Masamu a Roulette · Mfundo · mphindi 7

Kuyandikira pa Nthawi Yayitali: Lamulo la Manambala Akuluakulu mu Roulette

Mmene avareji imakhazikikira ku −2.70%, ndi chifukwa chake zimatenga nthawi yaitali kuposa mmene munthu angaganizire.

Yankho lalifupi

Kutayika kwa avareji pa kuzungulira kulikonse kumayandikira −1/37 pamene kuzungulira kukuchuluka, ndi kufalikira kumene kumachepa ngati 1/√N. Pambuyo pa kuzungulira 1,000 kwa zofiira avareji nthawi zambiri imakhala mkati mwa ±3% ya zoyembekezeka zake.

zoyembekezeka pa kuzungulira
−2.70%
kufalikira pambuyo pa N
σ/√N
N ya ±1%
~10,000
chiwerengero chonse sichiyandikira
chimachoka

Lamulo la manambala akuluakulu

Avareji yopitirira ya mabetcha odziyimira payokha imalowera ku mtengo woyembekezekamasamuMtengo woyembekezekaZotsatira zapakati pa betcha lililonse pa nthawi yayitali. −1/37 ya ndalama zobetcha pa betcha lililonse la ku Ulaya wamba.Werengani yonse →. Pambuyo pa kuzungulira N kwa even-money pa unitndalamaUnitNdalama zobetcha zoyambira zimene dongosolo kapena wosewera amagwiritsa ntchito. Maprogression amafotokozedwa mu ma unit kuti agwire ntchito pa tebulo lililonse.Werengani yonse → imodzi, zotsatira za avareji pa kuzungulira kulikonse zili ndi zoyembekezeka −1/37 ndi kupatuka kokhazikikamasamuKupatuka kokhazikikaMuzu wa sikweya wa kusinthasintha; mtunda wanthawi zonse wa zotsatira kuchokera ku mtengo woyembekezeka.Werengani yonse → 1/√N. Pa N = 100 kufalikira kumeneko ndi 10% ya ndalama zobetcha, pafupifupi kuwirikiza kanayi chizindikiro cha 2.7%. Pa N = 1,000 ndi 3.2%, pafupifupi chofanana ndi chizindikiro. Pa N = 10,000 ndi 1%, ndipo phindu la kasino likuoneka bwino. Phindu la kasino silioneka m’gawo limodzi la masewera koma silingalephereke kuoneka pa chaka.

kuzunguliraσ ya avareji pa kuzungulira (even money)phindu la kasino ngati gawo la σ
1031.6%0.09
10010.0%0.27
1,0003.2%0.85
10,0001.0%2.70
100,0000.3%8.54
Pa unit iliyonse yobetchedwa. Phindu la kasino limaonekera bwino mwa ziwerengero kwinakwake pakati pa kuzungulira 1,000 ndi 10,000.

Chimene chimayandikira ndi chimene sichiyandikira

Avareji pa kuzungulira kulikonse imayandikira. Chiwerengero chonse sichiyandikira: chimapita kutali ndi ziro pamene N ikukula, ndi pafupifupi 2.7% ya N mu zoyembekezeka, ndi kufalikira kwa √N mozungulira pamenepo. Wosewera amene wasewera kuzungulira 10,000 pa $10 akuyembekezeka kukhala pansi ndi $2,700, kuwonjezera kapena kuchotsa $1,000. Gawo lopitirira la zofiirabetchaZofiiraBetcha la even-money pa manambala 18 ofiira. Mu Chifalansa: rouge.Werengani yonse → lakhazikika kale pafupi ndi 48.65%; ndalama zopitirira sizinakhazikike paliponse.

