Okubala mu Roulette · Enkozesa · eddakiika 13

Akabi k'Okumalwako Ssente

Q: Okulinnyisa zzaala kukendeeza akabi k'okumalwako ssente?

Martingale ekakendeeza ku biseera by'okuzannya ebimpi era ekakuza nnyo ku biwanvu. Zzaala ey'omuwendo gumu ku yuniti ennene y'engeri ey'amazima ey'okukakendeeza.

Obusoboka bw'okufiirwa ssente zo zonna ez'okuzannyisa nga tonnatuuka ku kiruubirirwa.

Eky'okuddamu mu bufunze

Ku zzaala ya emu ku emu, akabi k'okumalwako ssente kagoberera ensengekera ya gambler’s ruin. Ne ssente z'okuzannyisa eza $500, zzaala za $10 n'ekiruubirirwa kya $600, otuuka ku kiruubirirwa nga 57% ku biseera ate ebisigadde ssente zikuggwaako.

ensengekera

gambler’s ruin

p (zzaala ya emu ku emu)

18/37

q/p

1.0556

ekivaamu ekisinga obukadde

Pascal–Fermat, 1656

Ekibuuzo

Olina yunitissenteYunitiSsente za zzaala ez'entandikwa enkola oba omuzannyi z'akozesa. Okulinnyisa zzaala kunnyonnyolwa mu yuniti kusobole okukola ku mmeeza yonna.Soma byonna → a ez'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 → era oyagala okutuuka ku yuniti a + b, ng'osiba yuniti emu omulundi gumu ku zzaala ya emu ku emuzzaalaZzaala ya emu ku emuEmmyufu/enzirugavu, ezitagabanyizika/ezigabanyizika, ennene/entono. Ennamba 18, esasula 1:1.Soma byonna → n'obusobokaokubalaObusobokaObusoboka bw'ekivaamu, okuva ku 0 okutuuka ku 1 oba 0% okutuuka ku 100%. Ennamba emu: 1/37 = 2.70%.Soma byonna → bw'okuwangula p = 18/37 n'obusoboka bw'okufiirwa q = 19/37. Obusoboka bw'okutuuka ku kiruubirirwa nga tonnatuuka ku zeero bwe buliwa? Eky'okuddamu kyabalibwa Pascal, Fermat ne Huygens mu myaka gya 1650 era kye kimu ku bivaamu ebisinga obukadde mu busoboka.

Blaise Pascal: Olugero lwa Nnamuziga wa Roulette

Ensengekera ya gambler’s ruin

P(okutuuka ku kiruubirirwa) = (1 − (q/p)ᵃ) / (1 − (q/p)ᵃ⁺ᵇ). Akabi k'okumalwako ssenteokubalaObusoboka bw'okumalawoObusoboka bw'okufiirwa ssente zonna ez'okuzannyisa nga tonnatuuka ku kiruubirirwa oba ku muwendo gw'okwetooloola.Soma byonna → kiba kimu kuggyako ekyo. Nga q/p = 19/18 ≈ 1.0556, omugerageranyo gukula mangu nnyo ng'omuwendo gwa yuniti gweyongera, kale ensengekera ebonereza nnyo yuniti entono: zzaala gye zikoma okuba ennyingi okutuuka ku kiruubirirwa, emirundi gye gikoma okuba mingi omusolo gwa 2.70% gwe gusasulwa mu kkubo.

ssente z'okuzannyisayunitiekiruubirirwazzaala okutuuka ku kiruubirirwap(okutuuka ku kiruubirirwa)akabi k'okumalwako ssente

$500$10$60010≈ 57%≈ 43%

$500$50$6002≈ 79%≈ 21%

$500$10$1,00050≈ 6%≈ 94%

$500$100$1,0005≈ 43%≈ 57%

$500$500$1,000148.6%51.4%

$100$10$20010≈ 37%≈ 63%

Zzaala ya emu ku emu, ssente za zzaala ezitakyuka, awatali la partage. Ekibalirizi ky'Akabi k'Okumalwako Ssente kibala ku miwendo gyonna.

