Okubala mu Roulette · Ekizibu ky'okubala · eddakiika 7

Ekizibu: Bbanga Ki Okutuusa Zeero lw'Ejja

Q: Zeero erina obusoboka obusingako ku nnamuziga abamu?

Si ku nnamuziga ow'obwenkanya. Ku nnamuziga asosola ekinnya kyonna kiyinza okuba bwe kityo, era kyandyetaaze okwetooloola enkumi n'enkumi okukimanya.

Zeero ejja omulundi gumu ku kwetooloola 37 ku kigero. Olinda bbanga ki ddala, era kino kikola ki ku musibi wa zzaala ya emu ku emu?

Eky'okuddamu mu bufunze

Okulinda zeero kugoberera geometric distribution: ekigero kuli okwetooloola 37, median 25, era okulinda kumu ku abiri kusukka okwetooloola 110. Mu kiseera ky'okuzannya eky'okwetooloola 200, omusibi wa zzaala ya emu ku emu asuubira zeero 5.4 era ajja kulaba wonna wakati wa 1 ne 10.

ekigero ky'okulinda

okwetooloola 37

median y'okulinda

okwetooloola 25

p(tewali zeero mu kwetooloola 100)

6.5%

zeero mu kwetooloola 200

5.4 ± 2.3

Ekizibu

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 → erina obusobokaokubalaObusobokaObusoboka bw'ekivaamu, okuva ku 0 okutuuka ku 1 oba 0% okutuuka ku 100%. Ennamba emu: 1/37 = 2.70%.Soma byonna → bwa 1/37 ku buli kwetooloola. (a) Obusoboka bw'obutabaawo zeero mu kwetooloola 37 okuddako bwe buliwa? (b) Median y'okulinda eri wa? (c) Mu kiseera ky'okuzannya eky'okwetooloola 200 eky'emu ku emu, omuzannyi alina kusuubira zeero mmeka, era obugazi bwe buliwa?

Eby'okuddamu

(a) (36/37)³⁷ = 36.3%. Okusinga ekimu kya kusatu ku mirundi, okwetooloola 37 kuyita nga tewali zeero n'emu, kwe kubala kwe kumu okulaga nti “waakiri okujja kumu ku straight upzzaalaStraight upEnnamba emu yokka, esasula 35:1.Soma byonna → mu kwetooloola 37” kuli 63.7% kyokka. (b) Okulinda W kugoberera geometric distribution; p(W > k) = (36/37)ᵏ; median ye k ekino w'kiyita ku 0.5, nga k ≈ 25. Ekitundu ky'okulinda kuli okwetooloola 25 oba okutono, ate ekitundu kiwanvu okusingawo; ekigero kya 37 kisikiddwa waggulu omukira omuwanvu. (c) Zeero mu kwetooloola 200 zigoberera binomial distribution ng'ekigero kiri 200/37 = 5.4 n'ekipimo ky'enjawukanaokubalaEkipimo ky'enjawukanaEkikolo kya kkubo bbiri eky'enjawulo y'ebivaamu; ebbanga ery'abulijjo ekivuddemu we kiba okuva ku muwendo ogusuubirwa.Soma byonna → √(200 × (1/37) × (36/37)) ≈ 2.3. Obugazi bwa 95% buli nga 1 okutuuka ku 10.

okulinda zeeroobusoboka

mu kwetooloola 1024.0%

mu kwetooloola 2549.6%

mu kwetooloola 3763.7%

mu kwetooloola 5074.6%

mu kwetooloola 10093.5%

okusukka okwetooloola 110≈ 5%

okusukka okwetooloola 2000.4%

p(W ≤ k) = 1 − (36/37)ᵏ. Ekigero 37, median 25.

