Kuyenda Pang’onopang’ono: Gawo la Martingale
Madola khumi pa zofiira, owirikizidwa pambuyo pa kuluza kulikonse, pa tebulo la $500. Kuzungulira ndi kuzungulira, kuphatikiza kuzungulira kumene kumathetsa.
Gawo loyerekezedwa la Martingale kuchokera pa ndalama zosewerera za $1,000. Kupambana kochepa makumi anayi ndi kamodzi, kenako kuluza kasanu ndi kamodzi motsatizana ndi betcha lachisanu ndi chiwiri lokanidwa. Gawo limatha litatsika ndi $220 litakhala patsogolo ndi $410, ndipo zimenezo ndi zimene dongosololi limachita.
Dongosolo
Betchani $10 pa zofiirabetchaZofiiraBetcha la even-money pa manambala 18 ofiira. Mu Chifalansa: rouge.Werengani yonse →. Mutaluza, wirikizani. Mutapambana, bwererani ku $10. Malire a tebulotebuloMalire a tebuloBetcha lochepa kwambiri ndi lalikulu kwambiri lololedwa. Malire apamwamba ndiwo amaimitsa maprogression owirikiza.Werengani yonse → $500, choncho ndalama zobetcha ndi 10, 20, 40, 80, 160, 320 kenako betcha la $640 limene tebulo lidzalikana. Kuluza kasanu ndi kamodzi motsatizana kumaswa dongosolo; kuyesa kulikonse kuli ndi (19/37)⁶ ≈ 1.8% yochita zimenezo, ndipo gawo la mazungulidwe 100 lili ndi mayesero pafupifupi 50. Zoyembekezeka: mwayi wa pafupifupi 60% woswa m’mazungulidwe 100, ndi kutaya $630 zikachitika.
Mazungulidwe 1–30
MartingalenjiraMartingaleProgression yowirikiza betcha pambuyo poluza kulikonse. Onani gawo la Njira kuti mudziwe zimene imachita ndi zimene siimachita.Werengani yonse → wamba: kuluza kamodzi mpaka katatu motsatizana, kulikonse kuthetsedwa ndi kupambana kopereka +$10. Pofika kuzungulira 30 tapambana nthawi 17, iliyonse ikutseka cycle, ndipo tili patsogolo ndi $170. Ndalama zobetcha zazikulu kwambiri mpaka pano zinali $80 pambuyo pa kuluza katatu. Kumamveka ngati makina osindikizira mapepala a $10.
Mazungulidwe 31–60
Zomwezo, ndi cycle imodzi ya kuluza kanayi (ndalama zobetcha mpaka $160, kenako kupambana) imene kwa kanthawi inaika $310 pa tebulo ndipo inamveka ngati kulimba mtima. Pambuyo pa mazungulidwe 60: ma cycle 41 amalizidwa, patsogolo ndi $410, ndipo malo otsika kwambiri a 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 → anali $1,040. Histogram ya gawo lililonse la Martingale imaoneka chonchi pa kutalika kwake kwakukulu.
Mazungulidwe 61–66
L L L L L L. Ndalama zobetcha 10, 20, 40, 80, 160, 320: $630 zatayika. Betcha lotsatira lingakhale $640; malire ndi $500. Dongosolo lasweka. Tikhoza kubetcha $500 (ndipo likapambana, tidzakhalabe titatsika ndi $130 pa cycle) kapena kubwerera ku $10 ndi kuvomera kutaya. ZakudabetchaZakudaBetcha la even-money pa manambala 18 akuda. Mu Chifalansa: noir.Werengani yonse → kapena zirogudumuZiroKabowo kamodzi kobiriwira kamene betcha la even-money, dazeni kapena mzati siliphimba; gwero la phindu la kasino. Imatchedwanso: ziro imodzi, 0.Werengani yonse → zisanu ndi chimodzi motsatizana zili ndi kuthekeramasamuKuthekeraMwayi wa zotsatira, kuchokera 0 mpaka 1 kapena 0% mpaka 100%. Nambala imodzi: 1/37 = 2.70%.Werengani yonse → kwa 1.8% pa cycle iliyonse. Tinali titayendetsa ma cycle pafupifupi 45. Mwayi wofika pamenepa kwinakwake m’ma cycle 45 unali pafupifupi 55%. Silinali tsoka; linali pakati penipeni.