Engeri y'okukisoma

Yuniti entono zirumya. Okugezaako okukubisaamu bbiri $500 ne zzaala za $10 kuyitamu 6% ku biseera; ne zzaala emu eya $500 kuyitamu 48.6% ku biseera. Okuzannya n'obuvumu, zzaala ntono era nnene, kwongera obusoboka bw'okutuuka ku kiruubirirwa mu muzannyo ogulina okusuubira okubi, kubanga kukendeeza emirundi enkizo ya kaasino gy'ekozesebwa. Era kwongera 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 → ku ebikutuukako, era kukomya akawungeezi mangu. Etteeka lino liyitibwa “bold play is optimal” era lyakakasibwa Dubins ne Savage mu 1965.

Obusoboka bw'okufuula $500 okuba $1,000 ku mmyufu%

zzaala emu eya $500

48.6%

zzaala za $100

≈ 43%

zzaala za $50

≈ 37%

zzaala za $20

≈ 21%

zzaala za $10

≈ 6%

zzaala za $5

≈ 0.5%

024.3048.6%

Zzaala gye zikoma okwetaagisa obungi, enkizo ya kaasino gy'ekoma okusasulwa emirundi mingi. Okuzannya n'okutya kugula nnyo.

Ekizibu gye kyatandikira

Ekibuuzo kino kikadde okusinga roulette. Mu 1656 Pascal yawa Fermat ekikokko: abazannyi babiri bakasuka ddayisi ssatu, buli omu ng'atandika n'obubonero 12; okukasuka 11 kujjuza akabonero ku ludda olumu, okukasuka 14 ku ludda olulala. Bombi baakigonjoola, era Huygens, eyakiwulira okuyita mu bbaluwa okuva eri omukugu mu kubala Pierre de Carcavi, yakikuba mu kyapa mu 1657 ng'ekizibu eky'okutaano eky'ekitabo ekyasooka ku busoboka, n'eky'okuddamu awatali bukakafu. Kkumi n'emu esobola okukasukibwa mu ngeri 27 ate kkumi na nnya mu 15 zokka, kale buli kabonero kagenda ku ludda lw'omuzannyi asooka emirundi 9 ku 14, era ensengekera eri waggulu, n'obubonero 12 buli omu, emufuula asoboka okuwangula byonna emirundi nga 1,157 okusinga okufiirwa byonna. Enkizo ya 2.70% ntono nnyo okusingawo, naye ensengekera y'emu eraga ky'ekola mu zzaala nnyingi.

Mu kikokko kya Pascal, buli kukasuka kwa ddayisi ssatu kujjuza akabonero kamu wakati w'abazannyi.

Zzaala ey'obuvumu ey'amazima

Mu Apuli 2004, Ashley Revell, omuvubuka Omungereza, yatunda kumpi buli kye yalina, nga mwe muli n'engoye ze, n'atwala $135,300 ku Plaza mu Las Vegas. Oluvannyuma lwa zzaala ntono, yateeka omuwendo gwonna ku mmyufuzzaalaEmmyufuZzaala ya emu ku emu ku nnamba 18 emmyufu. Mu Lufalansa: rouge.Soma byonna →, omulundi gumu. AkapiiraebikozesebwaAkapiiraAkapiira akatono akakasukibwa mu lugudo nga kadduka mu ludda olukontana n'olwa rotor. Obupiira obw'omulembe bwa ivorine oba Teflon, mm 18–21.Soma byonna → kaagwa ku mmyufu 7 n'afuluma ne $270,600. Ku nnamuziga alina 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 → bbiri, okwetooloola okwo okumu kwalina obusoboka bwa 47.37% era kwamugula $7,121 ku kigero, enkizo ya kaasino eya 5.26% ku zzaala emu. Nga zisaasaanyiziddwa ku zzaala za $10, ekiruubirirwa kye kimu kyandibadde kumpi tekisoboka. Okuzannya n'obuvumu tekufuula zzaala nnungi; kugifuula mpimpi nga bwe kisoboka.

Ssente zonna ez'okuzannyisa eza Ashley Revell ziri ku kwetooloola kumu okwa nnamuziga alina zeero bbiri.

Akabi k'okumalwako ssente awatali kiruubirirwa

Bw'ozannya buzannya okutuusa ssente lwe zikuggwaako oba n'oyimirira oluvannyuma lw'okwetooloola N, ekibuuzo kifuuka “obusoboka nti ssente zange ez'okuzannyisa zikoma ku zeero mu kwetooloola N bwe buliwa?”. Tewali nsengekera nnyangu ku N yonna naye ebyokugezesa ku mukutu guno bibubala: ssente z'okuzannyisa eza $500 ku $10 ku mmyufu kumpi teziggwaawo mu kwetooloola 100 (wansi wa 1%), ziggwaawo nga 9% ku biseera mu kwetooloola 500, ne nga 95% ku biseera mu 5,000. Awatali tteeka lya kuyimirira, obusoboka busemberera 100%, eyo y'engeri ey'ebbanga eddene ey'enkizo ya kaasinookubalaEnkizo ya kaasinoEkitundu kya buli ssente za zzaala kaasino ky'ekuuma ku kigero: 2.70% mu roulette ya Bulaaya.Soma byonna →.