Magawo khumi aatali: kuzungulira 1,000 pa $10 pa zofiirazotsatira poyerekeza ndi poyambira
+$440$0−$660+$160−$3300125250375500kuzungulirazotsatira
magawo 1,000 × kuzungulira 500 · wofiirira p10/p25/p75/p90, buluu wopepuka pakati, zitsanzo 79 zozimirira · sunthani pa tchati kuti muone ma quantile pa kuzungulira
  • p10 −$440
  • p25 −$280
  • pakati −$140
  • p75 +$0
  • p90 +$140
magawo 1,000 × kuzungulira 500 · mzere wa y wadulidwa pa peresentayilo ya 1–99 (monyanyira −$940 mpaka +$660) · kuzungulira 500 · loyambira $10 · even money
Pofika kuzungulira 1,000 mizere yambiri ili pansi pa ziro ndipo kufalikira kudakali kwakukulu. Phindu la kasino likupambana; kusinthasintha kudakali kokweza.

N’chifukwa chiyani maganizo athu amalakwa

Anthu amayembekezera kuti phindu la kasino lionekere msanga chifukwa 2.70% imamveka ngati yochuluka, ndipo amayembekezera kuti zotsatizana zazitali “zifanane” chifukwa lamulo la manambala akuluakulumasamuLamulo la manambala akuluakuluAvareji ya zotsatira zodziyimira payokha imayandikira mtengo woyembekezeka pamene chiwerengero cha mayesero chikukula.Werengani yonse → limati avareji zimayandikira. Maganizo onse awiri amalakwitsa kukula: phindu la kasino ndi laling’ono poyerekeza ndi kusinthasinthamasamuKusinthasinthaMuyeso wa kufalikira kwa zotsatira kuzungulira mtengo woyembekezeka. Kwakukulu pa straight up, kochepa pa mabetcha a even-money.Werengani yonse → kwa kuzungulira kumodzi (σ = unit 1 poyerekeza ndi EV = 0.027), choncho zimatenga (1/0.027)² ≈ kuzungulira 1,400 kuti lionekere pa sigma imodzi. Ndipo kuyandikira kwa avareji sikuchita kanthu kukoka chiwerengero chonse kubwerera; kumangosungunula kusinthasintha kwakale.

Kuyandikira pa mabetcha ena

Pa ma straight upbetchaStraight upNambala imodzi, amalipira 35:1.Werengani yonse → σ = 5.84, choncho kuwerengera komweko kumapereka (5.84/0.027)² ≈ kuzungulira 47,000 kuti phindu la kasino lifike pa sigma imodzi. Wosewera wa straight up angathe kusewera kwa zaka popanda phindu la kasino kusiyanitsidwa ndi mwayi m’mbiri yake, pamene akulipira ndendende 2.70% yofanana ndi wosewera wa zofiira amene amaliona mkati mwa masabata.

Tanthauzo lake pa kuyesa madongosolo

Aliyense wonena kuti dongosolo limagwira ntchito ayenera kutha kuliwonetsa pa kuzungulira 10,000 kapena kuposa ndi avareji yabwino yolembedwa. Pa kuzungulira 1,000 avareji yabwino pa even money ndi chochitika cha kamodzi pa kasanu pansi pa lingaliro la null; pa kuzungulira 100 ili pafupifupi ngati kuponya ndalama. Zoyerekezera za patsamba lino zimayendetsa magawo 2,000 a kutalika kumene mwasankha mu sekondi imodzi, umene ndi umboni wochuluka kuposa umboni wa munthu aliyense.

Fomula

avareji pa kuzungulira → −1/37
σ(avareji) = σ / √N
E[chonse] = −N/37 · σ(chonse) = σ√N

Mafunso

Ngati ndisewera nthawi yaitali mokwanira, kodi pamapeto pake sindidzakhala patsogolo?

KuthekeramasamuKuthekeraMwayi wa zotsatira, kuchokera 0 mpaka 1 kapena 0% mpaka 100%. Nambala imodzi: 1/37 = 2.70%.Werengani yonse → kokhalanso patsogolo kumatsikira ku ziro pamene mukusewera. Chiwerengero chonse chimatsika popanda malire.

Kodi lamulo la manambala akuluakulu mu roulette limatanthauza kuti gudumu limadzikonza?