- p10 −$1,000
- p25 −$1,000
- pakati −$1,000
- p75 +$790
- p90 +$1,690
Maakaunti
Patsogolo ndi $410 pambuyo pa mazungulidwe 60, pansi ndi $220 pambuyo pa 66. Zonse zobetchedwa: pafupifupi $2,100 pa mazungulidwe 66, poyerekeza ndi $660 kwa wobetcha mofanana $10. Kutayika koyembekezekamasamuKutayika koyembekezekaMtengo woyembekezeka kuchulukitsa ndi ndalama zonse zobetchedwa; kuchuluka kwapakati kwa ndalama zotayika mu gawo la masewera kapena nthawi inayake.Werengani yonse → pa $2,100 ya ndalama zonse zobetchedwandalamaNdalama zonse zobetchedwaNdalama zonse zobetchedwa mu gawo la masewera kapena nthawi inayake, kuphatikizapo ndalama zopambana zobetchedwanso. Zimatchedwanso: handle, action.Werengani yonse → ndi $57; −$220 yathu yeniyeni ili pafupifupi gawo limodzi mwa atatu a kupatuka kokhazikikamasamuKupatuka kokhazikikaMuzu wa sikweya wa kusinthasintha; mtunda wanthawi zonse wa zotsatira kuchokera ku mtengo woyembekezeka.Werengani yonse → pansi pa zimenezo, zomwe si zachilendo kwa dongosolo limene kagawidwe kake kali ndi mchira wautali kumanzere. Tikanasiya pa kuzungulira 60 ndi malire a phindunjiraMalire a phinduCholinga cha phindu chosankhidwa pasadakhale chimene mumathetsera gawo la masewera.Werengani yonse → a $400, tikanachoka patsogolo ndi $410, ndipo gawo lotsatira likanakhala ndi 1.8% yomweyo pa cycle iliyonse.
Zimene gawoli likusonyeza
Martingale imasandutsa betcha la 48.65% kukhala ndondomeko imene imapambana 98% ya ma cycle ake ndipo imataya ma unitndalamaUnitNdalama zobetcha zoyambira zimene dongosolo kapena wosewera amagwiritsa ntchito. Maprogression amafotokozedwa mu ma unit kuti agwire ntchito pa tebulo lililonse.Werengani yonse → 63 pa 2% yotsalayo. Siisintha kutayika koyembekezeka pa dola iliyonse; imachulukitsa madola. Wobetcha mofanana pambali pathu anabetcha gawo limodzi mwa atatu ndipo anataya, pa avareji, gawo limodzi mwa atatu. Wosewera amene amayendetsa dongosololi kwa chaka chimodzi adzapambana madzulo ambiri ndipo adzataya chakacho.
Kangati kuluza kotsatizana kumabwera
Betcha la even-money pa gudumu la ziro imodzi limaluza kuzungulira 19 mwa 37. Mzere uliwonse ndi kuthekera kwakuti kuzungulira kotsatizana kwa chiwerengero china konse kuluze, ndi zimene wosewera Martingale, amene amawirikiza akaluza kulikonse, wataya pofika nthawi imeneyo.
