Enfumo: Enteekateeka ya Zzaala Ewangula Bulijjo
“Nnina enkola ewangula 80% ku biseera.” Kiyinzika. Naye ekyafiiriza ssente.
Enkola esobola okufuula ebiseera eby'okuwangula okuba ebingi. Tesobola kufuula muwendo ogusuubirwa okuba waggulu wa zeero, kubanga buli zzaala gy'esiba eri −1/37 ku ssente zaayo, era emiwendo egisuubirwa gigattibwa. Enkola eziwangula emirundi egisinga ze zisinga okufiirwa ennyo bwe zifiirwa.
Ekyogerwa
Okukkiriza: wantu waliwo enteekateeka ya zzaala mu roulette ewangula bulijjo, enkola y'okukyusakyusa ssente za zzaala okusinziira ku bivuddemu eby'emabega efuula roulette omuzannyo ogw'okuwangula. Obukakafu obuweebwa: ebiseera eby'okuwangula ebiddiriŋŋana, vidiyo ku ngeri y'okuwangula roulette buli mulundi, obujulizi bw'omuntu, n'olupapula lw'okubala olw'wiiki ey'omukisa. Ekyogerwa kitera kuba kya mazima; omuntu akikkiriza kubanga kibadde kikola.
Lwaki kikyamu, mu sentensi emu
Emiwendo egisuubirwaokubalaOmuwendo ogusuubirwaEkivaamu eky'omu makkati ku buli zzaala mu bbanga eddene. −1/37 ya ssente za zzaala ku buli zzaala eya bulijjo eya Bulaaya.Soma byonna → gigattibwa. Singa buli zzaala erina EV = −1/37 ku ssente zaayo, olunyiriri lwonna olwa zzaala lulina EV = −1/37 ku mugatte ogusibiddwa, etteeka lyonna lye lyalonda ssente za zzaala. Enkola tteeka ly'okulonda ssente za zzaala. N'olwekyo buli nkola erina EV = −1/37 ku mugatte gwa zzaalassenteOmugatte gwa zzaalaOmugatte gwa ssente zonna ezisibiddwa mu kiseera ky'okuzannya oba mu bbanga, nga mw'otwalidde n'amagoba agaddamu okusibwa. Era guyitibwa: handle, action.Soma byonna →. Kino kyakakasibwa mu kubala (Doob ne Halmos baakikakasa mu myaka gya 1930; Thorp 1969 annyonnyola obukwakkulizo), era tekirina byekusifu eri amateeka ag'amagezi. Akakwakkulizo kamu akasaana okumanya ye zzaala esinga obutono: ekyokulabirako kya Thorp kisiba $1,000 ku emmyufuzzaalaEmmyufuZzaala ya emu ku emu ku nnamba 18 emmyufu. Mu Lufalansa: rouge.Soma byonna →, olwo ssente 90, olwo ssente 9 n'okweyongerayo, nga zikendeera emirembe gyonna. Ku busoboka 18/37 zzaala esooka ewangula era omuzannyi n'asigala waggulu emirembe gyonna, wadde ekivaamu ekisuubirwa kikyali −1/37 ku byonna ebisibiddwa. Zzaala esinga obutono ku mmeeza eya ddala ekikomya, era n'essuubi lyonna ery'okusigala waggulu mu bbanga eddene.
