Imibare ya Ruleti · Ishirwa mu ngiro · iminota 8

Ugushoboka kw'Urukurikirane muri Ruleti

Q: Urukurikirane rusobanura ko uruziga rubogamye?

Oya. Ukubogama kuboneka igihe tuzu tumwe dusohoka kenshi mu nzunguruka ibihumbi, si mu rukurikirane rw'ibara.

Urukurikirane rurerure rw'ibara rimwe ruraba kenshi. Kandi nta co ruvuze ku kuzunguruka gukurikira.

Inyishu ngufi

Inomero zitukura zitanu zikurikiranye: 2,7%. Cumi: 0,074%. Mu gihe c'ugukina c'inzunguruka 200, urukurikirane rw'inomero zitandatu z'ibara rimwe ruboneka kenshi kuruta uko rutaboneka.

5 zikurikiranye

2,73%

8 zikurikiranye

0,31%

10 zikurikiranye

0,074%

agahigo

zirabura 26, 1913

Ukuntu urukurikirane rw'ibihombo ruza kenshi

Itego rya rimwe kuri rimwe ku ruziga rwa zeru imwe rihomba mu kuzunguruka 19 kuri 37. Umurongo wose werekana ugushoboka ko inzunguruka zikurikirana zingana gutyo zose zihomba, n'ivyo umukinyi wa Martingale, akuba kabiri inyuma y'igihombo cose, amaze guhomba gushika ico gihe.

Itego ry'intango

ibihombo bikurikirana	ugushoboka	nka 1 kuri	ivyahombye gushika ubu	itego rikurikira
1	51,4%	2	$1	$2
2	26,4%	4	$3	$4
3	13,5%	7	$7	$8
4	7,0%	14	$15	$16
5	3,6%	28	$31	$32
6	1,8%	55	$63	$64
7	0,94%	106	$127	$128
8	0,48%	207	$255	$256
9	0,25%	403	$511	$512
10	0,13%	784	$1.023	$1.024
11	0,065%	1527	$2.047	$2.048
12	0,034%	2974	$4.095	$4.096
13	0,017%	5792	$8.191	$8.192
14	0,0089%	11279	$16.383	$16.384
15	0,0046%	21965	$32.767	$32.768

Ugushoboka ni 19/37 gukubwe nako ubwako incuro imwe kuri buri gihombo, guharurwa kuva ku kuzunguruka kumwe kwagenywe. Igihe c'ugukina kirekire kirimwo inzunguruka nyinshi aho urukurikirane nk'urwo rushobora gutangurira, rero mu mugoroba umwe birashoboka cane kuruta ivyo umurongo umwe werekana.

Urukurikirane rumwe

UgushobokaimibareUgushobokaUgushoboka kw'ivyavuyemwo, kuva kuri 0 gushika kuri 1 canke 0% gushika 100%. Inomero imwe: 1/37 = 2,70%.Soma vyose → ko inzunguruka k zikurikira zose zisohora inomero zitukuraitegoGitukuraItego rya rimwe kuri rimwe ku nomero 18 zitukura. Mu gifaransa: rouge.Soma vyose → ni (18/37)ᵏ. Zibiri: 23,7%. Zitanu: 2,7%. Cumi: 0,074%, nka 1 kuri 1.350. Makumyabiri: 1 kuri miliyoni 1,8. Makumyabiri na zitandatu, agahigo ka Monte Carlo: 1 kuri miliyoni 137. Ubwo ni ugushoboka kw'urukurikirane rwihariye rutangurira ku kuzunguruka kwihariye, ico kikaba ari ikibazo hafi ntawe abaza koko.

Ugushoboka kw'inomero zitukura k zikurikiranye%

1 ikurikiranye

48,65%

2 zikurikiranye

23,67%

3 zikurikiranye

11,51%

4 zikurikiranye

5,60%

5 zikurikiranye

2,72%

6 zikurikiranye

1,33%

7 zikurikiranye

0,645%

8 zikurikiranye

0,314%

9 zikurikiranye

0,153%

10 zikurikiranye

0,074%

12 zikurikiranye

0,018%

15 zikurikiranye

0,002%

024,3248,65%

(18/37)ᵏ ku rukurikirane rumwe rutangura ubu. Mu gihe kirekire c'ugukina, ugushoboka ko urwo rukurikirane ruboneka ahantu na hamwe ni kunini cane.

