Imibare ya Roulette · Ikibazo cy'imibare · iminota 7

Ikibazo: Bitwara Igihe Kingana Iki Ngo Zeru Isohoke

Q: Ese zeru isohoka kenshi ku nziga zimwe?

Si ku ruziga rutabogamye. Ku ruziga rubogamye, akazu ako ari ko kose gashobora kuba ari ko, kandi byasaba ibihumbi by'amazunguruka kugira ngo bimenyekane.

Zeru isohoka izunguruka rimwe muri 37 ku mpuzandengo. Mu by'ukuri utegereza igihe kingana iki, kandi ibyo bikorera iki utega itega ryishyura kimwe ku kindi?

Igisubizo kigufi

Gutegereza zeru bikurikiza itegeko rya geometric: impuzandengo amazunguruka 37, umuhuza 25, kandi igihe kimwe mu makumyabiri cyo gutegereza kirenga amazunguruka 110. Mu mukino w'amazunguruka 200, utega itega ryishyura kimwe ku kindi ateganya zeru 5,4 kandi azabona hagati ya 1 na 10.

impuzandengo yo gutegereza

amazunguruka 37

umuhuza wo gutegereza

amazunguruka 25

p(nta zeru mu mazunguruka 100)

6,5%

zeru mu mazunguruka 200

5,4 ± 2,3

Ikibazo

ZeruuruzigaZeruAkazu kamwe k'icyatsi katafatwa n'itega ryishyura kimwe ku kindi, irya dazeni cyangwa iry'inkingi; ni ho inyungu ya kazino ikomoka. Nanone: zeru imwe, 0.Soma byose → ifite amahirweimibareAmahirweAmahirwe y'igisubizo, kuva kuri 0 kugeza kuri 1 cyangwa kuva kuri 0% kugeza kuri 100%. Umubare umwe: 1/37 = 2,70%.Soma byose → ya 1/37 kuri buri zunguruka. (a) Amahirwe y'uko nta zeru izasohoka mu mazunguruka 37 akurikiraho ni angahe? (b) Umuhuza wo gutegereza ni uwuhe? (c) Mu mukino w'amazunguruka 200 ku itega ryishyura kimwe ku kindi, umukinnyi yagombye gutegereza zeru zingahe, kandi urugero rwazo ni uruhe?

Ibisubizo

(a) (36/37)³⁷ = 36,3%. Birenze kimwe cya gatatu cy'igihe, amazunguruka 37 arashira nta zeru na imwe isohotse, kandi ibyo ni imibare imwe n'iyerekana ko “nibura gufata rimwe kuri straight upitegaStraight upUmubare umwe, yishyura 35:1.Soma byose → mu mazunguruka 37” ari 63,7% gusa. (b) Igihe cyo gutegereza W gikurikiza itegeko rya geometric; p(W > k) = (36/37)ᵏ; umuhuza ni k aho ibi birenga 0,5, ari yo k ≈ 25. Kimwe cya kabiri cy'ibihe byo gutegereza ni amazunguruka 25 cyangwa make, ikindi gice ni birebire; impuzandengo ya 37 izamurwa n'umurizo muremure. (c) Zeru mu mazunguruka 200 zikurikiza itegeko rya binomial rifite impuzandengo ya 200/37 = 5,4 n'ikinyuranyo gisanzweimibareIkinyuranyo gisanzweUmuzi wa kare w'ihindagurika; intera isanzwe y'igisubizo uvuye ku gaciro gateganyijwe.Soma byose → cya √(200 × (1/37) × (36/37)) ≈ 2,3. Urugero rwa 95% ni hafi 1 kugeza 10.

gutegereza zeruamahirwe

mu mazunguruka 1024,0%

mu mazunguruka 2549,6%

mu mazunguruka 3763,7%

mu mazunguruka 5074,6%

mu mazunguruka 10093,5%

amazunguruka arenga 110≈ 5%

amazunguruka arenga 2000,4%

p(W ≤ k) = 1 − (36/37)ᵏ. Impuzandengo 37, umuhuza 25.

