Imibare ya Ruleti · Ikibazo c'imibare · iminota 7

Ikibazo: Bimara Igihe Kingana Gute Imbere ya Zeru

Zeru iza incuro imwe mu kuzunguruka 37 ku mpuzandengo. Urindira igihe kingana gute koko, kandi ivyo bigira ico bikora iki ku mutezi w'amatego ya rimwe kuri rimwe?

Inyishu ngufi

Ukurindira zeru gukurikira itegeko rya géométrique: impuzandengo ni ukuzunguruka 37, igitigiri c'agati ni 25, kandi ukurindira kumwe kuri makumyabiri kurenga ukuzunguruka 110. Mu gihe c'ugukina c'ukuzunguruka 200, umutezi w'amatego ya rimwe kuri rimwe yitega zeru 5,4 kandi azobona hagati ya 1 na 10.

impuzandengo y'ukurindira
ukuzunguruka 37
igitigiri c'agati c'ukurindira
ukuzunguruka 25
p(nta zeru mu kuzunguruka 100)
6,5%
zeru mu kuzunguruka 200
5,4 ± 2,3

Ikibazo

ZeruuruzigaZeruAkazu kamwe k'icatsi kibisi kadapfukwa n'itego rya rimwe kuri rimwe, ry'umurwi canke ry'inkingi; ni yo soko y'inyungu ya kazino. Kandi bita: zeru imwe, 0.Soma vyose → ifise ugushobokaimibareUgushobokaUgushoboka kw'ivyavuyemwo, kuva kuri 0 gushika kuri 1 canke 0% gushika 100%. Inomero imwe: 1/37 = 2,70%.Soma vyose → kwa 1/37 kuri buri kuzunguruka. (a) Ugushoboka kw'uko nta zeru iza mu kuzunguruka 37 gukurikira ni ukuhe? (b) Igitigiri c'agati c'ukurindira ni ikihe? (c) Mu gihe c'ugukina c'ukuzunguruka 200 ku matego ya rimwe kuri rimwe, umukinyi akwiye kwitega zeru zingahe, kandi urugero ni uruhe?

Inyishu

(a) (36/37)³⁷ = 36,3%. Incuro zirenga kimwe ca gatatu, ukuzunguruka 37 kurahita ata zeru n'imwe, kandi ni uguharura kumwe n'ukw'uko “nibura gufata rimwe kuri straight upitegoStraight upInomero imwe gusa, iriha 35:1.Soma vyose → mu kuzunguruka 37” ari 63,7% gusa. (b) Ukurindira W gukurikira itegeko rya géométrique; p(W > k) = (36/37)ᵏ; igitigiri c'agati ni k aho ivyo birenga 0,5, ari vyo k ≈ 25. Igice c'ukurindira ni ukuzunguruka 25 canke munsi, ikindi gice kirarenga; impuzandengo ya 37 yongerezwa n'umurizo muremure. (c) Zeru mu kuzunguruka 200 zikurikira itegeko rya binomiale rifise impuzandengo 200/37 = 5,4 n'itandukaniro risanzweimibareItandukaniro risanzweUmuzi kare w'ihindagurika ry'ivyavuyemwo; intera isanzwe iri hagati y'ivyavuyemwo n'agaciro kitezwe.Soma vyose → √(200 × (1/37) × (36/37)) ≈ 2,3. Urugero rwa 95% ni hafi kuva 1 gushika 10.

ukurindira zeruugushoboka
mu kuzunguruka 1024,0%
mu kuzunguruka 2549,6%
mu kuzunguruka 3763,7%
mu kuzunguruka 5074,6%
mu kuzunguruka 10093,5%
ukuzunguruka kurenga 110≈ 5%
ukuzunguruka kurenga 2000,4%
p(W ≤ k) = 1 − (36/37)ᵏ. Impuzandengo 37, igitigiri c'agati 25.

