Okubala mu Roulette · Ekizibu ky'okubala · eddakiika 10

Ekizibu: Ekkomo ly'Emmeeza

Martingale ya $10 ku mmeeza ya $500. Emirundi emeka gy'emenyeka, efiirwa ssente mmeka bw'emenyeka, era okwongeza ekkomo kuyamba?

Eky'okuddamu mu bufunze

Okufiirwa mukaaga omuddiriŋŋanwa kugimenya: 1.8% ku buli lunyiriri olujjuvu, nga 60% ku biseera by'okuzannya eby'okwetooloola 100. Okumenyeka kufiiriza $630. Okwongeza ekkomo okutuuka ku $5,000 kufuula okumenyeka okutono (0.25% ku buli lunyiriri olujjuvu) naye okunene ($5,110). Okufiirwa okusuubirwa ku buli ddoola esibiddwa kuli 2.70% ku kkomo lyonna.

entandikwa / ekkomo
$10 / $500
okufiirwa okuleeta okumenyeka
6
p(okumenyeka) ku buli lunyiriri olujjuvu
1.8%
okufiirwa ng'emenyese
$630

Ekizibu

Omuzannyi asiba $10 ku mmyufuzzaalaEmmyufuZzaala ya emu ku emu ku nnamba 18 emmyufu. Mu Lufalansa: rouge.Soma byonna → era akubisaamu emirundi ebiri buli lw'afiirwa, n'addayo ku ntandikwa ng'awangudde. Ekkomo ly'emmeeza ery'awaggulu liri $500. (a) Okufiirwa kumeka omuddiriŋŋanwa okumenya okulinnyisa zzaalaenteekateekaOkulinnyisa zzaalaEtteeka lyonna erikyusa ssente za zzaala okusinziira ku bivuddemu emabega. Okulinnyisa oluvannyuma lw'okufiirwa kuzirinnyisa ng'ofiiriddwa, okulinnyisa oluvannyuma lw'okuwangula kuzirinnyisa ng'owangudde.Soma byonna →? (b) ObusobokaokubalaObusobokaObusoboka bw'ekivaamu, okuva ku 0 okutuuka ku 1 oba 0% okutuuka ku 100%. Ennamba emu: 1/37 = 2.70%.Soma byonna → ku buli lunyiriri olujjuvu bwe buliwa? (c) Kiki ekifiirwa ng'emenyese? (d) Ekkomo lya $5,000 likyusa litya eby'okuddamu? (e) Waliwo ekkomo lyonna erifuula enkola eno ey'amagoba?

Ekkomo ly'Emmeeza ya Roulette

Eby'okuddamu (a)–(c)

Ssente za zzaala: 10, 20, 40, 80, 160, 320. Ey'omusanvu yandibadde 640 > 500, kale okufiirwa mukaaga kugimenya. (b) p(okufiirwa) = 19/37 ku mmyufu; (19/37)⁶ = 0.0183, nga 1.8% ku buli lunyiriri olujjuvu. Olunyiriri olujjuvu lumala okwetooloola nga kubiri ku kigero, kale ekiseera ky'okuzannya eky'okwetooloola 100 kirimu ennyiriri ezijjuvu nga 50 era p(waakiri okumenyeka kumu) ≈ 1 − 0.9817⁵⁰ ≈ 60%. (c) 10 + 20 + 40 + 80 + 160 + 320 = $630, nga yunitissenteYunitiSsente za zzaala ez'entandikwa enkola oba omuzannyi z'akozesa. Okulinnyisa zzaala kunnyonnyolwa mu yuniti kusobole okukola ku mmeeza yonna.Soma byonna → 63 ez'entandikwa, so ng'olunyiriri olujjuvu lwali lugezaako kuwangula $10.

ekkomookufiirwa okuleeta okumenyekap(okumenyeka) ku buli lunyiriri olujjuvuokufiirwa ng'emenyesep(okumenyeka mu kwetooloola 100)okuwangula okwetaagisa okuzzaawo
$100313.5%$70≈ 100%7
$50061.8%$630≈ 60%63
$1,00061.8%$630≈ 60%63
$2,00070.94%$1,270≈ 36%127
$5,00090.25%$5,110≈ 11%511
$20,000110.07%$20,470≈ 3%2,047
Buli lw'okubisaamu ekkomo emirundi ebiri, okumenyeka kufuuka nga kwa kitundu mu busoboka ate kwa mirundi ebiri mu bbeeyi. Ekivaamu ky'okukubisaamu tekikyuka.