Okusembera mu Bbanga Eddene: Etteeka ly'Emiwendo Eminene mu Roulette
Lwaki kirabika nga kikola
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 → oluvannyuma lw'okufiirwa kufuula ebiseera eby'okuwangula okuba ebingi. MartingaleenteekateekaMartingaleOkulinnyisa zzaala okukubisaamu zzaala bbiri oluvannyuma lwa buli kufiirwa. Laba ekitundu ky'Enteekateeka za Zzaala okumanya ky'ekola ne ky'etakola.Soma byonna → okuva ku $10 ku kkomo lya $500 ekomya nga 80% ku biseera eby'okwetooloola 100 nga biri waggulu yunitissenteYunitiSsente za zzaala ez'entandikwa enkola oba omuzannyi z'akozesa. Okulinnyisa zzaala kunnyonnyolwa mu yuniti kusobole okukola ku mmeeza yonna.Soma byonna → ntono. Omuzannyi agikozesa mu biseera abiri awangula kkumi na mukaaga ku byo era ekyo ky'ajjukira. Ebiseera ebina eby'okufiirwa buli kimu kifiirwa okusinga ebiseera kkumi eby'okuwangula bye bivaamu, era okubala ku biseera abiri kuli wansi wa zeero. Enkola tekyusizza kigero; ezzizza okufiirwa mu biseera ebitono, ebinene, we kyangu okukuyita omukisa omubi.
Ekigezo omuntu yenna ky'asobola okukola
“Ekyokugezesa Enteekateeka ya Zzaala” ku mukutu guno kizannya ebiseera 10,000 eby'enkola yonna, oba koodi yo, mu sikonda emu. Kiteeke ku nkola gy'okkiririzaamu osome ekigero. Singa ekigero kyali waggulu wa zeero ku nteekateeka yonna, olupapula luno lwandikyogedde. Buli nteekateeka, buli nkola, buli kkomo ly'emmeezaemmeezaEkkomo ly'emmeezaZzaala esinga obutono n'esinga obunene ekkirizibwa. Ekkomo ery'waggulu lye liyimiriza enkola ez'okukubisaamu bbiri.Soma byonna → biwa ekigero kya −2.70% ku mugatte gwa zzaala n'okukyukakyuka okutono. Obujulizi bw'abantu byokulabirako bya muntu omu; ekyokugezesa kiwa ebyokulabirako omutwalo gumu.
Enkola etasobola kufiirwa
Mu 1997 omuwandiisi wa poker Mike Caro yafulumya enkola ya roulette ng'akaseerezo, era Gambling Times n'egiddamu okufulumya mu 2001. Lukalala lwa zzaala z'olina okwewala: tosiba ku mmyufu oba enzirugavuzzaalaEnzirugavuZzaala ya emu ku emu ku nnamba 18 enzirugavu. Mu Lufalansa: noir.Soma byonna →, ezitagabanyizika oba ezigabanyizika, oba ku 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 →; tewali nnamba emmyufu etagabanyizika era tewali nzirugavu egabanyizika; era tewali kintu ku 30, oba ku lunyiriri oluwanvu olw'ebinnyaebikozesebwaEkinnyaKimu ku bisenge 37 ebiriko ennamba ku rotor. Era biyitibwa: slot, cup.Soma byonna → okuva ku 11 ng'oyita mu ludda essaawa lw'etambulamu okutuuka ku 14 ku nnamuziga wa Amerika. Gatta amateeka gonna awamu era tewali nnamba esigalawo. Ebinnya byokka ebiri ebweru w'olunyiriri olwo ye 0, 28, 9, 26, 30 ne 2; 30 egaaniddwa mu linnya, ate ezisigadde zeero, oba ezigabanyizika era enzirugavu, oba ezitagabanyizika era emmyufu. Omuzannyi agoberera enkola eno tasiba era tafiirwa. Enkizo yaayo zeero, era y'enkola ya roulette yokka ey'amazima ku ngeri gy'etuukamu awo.
Enkola ezirina amannya, buli emu mu sentensi emu
Enkola ezitundibwa n'erinnya, oba ng'enkola ya roulette ewangula, tezaawukana. Buli emu kibinja kya zzaala, era buli zzaala esasula nnamuziga 2.70% ye. Bollman (2024) ayita mu nkola eziwerako ku nnamuziga wa Amerika, buli emu we efiiriza 5.26%; wano ziri ku nnamuziga wa Bulaaya.