Ayi. Limatanthauza kuti kusinthasintha kwakale kumakhala gawo laling’ono la chitsanzo chachikulu.

Kodi ndi kuzungulira kangati ndisanadalire zotsatira?

Pa even money, pafupifupi 10,000 phindu la kasino lisanaoneke bwino. Pa ma straight up, pafupifupi 50,000.

Masamu Osangalatsa

Yesani nokha choyamba. Yankho lililonse labisika; litsegulireni mukakonzeka.

  1. Anzanu awiri akusewera maulendo 20 a masewera achilungamomasamuMasewera achilungamoMasewera amene palibe mbali yokhala ndi mwayi: betcha lililonse lili ndi mtengo woyembekezeka wa ziro.Werengani yonse →, kuponya ndalama kapena zofiirabetchaZofiiraBetcha la even-money pa manambala 18 ofiira. Mu Chifalansa: rouge.Werengani yonse → polimbana ndi zakudabetchaZakudaBetcha la even-money pa manambala 18 akuda. Mu Chifalansa: noir.Werengani yonse → ndi zirogudumuZiroKabowo kamodzi kobiriwira kamene betcha la even-money, dazeni kapena mzati siliphimba; gwero la phindu la kasino. Imatchedwanso: ziro imodzi, 0.Werengani yonse → zobwezedwa, ndipo akusunga chiwerengero chosalekeza. Werengani maulendo amene aliyense ali patsogolo (kufanana kumawerengedwa kwa amene anali patsogolo mwamsanga zisanachitike). Ndi chiti chotheka kwambiri: kuti kukhala patsogolo kugawidwe maulendo 10 ku 10, kapena kuti mnzanu mmodzi akhale patsogolo maulendo onse 20?

    Onetsani yankho

    Yankho Mnzanu mmodzi kukhala patsogolo maulendo onse 20 n’kotheka kwambiri: 35.2%, kuwerengera aliyense wa iwo, poyerekeza ndi 6.1% ya kugawana mofanana 10 ku 10.

    Kuthekera kwakuti chiwerengero chosalekeza chachilungamo chikhale chofanana pambuyo pa maulendo 2k ndi u = C(2k, k)/2²ᵏ: 0.246 pambuyo pa maulendo 10 ndi 0.176 pambuyo pa 20. Zotsatira zodziwika bwino, lamulo la arc-sine, zimati kuthekera kwakuti mnzanu mmodzi wotchulidwa akhale patsogolo maulendo 2k ndendende mwa 2n ndi u(2k) × u(2n − 2k).

    Kukhala patsogolo maulendo onse 20: u(20) × u(0) = 0.176 kwa mnzanu aliyense, 35.2% kwa aliyense wa iwo. Kugawana mofanana: u(10) × u(10) = 0.246² = 6.1%, kagawidwe kosatheka kwambiri kuposa kena konse.

    Choncho m’masewera achilungamo kukhala patsogolo sikusintha manja kawirikawiri. Wosewera amene wakhala patsogolo madzulo onse, kapena m’mbuyo madzulo onse, sanaone chachilendo chilichonse, ndipo zimenezo sizinena kanthu za gudumu kapena za luso. Epstein (2013) akupereka lamulo lomweli pa masewera ataliatali: theka la nthawi mbali yokhala ndi mwayi kwambiri imakhala patsogolo kwa 85% ya masewera kapena kuposerapo.

Nthabwala yopumitsa

Avareji imayandikira. Chiwerengero chonse chimangochoka.

Avareji imayandikira. Chiwerengero chonse chimangochoka.

Magwero

  1. Bernoulli, J. Ars Conjectandi. 1713. Lamulo la manambala akuluakulu.
  2. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, kope la 3, 1968. Gambler’s ruin, mutu XIV.
zinawunikidwa 2026-09-28chitsanzo: ya ku Ulaya, ziro imodzinjira zowerengera ↗magwero ↗