Ebiseera by'okuzannya kkumi, ssente z'okuzannyisa $500, $25 ku mmyufu, okwetooloola 200ekivuddemu ku ntandikwa

ebiseera 1,000 × okwetooloola 500 · kakobe p10/p25/p75/p90, bbululu omutangaavu wakati, ebyokulabirako 81 ebizibu okulaba · tambuza ku kipande olabe percentile ku kwetooloola

p10 −$500
p25 −$500
wakati −$500
p75 +$0
p90 +$350

ebiseera 1,000 × okwetooloola 500 · omusittale gwa y gukomezeddwa ku percentile 1–99 (enkomerero −$500 okutuuka +$1,500) · okwetooloola 500 · omusingi $25 · emu ku emu

Ennyiriri ezikoma wansi ssente zaggwaawo. Ne yuniti entono zandimaze ebbanga eddene okusingawo ne zikoma mu kifo kye kimu.

Okusembera mu Bbanga Eddene: Etteeka ly'Emiwendo Eminene mu Roulette

Bbanga ki, era mu magoba ki

Ebivaamu ebirala bibiri eby'edda biddamu ebibuuzo abazannyi bye babuuza ddala. Awatali kiruubirirwa, zzaala ya emu ku emu ey'omuwendo gumu emala ku kigero okwetooloola 37 ku buli yuniti ya ssente z'okuzannyisa ku nnamuziga wa Bulaaya ne 19 ku wa Amerika, kubanga buli kwetooloola kutwala 1/37 ya yuniti ku kigero (1/19 ku nnamuziga wa Amerika): yuniti 100 zimala okwetooloola 3,700 ku kigero, newankubadde ekitundu ky'ebiseera by'okuzannya ng'ebyo bikoma mu 3,134 (laba Obuwanvu bw'Ekiseera ky'Okuzannya ne Ssente Ze Kigula). Era ssente z'okuzannyisa ne bwe ziba nnyingi zitya, obusoboka ku nnamuziga wa Bulaaya obw'okuba mu magoba ga yuniti k ekiseera kyonna buba (18/19)ᵏ. Ekyo kiba 95% ku yuniti emu ne 58% ku kkumi, naye tewali ssente z'okuzannyisa, ne bwe ziba nnyingi zitya, ziwa obusoboka bwa kitundu ku kitundu obw'okuba mu magoba ga yuniti 13; ku nnamuziga wa Amerika obusoboka buba (9/10)ᵏ era bukka wansi w'ekitundu ku yuniti 7.

yuniti z'amagoba, ekiseera kyonnaBulaayaAmerika

194.7%90.0%

576.3%59.0%

1058.2%34.9%

1349.5%25.4%

2033.9%12.2%

506.7%0.5%

1000.45%0.003%

Zzaala ya emu ku emu, ssente za zzaala ezitakyuka, ssente z'okuzannyisa nnyingi ekimala obutaggwaawo. Obusoboka buba (18/19)ᵏ ku nnamuziga alina zeero emu ne (9/10)ᵏ ku alina zeero bbiri.

Obuwanvu bw'Ekiseera ky'Okuzannya ne Ssente Ze Kigula Nnamuziga n'Amateeka ga Roulette ya Amerika

Ssente z'okuzannyisa ez'obusoboka obwa kitundu ku kitundu

Kyusa ekibuuzo: olina okujja na ssente mmeka okufuna waakiri obusoboka bwa kitundu ku kitundu obw'okuwangula omuwendo ogugere nga tonnafiirwa byonna? Ku kuwangula okutono, si nnyingi. Ku okusingawo, ssente z'okuzannyisa ezeetaagisa zirinnya mangu nnyo, era oluvannyuma lw'ekifo ekimu tewali ssente z'okuzannyisa zimala, kubanga ne ezitaggwaawo ziwa obusoboka obutasukka kitundu ku kitundu obw'okutuuka mu magoba ago. Taylor (2021) akyogera mu ngeri endala: ku nnamuziga wa Amerika, okufuna obusoboka bwa kitundu ku kitundu obw'okutuuka ku yuniti 100 olina okutandika ne 94, ng'oteeka mu kabi 94 okuwangula 6. Ku nnamuziga wa Bulaaya wandyetaaze 88.