Eky'okuddamu (d)

Ku $5,000: ssente za zzaala okutuuka ku 2,560 zikkirizibwa; ey'ekkumi, 5,120, egaanibwa. Okufiirwa mwenda kugimenya: (19/37)⁹ ≈ 0.25% ku buli lunyiriri olujjuvu, nga 11% ku biseera by'okuzannya eby'okwetooloola 100. Okufiirwa ng'emenyese: 10 + 20 + … + 2,560 = $5,110. Omuzannyi aguze akabi akatono mu busoboka ku bbeeyi y'akabi akanene. Mu biseera by'okuzannya bingi, bbeeyi esuubirwa ey'okumenyeka eri p × okufiirwa ≈ 0.0183 × 630 = $11.5 ku buli lunyiriri olujjuvu ku kkomo lya $500 ne 0.0025 × 5,110 = $12.8 ku $5,000; mu kusemberezaamu omuwendo, gwe muwendo gwe gumu, era kwe kufiirwa okusuubirwaokubalaOkufiirwa okusuubirwaOmuwendo ogusuubirwa nga gukubisiddwamu ssente zonna ezisibiddwa; ssente ez'okufiirwa ku kigero mu kiseera ky'okuzannya oba mu kiseera ekimu.Soma byonna → okw'olunyiriri olujjuvu nga kugattiddwako $10 ennyiriri ezijjuvu eziwangula ze zifuna.

Eky'okuddamu (e)

Nedda. Okufiirwa okusuubirwa ku buli lunyiriri olujjuvu = (ssente za zzaala zonna ezisuubirwa mu lunyiriri) / 37, ku kkomo lyonna, kubanga buli zzaala eri −1/37 ku yo yennyini. Ekkomo lisalawo busalawo engeri okufiirwa gye kugabanyizibwamu wakati w'okuwangula okutono okungi n'okufiirwa okunene okutono. Awatali kkomo era ne 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 → ezitaggwaawo, okulinnyisa kwandi“kola”, mu ngeri nti tekwandimenyese, era kwandisibye ssente ezitaliiko kkomo n'okufiirwa okusuubirwa okwa 2.70% ku ssente ezo ezitaliiko kkomo. Ekkomo ly'emmeezaemmeezaEkkomo ly'emmeezaZzaala esinga obutono n'esinga obunene ekkirizibwa. Ekkomo ery'waggulu lye liyimiriza enkola ez'okukubisaamu bbiri.Soma byonna → si lye liziyiza MartingaleenteekateekaMartingaleOkulinnyisa zzaala okukubisaamu zzaala bbiri oluvannyuma lwa buli kufiirwa. Laba ekitundu ky'Enteekateeka za Zzaala okumanya ky'ekola ne ky'etakola.Soma byonna → okukola. Okubala kwe kukiziyiza.

Martingale ku ntandikwa ya $10, okwetooloola 100: ekivaamu eky'ekigero okusinziira ku kkomo (kyagezesebwa)$
ekkomo lya $500
≈ −$75
ekkomo lya $1,000
≈ −$75
ekkomo lya $2,000
≈ −$72
ekkomo lya $5,000
≈ −$70
$10 buli mulundi, ekkomo lyonna
$27
$
04080
Emiggo giraga obunene bw'okufiirwa. Okwongeza ekkomo kumpi tekukyusa kigero; okulinnyisa kusiba nga $2,800 mu kwetooloola 100 ka ekkomo libe lyenkana wa.

Emmeeza bbiri entuufu

Ekyokulabirako kya Thorp mmeeza ya $1 erina ekkomo ery'awaggulu lya $1,000, omuzannyi w'asuubira okuwangula $30 ez'eky'eggulo ddoola emu emu. Ssente za zzaala 1, 2, 4 … 512 zikkiriza zzaala kkumi, kale okufiirwa kkumi omuddiriŋŋanwa kumenya okulinnyisa: omulundi gumu ku nnyiriri ezijjuvu 785 ku nnamuziga wa Bulaaya (omulundi gumu ku 613 ku wa Amerika), ku bbeeyi ya $1,023. Ennyiriri ezijjuvu amakumi asatu zonna ziwangula 96.2% ku mirundi. Ebisigadde 3.8% bifiirwa nga $1,000, era ekivaamu eky'ekigero eky'akawungeezi kiri −$9.17, ekyenkana ddala 1/37 ku $339 ennyiriri ezijjuvu amakumi asatu ze zisiba ku kigero. Emmeeza ya $5 erina ekkomo lya $2,000 teyawukana: ssente za zzaala okutuuka ku $1,280 zikkiriza zzaala mwenda, era okumenyeka kujja omulundi gumu ku nnyiriri ezijjuvu 403 ku nnamuziga wa Bulaaya (omulundi gumu ku 323 ku wa Amerika) era kufiiriza $2,555.

