu la ku Ulaya 52% amatha ali patsogolo, 21% amataya zonse, ndipo zotsatira za avareji ndi ma unit −124. Ngakhale m’masewera opanda zirogudumuZiroKabowo kamodzi kobiriwira kamene betcha la even-money, dazeni kapena mzati siliphimba; gwero la phindu la kasino. Imatchedwanso: ziro imodzi, 0.Werengani yonse →, pamene betcha lililonse ndi lachilungamo, pafupifupi 60% okha akanatha ali patsogolo. Madzulo wamba ndi kupambana pang’ono; avareji imalipidwa ndi madzulo amene amathera pa ziro.
Phunziro
Makasino amaika malire kuti achepetse kusinthasinthamasamuKusinthasinthaMuyeso wa kufalikira kwa zotsatira kuzungulira mtengo woyembekezeka. Kwakukulu pa straight up, kochepa pa mabetcha a even-money.Werengani yonse → kwawo, osati kugonjetsa madongosolo. Kugonjetsa Martingale ndi zotsatira za m’mbali zimene amasangalala nazo, ndipo masamu akanaigonjetsa mulimonse. Wosewera amene akuganiza kuti malire ndiwo vuto wapeza phompho ndipo walingalira kuti ndi potsetsereka.
Fomula
Mafunso
Zimakuthandizani kupulumuka mpaka malire okwera, kumene kusweka kumakhala kosowa ndi kwakukulu. Kutayika koyembekezeka pa dola iliyonse sikusintha.
Ndalama zobetcha 10, 30, 70, 150, 310: malire a $500 amafikiridwa pambuyo pa kuluza kasanu, ndipo kusweka kumadula $570. 2.70% yomweyo.
Kuti wosewera mmodzi asabetche kuposa zimene ndalama zosungidwa za kasino zingalipire mosavuta. Kusamalira kusinthasintha.
Masamu Osangalatsa
Yesani nokha choyamba. Yankho lililonse labisika; litsegulireni mukakonzeka.
MartingalenjiraMartingaleProgression yowirikiza betcha pambuyo poluza kulikonse. Onani gawo la Njira kuti mudziwe zimene imachita ndi zimene siimachita.Werengani yonse → imayamba pa $100 pa zofiirabetchaZofiiraBetcha la even-money pa manambala 18 ofiira. Mu Chifalansa: rouge.Werengani yonse → ndipo imadzilola mabetcha n osaposa pa cycle iliyonse: pambuyo pa kuluza n motsatizana imasiya ndi kuyambiranso. Lembani zotsatira za avareji za cycle imodzi ngati njira yowerengera ya n, ndipo werengerani pa mabetcha 5, 6 ndi 7 pa gudumu la ku Ulaya.
Onetsani yankho
Yankho Avareji ndi 100 × (1 − (38/37)ⁿ): −$14.26 pa mabetcha 5, −$17.35 pa 6 ndi −$20.52 pa 7. Kulola mabetcha ochuluka kumapangitsa cycle ya avareji kukhala yoipa kwambiri, osati yabwino.
Cycle imapambana $100 pokhapokha mabetcha onse n ataluza, zimene zimachitika ndi kuthekera kwa qⁿ, pamene q = 19/37. Onse akaluza, ndalama zobetcha 100, 200 … 100 × 2ⁿ⁻¹ pamodzi ndi 100 × (2ⁿ − 1). Choncho avareji ndi 100 × (1 − qⁿ) − 100 × (2ⁿ − 1) × qⁿ = 100 × (1 − (2q)ⁿ).
Pano 2q = 38/37, pang’ono kuposa 1, choncho (2q)ⁿ imakula ndi n ndipo avareji imatsika: n = 5 imapereka 1.1426 ndi −$14.26; n = 6 imapereka 1.1735 ndi −$17.35; n = 7 imapereka 1.2052 ndi −$20.52. Makwerero ataliatali amataya kawirikawiri pang’ono, mu 3.6%, 1.8% ndi 0.9% ya ma cycle, koma kutaya kulikonse kumakhala kuwirikiza kawiri, ndipo ndalama zambiri zimadutsa patebulo pa cycle iliyonse, pa 2.70% ya betcha lililonse.
Pa gudumu la ku America 2q = 40/38 ndipo manambala ndi −$29.24, −$36.04 ndi −$43.20 (Taylor, 2021). M’masewera opanda zirogudumuZiroKabowo kamodzi kobiriwira kamene betcha la even-money, dazeni kapena mzati siliphimba; gwero la phindu la kasino. Imatchedwanso: ziro imodzi, 0.Werengani yonse → 2q = 1, ndipo cycle iliyonse imakhala ndi avareji ya ziro ndendende mosasamala kanthu za kutalika kwa makwerero.