Ruleti ya Monte Carlo

Mu gihe c'ugukina

Ikibazo abantu baba bashaka kubaza ni “urukurikirane rwa k ruzoboneka ahantu na hamwe mu gihe canje c'ugukina?”, kandi inyishu iraruta cane (18/37)ᵏ kubera ko igihe c'ugukina c'inzunguruka 200 gitanga ahantu nka 200 urukurikirane rushobora gutangurira. Urukurikirane rw'inomero zitandatu canke zirenga z'ibara rimwe, itukura canke iraburaitegoCiraburaItego rya rimwe kuri rimwe ku nomero 18 zirabura. Mu gifaransa: noir.Soma vyose →, ruboneka mu gihe c'ugukina c'inzunguruka 200 nka 94% vy'incuro; umunani canke zirenga nka 47%; cumi canke zirenga nka 14%. Iyo uvuze ibara imbere y'igihe, ugushoboka kuragabanuka, gushika nko kuri 75%, 27% na 7%. Umukinyi amara umugoroba ku meza azobona urukurikirane rurerure buri mugoroba.

urukurikirane rwa k nibura, itukura canke iraburamu nzunguruka 100mu nzunguruka 200mu nzunguruka 500

595,6%99,8%> 99,9%

675,7%94,4%99,9%

748,2%74,1%96,8%

826,7%47,3%80,4%

106,8%13,7%31,5%

121,6%3,4%8,5%

Nyavyo, vyaharuwe ukuzunguruka ku kundi ku ruziga rw'i Buraya rutabogamye; zeru ihagarika urukurikirane. Ku ibara rimwe rivuzwe imbere y'igihe, urukurikirane rw'inomero zitandatu mu nzunguruka 200 ni nka 75%.

Ni kubera iki bihambaye kuri Martingale

Buri yongerekanaingendo yo gutegaIyongerekanaItegeko ryose rihindura amahera y'itego hisunzwe ivyavuyemwo vyabanje. Iyongerekana rihakana riyongereza inyuma y'ibihombo, iryemeza inyuma y'itsinzi.Soma vyose → rihakana rifise uburebure bw'urukurikirane burivuna: ibihombo bitandatu uhereye kuri $10 ku rugero rwa $500, cumi kuri Fibonacciingendo yo gutegaFibonacciIyongerekana rikurikira urukurikirane 1, 1, 2, 3, 5, 8, 13…: intambwe imwe imbere inyuma y'igihombo, intambwe zibiri inyuma inyuma y'itsinzi.Soma vyose →, bitanu mu gukuba gatatu ku mirwiitegoUmurwi1–12, 13–24 canke 25–36, riha 2:1.Soma vyose →. Ugushoboka kw'urukurikirane rw'ibihombo bitandatu ku matego ya rimwe kuri rimwe ni (19/37)⁶ ≈ 1,8% kuri buri gerageza, kandi igihe c'ugukina c'inzunguruka 200 gishobora kugira amagerageza nka 100, ku buryo ukuvunika gushika hafi mu bihe vyo gukina bine kuri bitanu vy'ubwo burebure. Ugushoboka kw'urukurikirane kuri ruleti ni co gituma ico gihanamo kitaba gake.

Ingendo ya Fibonacci muri Ruleti

Inomero zishushe n'inomero zikanye

Iryo harura nyene rikora no kuri straight upitegoStraight upInomero imwe gusa, iriha 35:1.Soma vyose →. Mu nzunguruka 300, igitigiri citezwe kuri buri nomero ni 8,1; itandukaniro risanzweimibareItandukaniro risanzweUmuzi kare w'ihindagurika ry'ivyavuyemwo; intera isanzwe iri hagati y'ivyavuyemwo n'agaciro kitezwe.Soma vyose → ni nka 2,8. Inomero imwe izosohoka incuro 15 n'iyindi 2 ku bw'impfindo gusa, buri gihe. Ikibaho c'ivyavuyemwo cerekana inomero “zishushe” kiba cerekana impera yo hejuru y'ikwiragira risanzwe. Ikibanza c'Ubushakashatsi kirasobanura inzunguruka zingahe zikenewe imbere y'uko inomero ishusheumuganiInomero ishusheInomero yaje kenshi kuruta uko vyitezwe mu gihe ca vuba. Ku ruziga rutabogamye nta co ihanura.Soma vyose → igira ico ivuze (ibihumbi, ku ruziga rumwe ruzwi).

Ivyavuyemwo muri Ruleti: Gusoma Ikibaho

Ukudafatana ni yo ntumbero yose

Urukurikirane rw'inomero zitukura cumi ntirutuma irabura irushiriza gushoboka, kandi ntirutuma n'itukura irushiriza gushoboka. Vyompi ni 18/37. Urukurikirane ni kamere y'ibikurikirana vy'impfindo, kandi kutaboneka kwarwo ni kwo kwotera amakenga: ibikurikirana vy'inzunguruka 200 bitarimwo urukurikirane rurenze zine vyoba ari icemezo gikomeye cane c'uguhenda kuruta ibirimwo urukurikirane rwa cumi na zibiri.