Ssente za zzaala ezikubisibwamu zirinnya okutuuka ku kkomo ly'emmeeza ery'awaggulu so ng'eky'eggulo kirindiridde mu kisenge ekiddako.

Omuzannyi omugagga

Okulinnyisa kuwe ssente z'okuzannyisa nnyingi mu kifo ky'ekkomo ettono: yuniti 1,000, entandikwa ya yuniti emu n'okwetooloola 1,000 ku mmyufu, ng'oddamu okutandika ku yuniti emu buli lw'okukubisaamu okuddako kusukka ekisigaddewo. Twagezesa obuwungeezi obwo akakadde kamu. Ku nnamuziga wa Bulaaya 52% bumaliriza mu magoba, 21% bufiirwa buli kimu, era ekivaamu eky'ekigero kiri yuniti −124. Ne mu muzannyo ogutaliimu zeeronnamuzigaZeeroEkinnya kimu ekya kiragala ekitabikkibwa zzaala ya emu ku emu, eya dazeni oba ey'empagi; y'ensibuko y'enkizo ya kaasino. Era eyitibwa: zeero emu, 0.Soma byonna →, buli zzaala mw'eba ey'obwenkanya, nga 60% bwokka bwe bwandimalirizza mu magoba. Akawungeezi aka bulijjo kawangula katono; ekigero kisasulwa obuwungeezi obukoma ku zeero.

nnamuzigaokumaliriza mu magobaokufiirwa yuniti 1,000ekivaamu eky'ekigero
tewali zeero (omuzannyo ogw'obwenkanya)60%15%0
Wa Bulaaya52%21%yuniti −124
Wa Amerika45%30%yuniti −250
Okugezesa kwaffe, obuwungeezi akakadde kamu ku buli nnamuziga. Ebigero biri 1/37 ne 1/19 ku ekyo okulinnyisa kye kusiba mu kwetooloola 1,000: nga yuniti 4,600 ku nnamuziga wa Bulaaya ne 4,750 ku wa Amerika.

Ekyokuyiga

Kaasino ziteekawo ekkomo okukomya enjawulo y'ebivaamuokubalaEnjawulo y'ebivaamuEkipimo ky'engeri ebivaamu gye bisaasaanamu okwetooloola omuwendo ogusuubirwa. Kinene ku straight up, kitono ku zzaala za emu ku emu.Soma byonna → yaazo, so si kuwangula nkola. Okuwangula Martingale kiva kyokka mu ekyo, kye zisanyukira, era okubala kwandigiwangudde ne bwe kitandibadde bwe kityo. Omuzannyi alowooza nti ekkomo kye kizibu azudde ekiwonvu n'akitwala ng'ekkubo eriserengeta.

Ensengekera

p(okumenyeka) = (19/37)ᵏ, k = okufiirwa ekkomo kwe likkiriza
okufiirwa ng'emenyese = entandikwa · (2ᵏ − 1)
E[okufiirwa ku buli lunyiriri olujjuvu] = E[ssente za zzaala mu lunyiriri] / 37

Ebibuuzo

Ssente z'okuzannyisa ennyingi zandikigonjodde?

Zikusobozesa okuwangaala okutuuka ku kkomo ery'awaggulu, okumenyeka we kubeera okutono mu busoboka naye okunene. Okufiirwa okusuubirwa ku buli ddoola tekukyuka.

Ate “grand Martingale” eyongerako yuniti ku buli kukubisaamu?

Ssente za zzaala 10, 30, 70, 150, 310: ekkomo lya $500 lituukibwako oluvannyuma lw'okufiirwa ttaano, era okumenyeka kufiiriza $570. 2.70% ze zimu.

Lwaki kaasino zirina ekkomo ery'awaggulu n'akatono?

Omuzannyi omu aleme kusiba okusinga ssente kaasino z'eterese ze esobola okusasula awatali buzibu. Kuddukanya njawulo y'ebivaamu.

Okwesanyusa n'Okubala

Gezaako bino ggwe kennyini okusooka. Buli kugonjoola kuzingiddwa; kuggulewo ng'oli mwetegefu.