| kuluza motsatizana | kuthekera | pafupifupi 1 mwa | zotayika mpaka pano | betcha lotsatira |
|---|---|---|---|---|
| 1 | 51.4% | 2 | $1 | $2 |
| 2 | 26.4% | 4 | $3 | $4 |
| 3 | 13.5% | 7 | $7 | $8 |
| 4 | 7.0% | 14 | $15 | $16 |
| 5 | 3.6% | 28 | $31 | $32 |
| 6 | 1.8% | 55 | $63 | $64 |
| 7 | 0.94% | 106 | $127 | $128 |
| 8 | 0.48% | 207 | $255 | $256 |
| 9 | 0.25% | 403 | $511 | $512 |
| 10 | 0.13% | 784 | $1,023 | $1,024 |
| 11 | 0.065% | 1527 | $2,047 | $2,048 |
| 12 | 0.034% | 2974 | $4,095 | $4,096 |
| 13 | 0.017% | 5792 | $8,191 | $8,192 |
| 14 | 0.0089% | 11279 | $16,383 | $16,384 |
| 15 | 0.0046% | 21965 | $32,767 | $32,768 |
Kuthekera ndi 19/37 kuchulukitsidwa ndi kokha kamodzi pa kuluza kulikonse, kuwerengedwa kuchokera pa kuzungulira kumodzi kodziwika. Gawo lalitali la masewera lili ndi kuzungulira kwambiri kumene kuluza kotere kungayambire, choncho m’madzulo amodzi n’kotheka kwambiri kuposa zimene mzere umodzi ukusonyeza.
Mafunso
Kuluza kasanu ndi kanayi kumaliswa m’malo mwa kasanu ndi kamodzi: 0.25% pa cycle iliyonse, ndi $5,110 zotayika zikachitika. Phompho losowa kwambiri, phompho lalitali kwambiri, −2.70% yomweyo.
Likanapambana 48.65% ya nthawi ndi kusiya cycle pa −$130 mulimonse. Palibe chosuntha chabwino pambuyo pa Martingale yosweka; pali ndalama zobetcha zokha zimene musankhe kenako.
Inde, pa gawo limenelo. Osati pa avareji ya magawo onse.
Masamu Osangalatsa
Yesani nokha choyamba. Yankho lililonse labisika; litsegulireni mukakonzeka.
Patebulo la $1 mpaka $500, wosewera wa MartingalenjiraMartingaleProgression yowirikiza betcha pambuyo poluza kulikonse. Onani gawo la Njira kuti mudziwe zimene imachita ndi zimene siimachita.Werengani yonse → akuyamba pa $1 pa zofiirabetchaZofiiraBetcha la even-money pa manambala 18 ofiira. Mu Chifalansa: rouge.Werengani yonse → pa gudumu la zirogudumuZiroKabowo kamodzi kobiriwira kamene betcha la even-money, dazeni kapena mzati siliphimba; gwero la phindu la kasino. Imatchedwanso: ziro imodzi, 0.Werengani yonse → imodzi. Kodi kuluza kangati motsatizana kumaimitsa kuwirikiza kawiri, zingati zatayika pofika nthawi imeneyo, ndipo zimachitika kangati?
Onetsani yankho
Yankho Kuluza kasanu ndi kanayi: $511 yatayika, ndipo betcha lotsatira likanakhala $512. Zimachitika kamodzi pa zotsatizana pafupifupi 403.
Ndalama zobetcha ndi 1, 2, 4, 8, 16, 32, 64, 128 ndi 256: pamodzi $511. Yachikhumi ikanakhala $512, yoposa malire. Betcha la $500 limene lapambana limasiyabe wosewera m’mbuyo ndi $11; limene laluza limamusiya m’mbuyo ndi $1,011.
Zofiira zimaluza ndi kuthekera kwa 19/37, choncho kuluza kasanu ndi kanayi motsatizana kuli ndi kuthekera kwa (19/37)⁹ ≈ 0.25%, kamodzi pa zotsatizana pafupifupi 403. Zotsatizana zilizonse zomalizidwa zimapambana $1, choncho wosewera amayembekezera pafupifupi $402 ya kupambana kwakung’ono kusanachitike kutaya kumodzi kwa $511, ndipo 2.70% ya zonse zobetchedwa imatayikabe pa avareji.
Pa gudumu la ziro ziwiri kuthekera ndi (20/38)⁹, kamodzi pa pafupifupi 323. Bollman (2021) amasindikiza “pafupifupi 1 pa 833”, zomwe ndi (18/38)⁹, kuthekera kwa kupambana kasanu ndi kanayi motsatizana.
Nthabwala yopumitsa
Kupambana kochepa makumi anayi ndi kamodzi ndi kutaya kwakukulu kumodzi. Dongosolo lonse ndi limenelo.
Magwero
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”