Ico zeru itwara umutezi w'amatego ya rimwe kuri rimwe

Zeru yose itwara amahera y'itego rimwe, kandi zeru ni zo nyungu ya kazino yose ku gitukuraitegoGitukuraItego rya rimwe kuri rimwe ku nomero 18 zitukura. Mu gifaransa: rouge.Soma vyose →: mu kuzunguruka 37 kw'impuzandengo, itsinzi 18 n'ibihombo 18 birihanagura, kandi zeru imwe ni yo −1/37. Mu gihe c'ugukina c'ukuzunguruka 200 utega $10, zeru 5,4 zitezwe zitwara $54, ari vyo neza neza 200 × $10 / 37. Igihe c'ugukina gifise zeru 2 kiba cagize amahirwe meza ya $34; igihe c'ugukina gifise zeru 9 kiba cagize amahirwe mabi ya $36, kandi kizoboneka nk'aho cahenzwe. Ku meza afise la partageitegekoLa partageItegeko ry'Ubufaransa: iyo zeru ije, igice c'amahera y'itego rya rimwe kuri rimwe kirasubizwa. Rigabanya inyungu ya kazino kuri ayo matego gushika kuri 1,35%.Soma vyose →, zeru yose itwara igice c'amahera y'itego kandi ibitigiri bigabanuka mo kabiri.

Zeru mu gihe c'ugukina c'ukuzunguruka 200% y'ibihe vy'ugukina
0–1
2,5%
2–3
18%
4–5
34%
6–7
28%
8–9
13%
10 canke zirenga
4,5%
% y'ibihe vy'ugukina
01734%
Binomiale(200, 1/37). Umutezi wa $10 ku gitukura ariha $10 kuri zeru yose; ukwikwiragiza kwa zeru ni ukwikwiragiza kw'igiciro c'umugoroba.

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Ikibazo gikurikira

Ugushoboka kwo kubona zeru zibiri zikurikirana ni ukuhe? (1/37)² = 1/1.369. Muri kazino ikoresha ameza 20 ku kuzunguruka 50 ku isaha, ivyo ni hafi zeru zibiri zikurikirana ahantu runaka buri masaha 1,4. Abakinyi babibona bemeza ko uruziga rwononekaye; uguharura kuvuga ko ari umusi usanzwe nk'iyindi.

Bigerageze

Igikoresho co Kwigana Igihe c'Ugukina Ruleti giharura zeru muri buri gihe c'ugukina. Kina ukuzunguruka 100 incuro amajana makeyi maze ushushanye igitigiri: igishushanyo kiri hejuru kizoboneka, n'umurizo waco muremure iburyo. Uwo murizo ni wo inkuru zivamwo.

Ingingo y'imibare

p(W > k) = (36/37)ᵏ
E[W] = 37 · igitigiri c'agati ≈ 25
zeru mu kuzunguruka N ~ Binomiale(N, 1/37)

Ibibazo

Zeru yoba ishobora kuza cane ku nziga zimwe?

Si ku ruziga rutabogamye. Ku ruziga rubogamyeubushakashatsiUruziga rubogamyeUruziga rufise amakosa y'ivyuma atuma utuzu tumwe dushobora gufata kuruta 1/37. Ni gake, kandi rumenyekana gusa n'ukuzunguruka ibihumbi vyanditswe.Soma vyose →, akazuibikoreshoAkazuKimwe mu bibanza 37 bifise inomero kuri rotor. Kandi bita: slot, cup.Soma vyose → ako ari ko kose karashobora, kandi vyosaba ukuzunguruka ibihumbi kugira ngo bimenyekane.

Nkwiye guhora nshira jetoni kuri zeru nk'ingurane?

Ni itego rya 2,70% nk'ayandi yose. Rihindura isura y'igihe c'ugukina (zeru ihinduka itsinzi) ariko ntirihindura ico bigutwara.

Ni kubera iki igitigiri c'agati kiri munsi y'impuzandengo?

Kubera ko ukwikwiragiza kw'ukurindira kubogamye: ukurindira kugufi kwinshi, kurekure cane guke.

Agakuru ko gutwenga

Impuzandengo 37, igitigiri c'agati 25, n'umurizo muremure aho imigani iba.

Impuzandengo 37, igitigiri c'agati 25, n'umurizo muremure aho imigani iba.

Aho Twakuye

  1. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, isohorwa rya 3, 1968. Ugusahurwa kw'umutezi, igice ca XIV.
  2. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Igice ca 13, ruleti.
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