Icyo zeru itwara utega itega ryishyura kimwe ku kindi

Buri zeru itwara itega rimwe, kandi zeru ni zo nyungu ya kazino yose ku mutukuitegaUmutukuItega ryishyura kimwe ku kindi ku mibare 18 y'umutuku. Mu Gifaransa: rouge.Soma byose →: mu mazunguruka 37 y'impuzandengo, intsinzi 18 n'ibihombo 18 birasibana, naho zeru imwe ikaba −1/37. Mu mukino w'amazunguruka 200 ku $10, zeru 5,4 ziteganyijwe zitwara $54, ari byo neza 200 × $10 / 37. Umukino urimo zeru 2 uba wagize amahirwe meza ya $34; umukino urimo zeru 9 uba wagize amahirwe mabi ya $36, kandi uzumvikana nk'uwariganyijwe. Ku meza ya la partageitegekoLa partageItegeko ry'Igifaransa: iyo zeru isohotse, kimwe cya kabiri cy'itega ryishyura kimwe ku kindi kirasubizwa. Rigabanya inyungu ya kazino kuri ayo matega kabiri, ikagera kuri 1,35%.Soma byose →, buri zeru itwara kimwe cya kabiri cy'itega maze imibare ikagabanuka kabiri.

Zeru mu mukino w'amazunguruka 200% y'imikino

0–1

2,5%

2–3

18%

4–5

34%

6–7

28%

8–9

13%

10 cyangwa zirenga

4,5%

% y'imikino

01734%

Binomial(200, 1/37). Utega $10 ku mutuku yishyura $10 kuri buri zeru; ikwirakwira ry'umubare wa zeru ni ryo kwirakwira ry'igiciro cy'umugoroba.

Itegeko rya Roulette rya La Partage Ese Roulette yo kuri Interineti Iriganya? Igihuha

Ikibazo gikurikiraho

Amahirwe ya zeru ebyiri zikurikiranye ni angahe? (1/37)² = 1/1.369. Muri kazino ifite ameza 20 akora amazunguruka 50 ku isaha, ibyo ni hafi impea imwe ya zeru zikurikiranye ahantu runaka buri masaha 1,4. Abakinnyi babibona banzura ko uruziga rwangiritse; imibare ivuga ko ari umunsi usanzwe.

Gerageza

Igerageza ry'Umukino wa Roulette ribara zeru muri buri mukino. Kina amazunguruka 100 incuro magana make maze ushushanye umubare: histogram iri hejuru izagaragara, n'umurizo wayo muremure w'iburyo. Uwo murizo ni wo inkuru zikomokaho.

Formula

p(W > k) = (36/37)ᵏ

E[W] = 37 · umuhuza ≈ 25

zeru mu mazunguruka N ~ Binomial(N, 1/37)

Ibibazo

Ese zeru isohoka kenshi ku nziga zimwe?

Si ku ruziga rutabogamye. Ku ruziga rubogamyelaboratwariUruziga rubogamyeUruziga rufite inenge z'umubiri zituma utuzu tumwe tugira amahirwe arenze 1/37. Ni gake, kandi rutahurwa gusa n'amazunguruka ibihumbi byanditswe.Soma byose →, akazuibikoreshoAkazuKamwe mu tuzu 37 twanditseho imibare turi kuri rotor. Nanone: slot, cup.Soma byose → ako ari ko kose gashobora kuba ari ko, kandi byasaba ibihumbi by'amazunguruka kugira ngo bimenyekane.

Ese nagombye guhora nshyira jeto kuri zeru nk'ubwishingizi?

Ni itega rya 2,70% nk'ayandi yose. Rihindura imiterere y'umukino (zeru iba intsinzi) ariko ntirihindura ikiguzi.

Kuki umuhuza uri munsi y'impuzandengo?

Kuko imigabane y'ibihe byo gutegereza ibogamiye ku ruhande rumwe: ibihe byinshi bigufi, bike birebire cyane.

Akanya k'urwenya

$Impuzandengo 37, umuhuza 25, n'umurizo muremure aho imigani iba.$

Impuzandengo 37, umuhuza 25, n'umurizo muremure aho imigani iba.

Inkomoko

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3rd ed., 1968. Gushira igishoro k'umukinnyi w'urusimbi, igice cya XIV.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Igice cya 13, roulette.

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