Ekituufu
Enkola zikyusa enfaanana y'ekiseera ky'okuzannya: emirundi gy'owangula, obunene bw'okuwangula, n'obubi bw'embeera esinga obubi. Ebyo by'okulondako bya ddala era omuzannyi ayinza okwagala enfaanana emu okusinga endala. Enkola kye zitakyusa gwe muwendo, nga gwe 2.70% ku byonna ebisibiddwa, era kubanga okulinnyisa zzaala kusiba bingi okusinga zzaala ey'omuwendo gumuenteekateekaZzaala ey'omuwendo gumuOkusiba ssente ze zimu buli kwetooloola. Kye kipimo buli kulinnyisa zzaala kwe kugeraageranyizibwako.Soma byonna →, kusasula bingi ku gwo.
Ebibuuzo
Emyezi mukaaga egy'ebiseera bya buli wiiki biba nga ebiseera 25. Martingale ewangula 80% ku byo. Ebiseera eby'okufiirwa bijja, era binene.
Etteeka ly'okukoma likendeeza omugatte gwa zzaala, bwe kityo ne likendeeza okufiirwa okusuubirwaokubalaOkufiirwa okusuubirwaOmuwendo ogusuubirwa nga gukubisiddwamu ssente zonna ezisibiddwa; ssente ez'okufiirwa ku kigero mu kiseera ky'okuzannya oba mu kiseera ekimu.Soma byonna →. Teririfuula kuba waggulu wa zeero.
Si ku nnamuziga omwenkanya. Ku nnamuziga asosolalaabuNnamuziga asosolaNnamuziga alina obulema mu mubiri bwe obufuula ebinnya ebimu okujja okusinga 1/37. Tebitera kubaawo, era bizuulibwa wokka n'okwetooloola enkumi n'enkumi okuwandiikiddwa.Soma byonna →, ekyo kizibu kya fizikisi, so si nkola.
Okwesanyusa n'Okubala
Gezaako bino ggwe kennyini okusooka. Buli kugonjoola kuzingiddwa; kuggulewo ng'oli mwetegefu.
Enkola ey'okusaaga eya Mike Caro eya 1997 ku nnamuziga wa Amerika ewera emmyufuzzaalaEmmyufuZzaala ya emu ku emu ku nnamba 18 emmyufu. Mu Lufalansa: rouge.Soma byonna → n'enzirugavuzzaalaEnzirugavuZzaala ya emu ku emu ku nnamba 18 enzirugavu. Mu Lufalansa: noir.Soma byonna →, ezitagabanyizika n'ezigabanyizika, ne 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 →; ennamba emmyufu ezitagabanyizika n'enzirugavu ezigabanyizika; ennamba 30; ne buli kinnyaebikozesebwaEkinnyaKimu ku bisenge 37 ebiriko ennamba ku rotor. Era biyitibwa: slot, cup.Soma byonna → mu lunyiriri okuva ku 11 okwetooloola ng'essaawa bw'etambula okutuuka ku 14. Kozesa amateeka limu limu. Nnamba ki ezisigaddewo okusibako?
Laga okugonjoola
Eky'okuddamu Tewali. Enkola tesiba zzaala n'akatono, n'olwekyo enkizo ya kaasino yaayo eri zeero ddala.
Okuwera emmyufu, enzirugavu, ezitagabanyizika, ezigabanyizika ne zeero kulekawo ennamba emu emu n'ebibinja ebitono mu 1 okutuuka ku 36.
Obutaba na mmyufu ezitagabanyizika era obutaba na nzirugavu ezigabanyizika kulekawo emmyufu ezigabanyizika (12, 14, 16, 18, 30, 32, 34, 36) n'enzirugavu ezitagabanyizika (11, 13, 15, 17, 29, 31, 33, 35): ennamba kkumi na mukaaga. Okuwera 30 kulekawo kkumi na ttaano.