  1. MartingaleenteekateekaMartingaleOkulinnyisa zzaala okukubisaamu zzaala bbiri oluvannyuma lwa buli kufiirwa. Laba ekitundu ky'Enteekateeka za Zzaala okumanya ky'ekola ne ky'etakola.Soma byonna → etandikira ku $100 ku mmyufuzzaalaEmmyufuZzaala ya emu ku emu ku nnamba 18 emmyufu. Mu Lufalansa: rouge.Soma byonna → era yeekkiriza zzaala ezitasukka n mu lunyiriri olujjuvu: oluvannyuma lw'okufiirwa n omuddiriŋŋanwa eva ku mulamwa n'etandika buggya. Wandiika ekivaamu eky'ekigero eky'olunyiriri olujjuvu olumu ng'ensengekera mu n, okibale ku zzaala 5, 6 ne 7 ku nnamuziga wa Bulaaya.

    Laga okugonjoola

    Eky'okuddamu Ekigero kiri 100 × (1 − (38/37)ⁿ): −$14.26 ku zzaala 5, −$17.35 ku 6 ne −$20.52 ku 7. Okwekkiriza zzaala ennyingi kufuula olunyiriri olujjuvu olw'ekigero okuba olubi okusingawo, so si olulungi.

    Olunyiriri olujjuvu luwangula $100 okuggyako nga zzaala zonna n zifiirwa, ekibaawo n'obusoboka qⁿ, q nga eri 19/37. Zonna bwe zifiirwa, ssente za zzaala 100, 200 … 100 × 2ⁿ⁻¹ zigattibwa ne ziba 100 × (2ⁿ − 1). Kale ekigero kiri 100 × (1 − qⁿ) − 100 × (2ⁿ − 1) × qⁿ = 100 × (1 − (2q)ⁿ).

    Wano 2q = 38/37, katono okusinga 1, kale (2q)ⁿ ekula ne n era ekigero kikka: n = 5 ewa 1.1426 ne −$14.26; n = 6 ewa 1.1735 ne −$17.35; n = 7 ewa 1.2052 ne −$20.52. Amadaala amawanvu gafiirwa emirundi mitono, mu 3.6%, 1.8% ne 0.9% ku nnyiriri ezijjuvu, naye buli kufiirwa kukubisaamu emirundi ebiri, era ssente nnyingi ziyita ku mmeeza buli lunyiriri olujjuvu, ku 2.70% ku buli zzaala.

    Ku nnamuziga wa Amerika 2q = 40/38 era emiwendo giri −$29.24, −$36.04 ne −$43.20 (Taylor, 2021). Mu muzannyo ogutaliimu zeeronnamuzigaZeeroEkinnya kimu ekya kiragala ekitabikkibwa zzaala ya emu ku emu, eya dazeni oba ey'empagi; y'ensibuko y'enkizo ya kaasino. Era eyitibwa: zeero emu, 0.Soma byonna → 2q = 1, era buli lunyiriri olujjuvu luba n'ekigero kya zeero ddala ne bwe gabeera amadaala mawanvu gatya.

  2. “Grand Martingale” ekubisaamu emirundi ebiri ssente za zzaala oluvannyuma lw'okufiirwa n'eyongerako yunitissenteYunitiSsente za zzaala ez'entandikwa enkola oba omuzannyi z'akozesa. Okulinnyisa zzaala kunnyonnyolwa mu yuniti kusobole okukola ku mmeeza yonna.Soma byonna → emu, kale ssente za zzaala zigenda 1, 3, 7, 15, 31 … Oli mu magoba ga kyenkana wa okuwangula okusooka bwe kujja ku zzaala 1, 2, 3 oba ku zzaala eya k? Ku yuniti ya $10 n'ekkomo lya $500, olunyiriri olujjuvu lumenyeka emirundi emeka, era olunyiriri olujjuvu lugula ki ku kigero?

    Laga okugonjoola

    Eky'okuddamu Okuwangula ku zzaala eya k kukuleka mu magoba ga yuniti k: +1, +2, +3 n'ebirala. Ku $10 ne $500 olunyiriri olujjuvu lumenyeka oluvannyuma lw'okufiirwa ttaano, 3.57% ku nnyiriri ezijjuvu, ku −$570. Ku kigero olunyiriri olujjuvu lufiirwa $2.32 ku $85.73 ezisibiddwa: 2.70%.

    Ssente za zzaala eza k ziba yuniti 2ᵏ − 1: 1, 3, 7, 15, 31. Ssente za zzaala k − 1 ezisooka zigattibwa ne ziba 2ᵏ − 2 − (k − 1) = 2ᵏ − k − 1. Okuwangula ku zzaala eya k kusasula 2ᵏ − 1, kale olunyiriri olujjuvu lukoma nga lwa magoba ga yuniti (2ᵏ − 1) − (2ᵏ − k − 1) = k: yuniti emu ey'enjawulo ku buli kufiirwa nga okuwangula tekunnajja.