“Grand Martingale” imawirikiza kawiri ndalama zobetcha pambuyo pa kuluza ndipo imaonjezera unitndalamaUnitNdalama zobetcha zoyambira zimene dongosolo kapena wosewera amagwiritsa ntchito. Maprogression amafotokozedwa mu ma unit kuti agwire ntchito pa tebulo lililonse.Werengani yonse → imodzi, choncho ndalama zobetcha zimayenda 1, 3, 7, 15, 31 … Muli patsogolo ndi zingati pamene kupambana koyamba kwabwera pa betcha la 1, la 2, la 3 kapena la k? Ndi unit ya $10 ndi malire a m’mwamba a $500, cycle imasweka kangati, ndipo cycle imawononga zingati pa avareji?
Onetsani yankho
Yankho Kupambana pa betcha la k kumakusiyani patsogolo ndi ma unit k: +1, +2, +3 ndi zina zotero. Pa $10 ndi $500 cycle imasweka pambuyo pa kuluza kasanu, 3.57% ya ma cycle, kutaya −$570. Pa avareji cycle imataya $2.32 mwa $85.73 yobetchedwa: 2.70%.
Ndalama zobetcha za k ndi ma unit 2ᵏ − 1: 1, 3, 7, 15, 31. Ndalama zobetcha k − 1 zoyamba pamodzi ndi 2ᵏ − 2 − (k − 1) = 2ᵏ − k − 1. Kupambana pa betcha la k kumalipira 2ᵏ − 1, choncho cycle imatha patsogolo ndi ma unit (2ᵏ − 1) − (2ᵏ − k − 1) = k: unit imodzi yowonjezera pa kuluza kulikonse kusanachitike kupambana.
Pa $10 pa unit ndalama zobetcha ndi $10, $30, $70, $150 ndi $310; yotsatira, $630, ndi yoposa malire a m’mwamba a $500. Kuluza kasanu motsatizana, (19/37)⁵ = 3.57%, kumawononga 10 + 30 + 70 + 150 + 310 = $570.
Avareji: kupambana kumabweretsa $10 × k ndi kuthekera kwa (19/37)ᵏ⁻¹ × 18/37 pa k = 1 mpaka 5, ndipo kusweka kumatenga $570 ndi kuthekera kwa 3.57%; pamodzi −$2.32. Ndalama zobetchedwa ndi avareji ya $85.73 pa cycle iliyonse, ndipo 2.32/85.73 = 2.70%. Martingale wamba patebulo lomwelo imasweka pambuyo pa kuluza kasanu ndi kamodzi, 1.83% ya ma cycle, kutaya −$630, ndipo imataya $1.74 mwa $64.20 yobetchedwa: 2.70% kachiwiri.
Wosewera akukonzekera Martingale pa zofiira ndi betcha loyamba la $1 patebulo limene malire ake ndi $1,000, choncho mabetcha khumi n’zotheka: $1, $2, $4 ndi zina zotero mpaka $512. Kodi cycle imataya onse khumi kangati, zimenezo zimatenga nthawi yaitali bwanji pa avareji, ndipo madzulo a mabetcha 200 amatha choncho kangati?
Onetsani yankho
Yankho Cycle imataya onse khumi pafupifupi kamodzi pa 784, zimene zimawononga $1,023. Zimenezo ndi pafupifupi mabetcha 1,600 pa avareji, ndipo madzulo a mabetcha 200 amagunda khoma pafupifupi 11% ya nthawi. Cycle imatayabe $0.31 pa avareji mwa $11.31 yobetchedwa: 2.70%.
Betcha pa zofiira limaluza ndi kuthekera kwa 19/37, kuphatikizapo ziro. Khumi motsatizana: (19/37)¹⁰ ≈ 0.00128, pafupifupi 1 pa 784. Ndalama zobetcha 1 + 2 + 4 + … + 512 pamodzi ndi $1,023.
Cycle imatenga mabetcha 2.05 pa avareji, choncho ma cycle 784 amatenga pafupifupi mabetcha 1,600. Kuwerengera kuzungulira ndi kuzungulira, zotsatizana za kuluza khumi zimapezeka kwinakwake m’mabetcha 200 11.3% ya nthawi.
Pakati pa masoka wosewera amapambana $1 pa cycle iliyonse: pafupifupi $783 cycle yoipa isanabwere, kenako −$1,023, pafupifupi −$240 pa nthawi yonseyo. Pa cycle iliyonse: 1 × (1 − 0.00128) − 1,023 × 0.00128 ≈ −$0.31. Ndalama zobetchedwa pa cycle iliyonse: 1 + 2 × (19/37) + 4 × (19/37)² + … + 512 × (19/37)⁹ ≈ $11.31. Ndipo −0.31/11.31 = −2.70%.
Yerekezerani ndi betcha loyamba la $10 pa malire a $500, mabetcha asanu ndi limodzi: khoma limabwera kamodzi pa ma cycle 55, ndipo madzulo a mabetcha 200 amakumana nalo 84% ya nthawi. Malire okwera amapangitsa kugwa kukhala kosowa komanso kwakukulu, osati kotsika mtengo.
Nthabwala yopumitsa
Kosowa ndi kwakukulu, pa malire aliwonse. Kuchulukitsa kwake sikusintha.
Magwero
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.