okuwangulaBulaayaAmerika

yuniti 122

yuniti 233

yuniti 345

yuniti 468

yuniti 5712

yuniti 6921

yuniti 712tewali ssente z'okuzannyisa zimala

yuniti 815tewali ssente z'okuzannyisa zimala

yuniti 1024tewali ssente z'okuzannyisa zimala

yuniti 1246tewali ssente z'okuzannyisa zimala

yuniti 13 oba okusingawotewali ssente z'okuzannyisa zimalatewali ssente z'okuzannyisa zimala

Ssente z'okuzannyisa ezisinga obutono, mu yuniti, eziwa waakiri obusoboka bwa kitundu ku kitundu obw'okuwangula omuwendo nga tonnafiirwa ssente z'okuzannyisa, ne zzaala ya emu ku emu ey'omuwendo gumu. Okubala kwaffe okuva ku nsengekera eri waggulu.

Ekyokuyiga eky'enkola

Salawo ky'ogezaako okukola. Singa ekigendererwa kuwangula muwendo gugere, siba nnene era ntono. Singa ekigendererwa kawungeezi kawanvu, siba ntono era kkiriza nti enkizo ya kaasino ejja kutwala 2.70% zaayo ez'omugatte 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 → omunene. Singa ekigendererwa byombi, ekimu kiteekwa okulekebwa, era emirundi mingi kiba kiruubirirwa.

Ensengekera

P(ekiruubirirwa) = (1 − (q/p)ᵃ) / (1 − (q/p)ᵃ⁺ᵇ)

akabi k'okumalwako ssente = 1 − P(ekiruubirirwa)

q/p = 19/18 ku zzaala ya emu ku emu

okwetooloola okw'ekigero okutuuka ku kumalwako, awatali kiruubirirwa = 37 × yuniti

P(okuba mu magoba ga yuniti k ekiseera kyonna) = (18/19)ᵏ

Ebibuuzo

Okulinnyisa zzaala kukendeeza akabi k'okumalwako ssente?

MartingaleenteekateekaMartingaleOkulinnyisa zzaala okukubisaamu zzaala bbiri oluvannyuma lwa buli kufiirwa. Laba ekitundu ky'Enteekateeka za Zzaala okumanya ky'ekola ne ky'etakola.Soma byonna → ekakendeeza ku biseera by'okuzannya ebimpi era ekakuza nnyo ku biwanvu. Zzaala ey'omuwendo gumuenteekateekaZzaala ey'omuwendo gumuOkusiba ssente ze zimu buli kwetooloola. Kye kipimo buli kulinnyisa zzaala kwe kugeraageranyizibwako.Soma byonna → ku yuniti ennene y'engeri ey'amazima ey'okukakendeeza.

Ate zzaala za straight up?

Ensengekera eri waggulu ya zzaala ya emu ku emu. Ku zzaala ez'enjawulo y'ebivaamu ennene, okumalwako ssente kusoboka nnyo ku ssente za zzaala entono era ekiruubirirwa kituukibwako mu ngeri ey'ebitole; kozesa ekibalirizi.

Lwaki q/p gwe muwendo omukulu?

Buli ddaala erigenda ku kiruubirirwa terisoboka nga buli ddaala erigenda ku kumalwako; omugerageranyo gweyongera mu muwendo gw'amadaala.