Ingingo y'imibare

p(k zikurikiranye, intango yihariye) = (18/37)ᵏ

p(urukurikirane ≥ k ahantu na hamwe mu nzunguruka N) ≈ 1 − exp(−N · pᵏ · (1 − p))

Ibibazo

Ni uruhe rukurikirane rw'ibara rurerure kuruta izindi rwigeze kwandikwa kuri ruleti?

Inomero zirabura 26 i Monte Carlo ku wa 18 Nyandagaro 1913 ni rwo ruzwi cane. Inomero zitukura 32 zikurikiranye zavuzwe muri kazino yo muri Amerika mu 1943. Vyompi birahuye n'impfindo ukurikije inzunguruka nyinshi amakazino akora.

Inyuma y'inomero zitukura zitanu, nkwiye gutega ku zirabura?

Ni 18/37 uko vyogenda kwose. Tega ivyo umugambi wawe uvuga, canke ntutege.

Urukurikirane rusobanura ko uruziga rubogamye?

Oya. Ukubogama kuboneka igihe tuzuibikoreshoAkazuKimwe mu bibanza 37 bifise inomero kuri rotor. Kandi bita: slot, cup.Soma vyose → tumwe dusohoka kenshi mu nzunguruka ibihumbi, si mu rukurikirane rw'ibara.

Twinezwe n'Imibare

Banza ubigerageze wewe nyene. Inyishu yose irapfutse; yugurure igihe witeguye.