Zeero ky'efiiriza omusibi wa zzaala ya emu ku emu

Buli zeero efiiriza ssente za zzaala omulundi gumu, era zeero ze nkizo yonna ku mmyufuzzaalaEmmyufuZzaala ya emu ku emu ku nnamba 18 emmyufu. Mu Lufalansa: rouge.Soma byonna →: mu kwetooloola 37 okw'ekigero, okuwangula 18 n'okufiirwa 18 byegyawo, era zeero emu y'eba −1/37. Mu kiseera ky'okuzannya eky'okwetooloola 200 ku $10, zeero 5.4 ezisuubirwa zifiiriza $54, ekyenkanankana ddala ne 200 × $10 / 37. Ekiseera ky'okuzannya ekirimu zeero 2 kifunye omukisa omulungi gwa $34; ekirimu zeero 9 kifunye omukisa omubi gwa $36, era kijja kuwulira ng'ekikumpanyiziddwa. Ku mmeeza ya la partageetteekaLa partageEtteeka ery'e Bufalansa: zeero bw'ejja, ekitundu kya ssente za zzaala ya emu ku emu kizzibwayo. Likendeeza enkizo ya kaasino ku zzaala ezo ku kitundu, okutuuka ku 1.35%.Soma byonna → buli zeero efiiriza ekitundu kya ssente za zzaala era emiwendo gisalwamu ebitundu bibiri.

Zeero mu kiseera ky'okuzannya eky'okwetooloola 200% ku biseera by'okuzannya

0–1

2.5%

2–3

18%

4–5

34%

6–7

28%

8–9

13%

10 oba okusingawo

4.5%

% ku biseera by'okuzannya

01734%

Binomial(200, 1/37). Omusibi wa $10 ku mmyufu asasula $10 ku buli zeero; okusaasaana kwa zeero kwe kusaasaana kwa bbeeyi y'akawungeezi.

Etteeka lya La Partage mu Roulette Roulette ku Mutimbagano Ekumpanyizibwa? Enfumo

Ekiddirira

Obusoboka bwa zeero bbiri omuddiriŋŋanwa bwe buliwa? (1/37)² = 1/1,369. Mu kaasino eriko emmeeza 20 nga zeetoolooza emirundi 50 buli ssaawa, ekyo kitegeeza zeero bbiri omuddiriŋŋanwa awamu nga buli ssaawa 1.4. Abazannyi abakiraba basalawo nti nnamuziga yonoonese; okubala kugamba nti lunaku lwa bulijjo.

Gezaako

Ekyokugezesa Ekiseera ky'Okuzannya kibala zeero mu buli kiseera ky'okuzannya. Zannya okwetooloola 100 emirundi ebikumi ebitonotono okole ekifaananyi ky'omuwendo: ekifaananyi ekiri waggulu kijja kulabika, n'omukira gwakyo omuwanvu ku ddyo. Omukira ogwo gwe guvaamu engero.

Ensengekera

p(W > k) = (36/37)ᵏ

E[W] = 37 · median ≈ 25

zeero mu kwetooloola N ~ Binomial(N, 1/37)

Ebibuuzo

Zeero erina obusoboka obusingako ku nnamuziga abamu?

Si ku nnamuziga ow'obwenkanya. 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 → ekinnyaebikozesebwaEkinnyaKimu ku bisenge 37 ebiriko ennamba ku rotor. Era biyitibwa: slot, cup.Soma byonna → kyonna kiyinza okuba bwe kityo, era kyandyetaaze okwetooloola enkumi n'enkumi okukimanya.

Bulijjo nteeke cipu ku zeero ng'okwekuuma?

Zzaala ya 2.70% nga endala zonna. Ekyusa enkula y'ekiseera ky'okuzannya (zeero efuuka okuwangula) so si bbeeyi.

Lwaki median ntono okusinga ekigero?

Kubanga engabanya y'okulinda tegenda kyenkanyi: okulinda okumpi kungi, okuwanvu ennyo kutono.

Eky'okusesa

$Ekigero 37, median 25, n'omukira omuwanvu engero mwe zibeera.$

Ekigero 37, median 25, n'omukira omuwanvu engero mwe zibeera.

Ensibuko

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3rd ed., 1968. Gambler’s ruin, essuula XIV.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Essuula 13, roulette.

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