Okwesanyusa n'Okubala

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

Olina $100 era oyagala $1,000, ng'osiba ku mmyufuzzaalaEmmyufuZzaala ya emu ku emu ku nnamba 18 emmyufu. Mu Lufalansa: rouge.Soma byonna → kyokka. Enteekateeka esooka: siba $1 buli mulundi. Enteekateeka ey'okubiri: siba byonna by'olina okutuusa lw'osukka $500, oluvannyuma siba ebimala okutuuka ku $1,000 kyokka. Enteekateeka ki esinga, era esinga kyenkana wa?
Laga okugonjoola
Eky'okuddamu Ey'okubiri, ewala nnyo. Etuuka ku $1,000 nga 9.0% ku mirundi, okumpi ne 10% ez'obwenkanya. Esooka ewangula nga emirundi 7 ku 10²².
Mu muzannyo ogw'obwenkanyaokubalaOmuzannyo ogw'obwenkanyaOmuzannyo mwe watali ludda lulina nkizo: buli zzaala erina omuwendo ogusuubirwa ogwa zeero.Soma byonna → wandituuse ku $1,000 okuva ku $100 omulundi gumu ku kkumi ka kye wandikoze kibe kitya, kubanga omuwendo ogw'ekigero ogwa ssente zo gusigala ku $100.
Enkizo etwala 2.70% ku buli zzaala, kale gy'okoma okusiba ekitono mu mugatte, gy'okoma okusigala okumpi n'emu ku kkumi. Enteekateeka ey'okubiri esalawo ensonga mu zzaala ntono: $100 zifuuka $200, $400, $800, n'oluvannyuma $200 zimala. Ewangula nga 9.0% ku mirundi. Enteekateeka esooka etwala zzaala enkumi n'enkumi olugendo nga terunnaggwa, era enkizo, entono ku buli emu, egatta n'etuuka kumpi ku kumalwako ssente okukakafu.
Kino kye kivaamu kya Dubins–Savage mu ngeri yaakyo esinga obwangu (Epstein, 2013): mu muzannyo ogusanyusa kaasino, siba ebyo by'oyetaaga, emirundi emitono nga bw'osobola.
Olina $500 era oyagala $1,000, ng'oyimirira amangu ddala ng'ozifunye. Olonda ekika kimu ekya zzaala n'okiddiŋŋana okutuusa lw'ewangula omulundi gumu oba ssente lwe ziggwaawo. Ekika ki ekiwa obusoboka obusinga?
Laga okugonjoola
Eky'okuddamu Zzaala emu eya $500 ku mmyufu: 48.6%. Buli nteekateeka egabanya ssente mu zzaala entono ekola bubi okusingawo.
Londa buli ssente za zzaala nti okuwangula kumu kumala: $30 ku straight upzzaalaStraight upEnnamba emu yokka, esasula 35:1.Soma byonna → ziwangula $1,050, $60 ku splitzzaalaSplitEnnamba bbiri eziriraanaganye, esasula 17:1.Soma byonna → ziwangula $1,020, n'ebirala. Oluvannyuma bala obusoboka nti waakiri zzaala emu ewangula nga ssente tezinnaggwaawo. Straight up kkumi na mukaaga eza $30 zonna tezijja n'obusoboka bwa (36/37)¹⁶ = 64.5%, kale zituuka ku $1,000 35.5% ku mirundi.
Ekipande kiraga buli zzaala. Emmyufu y'esinga kubanga etuukayo mu zzaala emu, kale enkizo esasulwa omulundi gumu, ku $500. Six linezzaalaSix lineEnnamba mukaaga mu nnyiriri bbiri eziriraanaganye, esasula 5:1. Mu Lufalansa: sixain.Soma byonna → y'eddako kubanga yeetaaga ssatu zokka. Zzaala emu eya dazenizzaalaDazeni1–12, 13–24 oba 25–36, esasula 2:1.Soma byonna → y'esinga obubi, obusoboka bwa 12/37; ne bw'egizannya mu yunitissenteYunitiSsente za zzaala ez'entandikwa enkola oba omuzannyi z'akozesa. Okulinnyisa zzaala kunnyonnyolwa mu yuniti kusobole okukola ku mmeeza yonna.Soma byonna → za $250 okutuusa lw'ofuna $1,000 oba okusingawo, dazeni etuukayo 46.4% ku mirundi kyokka.
Bollman (2024) azimba ekipande kye kimu ku nnamuziga wa Amerika. Olunyiriri lwe olwa dazeni lulimu ensobi: lwandisomye 12/38 = 31.6%.
zzaalassente za zzaala × omuwendo gwa zzaalaobusoboka bw'okutuuka ku $1,000
Straight up$30 × 1635.5%
Split$60 × 835.9%
Street$90 × 534.5%
Corner$125 × 436.7%
Six line$166, $166, $16841.2%
Dazeni$500 × 132.4%
Emmyufu$500 × 148.6%