    Ku $10 buli yuniti ssente za zzaala ziri $10, $30, $70, $150 ne $310; eddako, $630, esukka ekkomo lya $500. Okufiirwa ttaano omuddiriŋŋanwa, (19/37)⁵ = 3.57%, kufiiriza 10 + 30 + 70 + 150 + 310 = $570.

    Ekigero: okuwangula kuleeta $10 × k n'obusoboka (19/37)ᵏ⁻¹ × 18/37 ku k = 1 okutuuka ku 5, ate okumenyeka kutwala $570 n'obusoboka bwa 3.57%; awamu −$2.32. Ssente ezisibiddwa ziba $85.73 ku kigero buli lunyiriri olujjuvu, ne 2.32/85.73 = 2.70%. Martingale eya bulijjo ku mmeeza y'emu emenyeka oluvannyuma lw'okufiirwa mukaaga, 1.83% ku nnyiriri ezijjuvu, ku −$630, era efiirwa $1.74 ku $64.20 ezisibiddwa: 2.70% nate.

  3. Omuzannyi ateekateeka Martingale ku mmyufu ng'atandika ku zzaala ya $1 ku mmeeza erina ekkomo lya $1,000, kale zzaala kkumi zisoboka: $1, $2, $4 n'ebirala okutuuka ku $512. Olunyiriri olujjuvu lufiirwa zonna kkumi emirundi emeka, ekyo kitwala bbanga ki ku kigero, era akawungeezi aka zzaala 200 kakoma bwe kati emirundi emeka?

    Laga okugonjoola

    Eky'okuddamu Olunyiriri olujjuvu lufiirwa zonna kkumi nga omulundi gumu ku 784, ekifiiriza $1,023. Ezo zzaala nga 1,600 ku kigero, era akawungeezi aka zzaala 200 katomera ekisenge nga 11% ku mirundi. Olunyiriri olujjuvu lukyafiirwa $0.31 ku kigero ku $11.31 ezisibiddwa: 2.70%.

    Zzaala ku mmyufu efiirwa n'obusoboka bwa 19/37, zeero mw'ebalirwa. Kkumi omuddiriŋŋanwa: (19/37)¹⁰ ≈ 0.00128, nga 1 ku 784. Ssente za zzaala 1 + 2 + 4 + … + 512 zigattibwa ne ziba $1,023.

    Olunyiriri olujjuvu lutwala zzaala 2.05 ku kigero, kale ennyiriri ezijjuvu 784 zitwala zzaala nga 1,600. Ng'obala okwetooloola kumu kumu, omutendera gw'okufiirwa kkumi gulabika awamu mu zzaala 200 11.3% ku mirundi.

    Wakati w'obuzibu omuzannyi awangula $1 buli lunyiriri olujjuvu: nga $783 nga olubi terunnajja, oluvannyuma −$1,023, nga −$240 ku bbanga lyonna. Ku buli lunyiriri olujjuvu: 1 × (1 − 0.00128) − 1,023 × 0.00128 ≈ −$0.31. Ssente ezisibiddwa ku buli lunyiriri olujjuvu: 1 + 2 × (19/37) + 4 × (19/37)² + … + 512 × (19/37)⁹ ≈ $11.31. Ne −0.31/11.31 = −2.70%.

    Geraageranya zzaala esooka eya $10 ku kkomo lya $500, zzaala mukaaga: ekisenge kijja omulundi gumu ku nnyiriri ezijjuvu 55, era akawungeezi aka zzaala 200 kakisanga 84% ku mirundi. Ekkomo ery'awaggulu lifuula okugwa okutono mu busoboka naye okunene, so si okw'obuseere obutono.

Eky'okusesa

Kutono mu busoboka era kunene, ku kkomo lyonna. Ekivaamu ky'okukubisaamu tekikyuka.

Kutono mu busoboka era kunene, ku kkomo lyonna. Ekivaamu ky'okukubisaamu tekikyuka.

Ensibuko

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Essuula 13, roulette.
  2. Thorp, E. O. “Optimal gambling systems for favorable games.” Review of the International Statistical Institute 37(3), 1969.
  3. Thorp, E. O. The Mathematics of Gambling. Gambling Times / Lyle Stuart, 1984.
  4. Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed. Academic Press, 2013.
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kyakeberebwa 2026-09-28ekyokulabirako: roulette ya Bulaaya, zeero emuenkola y'okubalirira ↗ensibuko ↗