Ku ruziga rw'i Buraya, hakenerwa ukuzunguruka kungahe, ku mpuzandengo, imbere y'uko inomero zose 37 zisohoka nibura incuro imwe?
Erekana inyishu
Inyishu Nka kuzunguruka 155 ku mpuzandengo; igitigiri c'impagati ni 147.
Harura ukurindira inomero nshasha imwe imwe. Ukuzunguruka kwa mbere kwama kwerekana inomero nshasha. Umaze kubona inomero 1, utuzuibikoreshoAkazuKimwe mu bibanza 37 bifise inomero kuri rotor. Kandi bita: slot, cup.Soma vyose → 36 muri 37 ni dushasha, ku buryo inomero nshasha ikurikira isaba ukuzunguruka 37/36 ku mpuzandengo. Umaze kubona inomero k, bisaba 37/(37 − k).
Teranya ivyo vyo kurindira: 37/37 + 37/36 + 37/35 + … + 37/1 = 37 × (1 + 1/2 + 1/3 + … + 1/37) ≈ 37 × 4,20 = 155,5 vy'ukuzunguruka.
Igice kinini c'ivyo ni ku mpera. Inomero ya nyuma yonyene isaba ukuzunguruka 37 ku mpuzandengo, izitanu za nyuma nka 85. Ku ruziga rw'Amerika, iteranya nyene ritanga nka 161. Iki ni ikibazo c'umukoranya w'amakupo (coupon collector); impuzandengo nyene ivamwo n'iharura risanzwe.
Mu kuzunguruka 37 ku ruziga rw'i Buraya, ukuzunguruka kumwe kuri buri kazu, wokwitega kubona inomero zitandukanye zingahe?
Erekana inyishu
Inyishu Nka 23,6. Hafi kimwe ca gatatu c'inomero, nka 13, ntizisohoka na rimwe.
Fata inomero imwe, nk'akarorero 17. Kuri buri kuzunguruka ntisohoka ku gushoboka kwa 36/37, ku buryo ihusha ukuzunguruka 37 kwose ku gushoboka kwa (36/37)³⁷ ≈ 0,363.
Inomero yose ifise ugushoboka nk'ukwo, ku buryo ku mpuzandengo inomero 37 × 0,363 ≈ 13,4 zibura kandi 37 − 13,4 ≈ 23,6 zigasohoka, nyinshi muri zo incuro zibiri canke zirenga.
Abakinyi ba ruleti bavyita itegeko ry'ibice bitatu (law of thirds). Si itegeko, ni harure gusa y'ivyisubiramwo: mu murongo muremure ungana n'uruziga, nka kimwe ca gatatu c'inomero ntizisohoka, ku ruziga rutabogamye nk'uko biri ku rundi rwose. Ku tuzu 38, igipimo na co ni (37/38)³⁸ ≈ 0,363; ku ruziga runini kigera hafi ya 1/e ≈ 0,368.
Umugenzi wawe akwereka intonde zibiri z'amabara 50, gitukuraitegoGitukuraItego rya rimwe kuri rimwe ku nomero 18 zitukura. Mu gifaransa: rouge.Soma vyose → canke ciraburaitegoCiraburaItego rya rimwe kuri rimwe ku nomero 18 zirabura. Mu gifaransa: noir.Soma vyose →, bivugwa ko zose zivuye ku ruziga bakuyeko 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 →. Rumwe ruhindura ibara incuro 25 kandi umurongo warwo muremure kuruta iyindi ni wa gatandatu. Urundi ruhindura incuro 35 kandi ntirurenza gatatu. Ni uruhe rwahimbwe?
Erekana inyishu
Inyishu Urwa kabiri. Urutonde nyakuri ruhindura nka 24 canke 25. Uruhindura incuro 35 ruboneka nka rimwe mu ntonde 500, kandi urudafise umurongo urenza gatatu nka kabiri muri 100.
Ibara rishasha ryose rirasubiramwo irya nyuma canke rigahindura, igice ku kindi, ku buryo uburyo 49 bwo guhindura butanga impuzandengo ya 24,5 vy'ihinduka, wongeyeko canke ukuyeko nka 3,5. Mirongo itatu na zitanu ni intambwe zitatu nk'izo hejuru y'impuzandengo; uruziga rutabogamye rutanga ihinduka ringana rityo nka rimwe mu ntonde 500.
Imirongo ivuga inkuru nyene. Urutonde nyakuri rw'amabara 50 rugira umurongo wa kane canke urenga nka 98% vy'incuro, kandi umurongo warwo muremure kuruta iyindi kenshi ni wa gatanu canke wa gatandatu.
Abantu basabwe guhimba urutonde rw'impfindo bahindura kenshi cane, kuko umurongo wa kane canke wa gatanu ubabonekera nk'akarorero gasubirwamwo. Taylor (2021) yerekana ikimenyetso nk'ico mu ntonde z'ugutera igiceri zahimbwe n'abanyeshure: impfindo nyakuri igira imirongo myinshi kuruta uko abantu bitega.
Igitabu c'inkuru za kazino kivuga umukinyi inomero yiwe yasohotse incuro zitanu zikurikirana kikabwita agahigo. Ivyo ni gake gute ku ruziga rw'i Buraya? Kandi vyoba kangahe ahantu muri kazino imwe ifise ameza 20, ayo yose azunguruka incuro 40 ku isaha, ku manywa n'ijoro?
Erekana inyishu
Inyishu Inomero yavuzwe imbere isohotse incuro zitanu zikurikirana: 1 muri miliyoni 69. Inomero iyo ari yo yose isohotse izindi ncuro zine inyuma yo gusohoka ubwa mbere: 1 muri miliyoni 1,87. Iyo kazino izunguruka nka miliyoni 7 z'incuro ku mwaka, ku buryo yokwitega kubona umurongo wa gatanu incuro zitatu canke zine ku mwaka.
Inomero yavuzwe imbere isohoka ku gushoboka kwa 1/37 kuri buri kuzunguruka, ku buryo zitanu zikurikirana zifise ugushoboka kwa (1/37)⁵ = 1 muri 69.343.957. Ariko nta n'umwe avuga inomero imbere. Ico ari co cose gisohotse mbere, ukuzunguruka kune gukurikira gutegerezwa kugisubiramwo: (1/37)⁴ = 1 muri 1.874.161.
Ameza 20 × ukuzunguruka 40 × amasaha 24 × imisi 365 = ukuzunguruka 7.008.000 ku mwaka. Ukuzunguruka kwose gushobora gutangura umurongo, ku buryo kazino yitega 7.008.000/1.874.161 ≈ 3,7 vy'imirongo ya gatanu ku mwaka.
Nta gahigo kemewe nk'ako kabaho, kandi nta co gakenewe: ikintu kidasanzwe ku meza amwe ni ikintu gisanzwe mu kazino yose, kandi inkuru zivugwa ku meza vyabereyeko. Inkuru, muri Goldman (2007), ibera ku ruziga rufise zeru zibiri, aho ibitigiri ari 1 muri miliyoni 79 na 1 muri miliyoni 2,09.

Agakuru ko gutwenga

$Urukurikirane rurerure ni ko impfindo isa.$

Urukurikirane rurerure ni ko impfindo isa.

Aho Twakuye

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, isohorwa rya 3, 1968. Gambler’s ruin, igice ca XIV.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Igice ca 13, ruleti.
Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021.

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