Osiba yuniti emu ku mmyufu, okwetooloola ku kwetooloola, 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. Oluvannyuma lw'okwetooloola okusooka oli mu magoba ga yuniti emu oba mu kufiirwa kwa yuniti emu. Obusoboka nti olidda ku kwenkanankana ddala bwe buliwa?
Laga okugonjoola
Eky'okuddamu 36 ku 37, 97.3%. Ku nnamuziga wa Amerika buli 36 ku 38, 94.7%.
Singa okwetooloola okusooka kuwangula (emirundi 18 ku 37), oli mu magoba ga yuniti emu, era enkizo esika wansi buli kiseera ky'okuzannya ekitakoma, kale emabega oba mu maaso olidda okuyita ku kwenkanankana: ekyo kikakafu. Singa kufiirwa (emirundi 19 ku 37), olina okulinnya yuniti emu, era obusoboka bw'okubaako mu magoba ga yuniti emu buli 18/19 (laba ekipande waggulu).
Awamu: 18/37 + 19/37 × 18/19 = 18/37 + 18/37 = 36/37.
Mu bulijjo obusoboka buli 1 ng'oggyeko enjawulo wakati w'obusoboka bw'okuwangula n'obw'okufiirwa okwetooloola: 1 − 1/37 ku nnamuziga wa Bulaaya, 1 − 2/38 ku wa Amerika. 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 → enjawulo teriiwo era obusoboka buli 1: obubonero bulijjo budda ku kwenkanankana. Epstein (2013) awa etteeka erya bulijjo.
Ekikwekweto kya Pascal ekya 1656: abazannyi babiri bakasuka ddayisi ssatu, buli omu ng'atandika n'obubonero 12. Buli 11 etambuza akabonero eri omuzannyi asooka, buli 14 etambuza kamu eri ow'okubiri; okukanyuga okulala tekubalibwa. Obusoboka nti omuzannyi asooka awangula zonna 24 bwe buliwa? Era bw'osiba yuniti 1 ku mmyufu buli kwetooloola ng'ozannya ne mukwano gwo akola nga bbanka, yuniti 12 buli omu, obusoboka bwo obw'okuwangula zonna 24 bwe buliwa?
Laga okugonjoola
Eky'okuddamu Omuzannyi asooka awangula nga emirundi 1,157 ku 1,158. Ggwe, ku mmyufu, owangula yuniti zonna 24 nga 34% ku mirundi kyokka.
Ddayisi ssatu zikola 11 mu ngeri 27 ne 14 mu ngeri 15, kale buli kabonero akatambula kagenda eri omuzannyi asooka emirundi 27 ku 42, emirundi 9 ku 14. Buli ludda bwe lutandika ku 12, obusoboka bw'okutwala byonna buli 1/(1 + r¹²), r nga gwe mugerageranyo gw'obusoboka bw'oludda olulala ku bubwo.
Ku muzannyi asooka r = 5/9, ne (5/9)¹² ≈ 0.00086, kale obusoboka buli nga 0.99914: emikisa gya 9¹² ku 5¹², oba 282,429,536,481 ku 244,140,625, nga 1,157 ku 1. Huygens yakuba emiwendo egyo gyennyini mu 1657.
Ku mmyufu, r = 19/18 olwa zeero, ne (19/18)¹² ≈ 1.913: obusoboka bwo buli 1/2.913 ≈ 34.3%. Sente yandiwadde 50%. Enkizo ya 2.70% ku buli zzaala egatta, ku zzaala ennyingi ezeetaagisa, ne etuuka ku njawulo ya bubonero 16.

Eky'okusesa

$Okuzannya n'obuvumu kwe kusinga. Era kuggwa mangu.$

Okuzannya n'obuvumu kwe kusinga. Era kuggwa mangu.

Ensibuko

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3rd ed., 1968. Gambler’s ruin, essuula XIV.
Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed. Academic Press, 2013.
Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021.
Carcavi, P. de. Ebbaluwa eri Huygens, 28 Sebuttemba 1656, ku kizibu Pascal kye yawa Fermat. Œuvres complètes de Christiaan Huygens, vol. 1, 1888, pp. 492–494.
Huygens, C. De Ratiociniis in Ludo Aleae. 1657. Ekiwandiiko ekyasooka okukubibwa mu kyapa ku kusuubira.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Essuula 13, roulette.
Reuters. “Briton bets it all on roulette spin, and wins.” Apuli 2004.
Las Vegas Sun. “Man wagers life’s worth.” 12 Apuli 2004.

kyakeberebwa 2026-09-28ekyokulabirako: roulette ya Bulaaya, zeero emuenkola y'okubalirira ↗ensibuko ↗