Ku nnamuziga wa Amerika, olunyiriri okuva ku 11 ng'essaawa bw'etambula okutuuka ku 14 lubikka ebinnya 32 ku 38. Ebinnya mukaaga ebiri ebweru waalwo bye 0, 28, 9, 26, 30 ne 2. Ennamba zonna kkumi na ttaano ezisigaddewo ziri munda mu lunyiriri, n'olwekyo etteeka erisembayo nazo lizigyawo. Enkola etasiba zzaala n'akatono y'emu yokka etafiirwa n'akatono, era ekyo Caro kye yali ategeeza.
Kryptos eddukanya MartingaleenteekateekaMartingaleOkulinnyisa zzaala okukubisaamu zzaala bbiri oluvannyuma lwa buli kufiirwa. Laba ekitundu ky'Enteekateeka za Zzaala okumanya ky'ekola ne ky'etakola.Soma byonna → ssatu omulundi gumu, emu ku buli bibiri bya zzaala ya emu ku emuzzaalaZzaala ya emu ku emuEmmyufu/enzirugavu, ezitagabanyizika/ezigabanyizika, ennene/entono. Ennamba 18, esasula 1:1.Soma byonna → (ennene oba entono, ezitagabanyizika oba ezigabanyizika, emmyufu oba enzirugavu), ne ssente za zzaala 1, 2, 4, 8, 16, 32 n'okukoma oluvannyuma lw'okufiirwa mukaaga. Twala emu ku ssatu ku nnamuziga wa Bulaaya. Emirundi emeka efiirwa zzaala zonna omukaaga, olunyiriri olujjuvu lumu lufuna ki ku kigero, era ekyo kitundu ki ku ssente ezisibiddwa?
Laga okugonjoola
Eky'okuddamu Efiirwa zonna omukaaga nga omulundi gumu mu nnyiriri enjjuvu 55, 1.83% ku biseera, era ekyo kigula yunitissenteYunitiSsente za zzaala ez'entandikwa enkola oba omuzannyi z'akozesa. Okulinnyisa zzaala kunnyonnyolwa mu yuniti kusobole okukola ku mmeeza yonna.Soma byonna → 63. Ku kigero olunyiriri olujjuvu lufiirwa nga yuniti 0.17 ku yuniti 6.42 ezisibiddwa: 2.70%, omuwendo gwa buli zzaala ku nnamuziga.
Zzaala efiirwa n'obusoboka 19/37, nga mw'otwalidde zeero. Mukaaga okuddiriŋŋana: (19/37)⁶ = 0.0183, nga 1 ku 55, era olwo ssente za zzaala 1 + 2 + 4 + 8 + 16 + 32 = 63 ziweddewo. Bwe kitaba bwe kityo olunyiriri olujjuvu lukoma n'okuwangula ne +1 yuniti.
Ekigero: 1 × (1 − 0.0183) − 63 × 0.0183 = 1 − 64 × 0.0183 = −0.17 yuniti.
Ssente ezisibiddwa: zzaala esooka bulijjo esibibwa, ey'okubiri oluvannyuma lw'okufiirwa kwokka, n'ebirala: 1 + 2 × (19/37) + 4 × (19/37)² + … + 32 × (19/37)⁵ = yuniti 6.42. Ate −0.17/6.42 = −2.70%.
Okwetooloola omukaaga okwawandiikibwa kusalawo bwesalazi ludda ki buli zzaala ky'eriko, era nnamuziga tasobola kukumanya. Okuddukanya zonna essatu kukubisaamu ssatu ssente ezisibiddwa n'okufiirwa okwa wakati wamu nazo. Bollman (2024) akola ku nkola eno ku nnamuziga wa Amerika, buli emu ku zo gy'efiirwa mukaaga okuddiriŋŋana 2.1% ku biseera.
Eky'okusesa
Okuwangula emirundi mingi n'okuwangula ssente miwendo gya njawulo.
Ensibuko
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Doob, J. L. “Note on probability.”
- Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.”
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed.