Kuthekera kwa Zotsatizana mu Roulette
Zotsatizana zazitali za mtundu umodzi ndi zofala. Ndiponso zilibe tanthauzo pa kuzungulira kotsatira.
Zofiira zisanu motsatizana: 2.7%. Khumi: 0.074%. Pa gawo la masewera la kuzungulira 200, zotsatizana za zisanu ndi chimodzi za mtundu umodzi zimaonekera kawirikawiri kuposa kusaonekera.
Kangati kuluza kotsatizana kumabwera
Betcha la even-money pa gudumu la ziro imodzi limaluza kuzungulira 19 mwa 37. Mzere uliwonse ndi kuthekera kwakuti kuzungulira kotsatizana kwa chiwerengero china konse kuluze, ndi zimene wosewera Martingale, amene amawirikiza akaluza kulikonse, wataya pofika nthawi imeneyo.
| kuluza motsatizana | kuthekera | pafupifupi 1 mwa | zotayika mpaka pano | betcha lotsatira |
|---|---|---|---|---|
| 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 |
Kuthekera ndi 19/37 kuchulukitsidwa ndi kokha kamodzi pa kuluza kulikonse, kuwerengedwa kuchokera pa kuzungulira kumodzi kodziwika. Gawo lalitali la masewera lili ndi kuzungulira kwambiri kumene kuluza kotere kungayambire, choncho m’madzulo amodzi n’kotheka kwambiri kuposa zimene mzere umodzi ukusonyeza.
Zotsatizana zimodzi
KuthekeramasamuKuthekeraMwayi wa zotsatira, kuchokera 0 mpaka 1 kapena 0% mpaka 100%. Nambala imodzi: 1/37 = 2.70%.Werengani yonse → koti kuzungulira k kotsatira konse kukhale zofiirabetchaZofiiraBetcha la even-money pa manambala 18 ofiira. Mu Chifalansa: rouge.Werengani yonse → ndi (18/37)ᵏ. Ziwiri: 23.7%. Zisanu: 2.7%. Khumi: 0.074%, pafupifupi 1 pa 1,350. Makumi awiri: 1 pa 1.8 miliyoni. Makumi awiri ndi zisanu ndi chimodzi, mbiri yapamwamba ya Monte Carlo: 1 pa 137 miliyoni. Awa ndi kuthekera kwa zotsatizana zinazake zoyambira pa kuzungulira kwinakwake, limene ndi funso limene pafupifupi palibe amene akufunsa kwenikweni.
M’gawo la masewera
Funso limene anthu amatanthauza ndi “kodi zotsatizana za k zidzaonekera kwinakwake m’gawo langa?”, ndipo yankho ndi lalikulu kwambiri kuposa (18/37)ᵏ chifukwa gawo la kuzungulira 200 limapereka malo pafupifupi 200 oti zotsatizana ziyambe. Zotsatizana za zisanu ndi chimodzi kapena kuposa za mtundu umodzi, zofiira kapena zakudabetchaZakudaBetcha la even-money pa manambala 18 akuda. Mu Chifalansa: noir.Werengani yonse →, zimaonekera m’gawo la kuzungulira 200 pafupifupi 94% ya nthawi; zisanu ndi zitatu kapena kuposa pafupifupi 47%; khumi kapena kuposa pafupifupi 14%. Tchulani mtundu pasadakhale ndipo mwayi umatsika, kufika pafupifupi 75%, 27% ndi 7%. Wosewera amene akhala madzulo onse adzaona zotsatizana zazitali madzulo aliwonse.
N’chifukwa chiyani Martingale ikukhudzidwa
ProgressionnjiraProgressionLamulo lililonse limene limasintha ndalama zobetcha potengera zotsatira zakale. Maprogression olakwika amazikweza pambuyo poluza, abwino pambuyo popambana.Werengani yonse → iliyonse yolakwika ili ndi kutalika kwa zotsatizana kumene kumaiswa: kuluza kasanu ndi kamodzi kuchokera pa maziko a $10 ndi malire a $500, kakhumi pa FibonaccinjiraFibonacciProgression yotsatira ndandanda 1, 1, 2, 3, 5, 8, 13…: sitepe imodzi kutsogolo pambuyo poluza, masitepe awiri kumbuyo pambuyo popambana.Werengani yonse →, kasanu pa kuwirikiza katatu pa madazenibetchaDazeni1–12, 13–24 kapena 25–36, amalipira 2:1.Werengani yonse →. Kuthekera kwa kuluza kasanu ndi kamodzi motsatizana pa even money ndi (19/37)⁶ ≈ 1.8% pa kuyesa kulikonse, ndipo gawo la kuzungulira 200 lili ndi mwina kuyesa 100, choncho kusweka kumafika pafupifupi m’magawo anayi pa asanu a kutalika kumeneko. Kuthekera kwa zotsatizana mu roulette ndiko chifukwa chake phompho silili losowa.
Manambala otentha ndi ozizira
Masamu omwewo amagwira ntchito pa ma straight upbetchaStraight upNambala imodzi, amalipira 35:1.Werengani yonse →. Pa kuzungulira 300 chiwerengero choyembekezeka pa nambala iliyonse ndi 8.1; kupatuka kokhazikikamasamuKupatuka kokhazikikaMuzu wa sikweya wa kusinthasintha; mtunda wanthawi zonse wa zotsatira kuchokera ku mtengo woyembekezeka.Werengani yonse → ndi pafupifupi 2.8. Nambala ina idzaonetsa kugunda 15 ndipo ina 2 mwangozi chabe, nthawi zonse. Bolodi la zotsatira loonetsa manambala “otentha” likuonetsa pamwamba pa kagawidwe ka normal. Labu ya Roulette imafotokoza kuchuluka kwa kuzungulira kofunikira nambala yotenthanthanoNambala yotenthaNambala imene yatuluka kawirikawiri kuposa moyembekezeka posachedwapa. Pa gudumu lachilungamo siilosera chilichonse.Werengani yonse → isanatanthauze chilichonse (masauzande, kuchokera pa gudumu limodzi lodziwika).
Kudziyimira payokha ndiyo mfundo yonse
Zofiira khumi motsatizana sizipangitsa zakuda kukhala zotheka kwambiri, ndiponso sizipangitsa zofiira kukhala zotheka kwambiri. Zonse ndi 18/37. Zotsatizana ndi khalidwe la zotsatizana zachisawawa ndipo kusapezeka kwake kukanakhala kokayikitsa: zotsatizana za kuzungulira 200 zopanda zotsatizana zazitali kuposa zinayi zikanakhala umboni wamphamvu kwambiri wa kusokoneza kuposa zokhala ndi zotsatizana za khumi ndi ziwiri.
Fomula
Mafunso
Zakuda 26 ku Monte Carlo pa 18 August 1913 ndizo zodziwika kwambiri. Zofiira 32 motsatizana zinanenedwa m’kasino ina ya ku America mu 1943. Zonse ziwiri zikugwirizana ndi mwangozi poganizira kuchuluka kwa kuzungulira kumene makasino amachita.
Ndi 18/37 mulimonse. Betchani zimene dongosolo lanu likunena, kapena musabetche.
Ayi. Kukondera kumaonekera ngati tibowozipangizoKabowoChimodzi mwa tibowo 37 tokhala ndi manambala pa rotor. Kamatchedwanso: slot, cup.Werengani yonse → tina tikugundidwa kawirikawiri pa kuzungulira masauzande, osati ngati zotsatizana za mtundu.
Masamu Osangalatsa
Yesani nokha choyamba. Yankho lililonse labisika; litsegulireni mukakonzeka.
Pa avareji, pamafunika kuzungulira kangati kwa gudumu la ku Ulaya kuti nambala iliyonse mwa manambala 37 ituluke kamodzi kapena kuposerapo?
Onetsani yankho
Yankho Pafupifupi kuzungulira 155 pa avareji; chapakati ndi 147.
Werengerani kudikira nambala yatsopano imodzi pa nthawi. Kuzungulira koyamba nthawi zonse kumasonyeza nambala yatsopano. Mukaona nambala 1, tibowozipangizoKabowoChimodzi mwa tibowo 37 tokhala ndi manambala pa rotor. Kamatchedwanso: slot, cup.Werengani yonse → 36 mwa 37 ndi tatsopano, choncho nambala yatsopano yotsatira imatenga kuzungulira 37/36 pa avareji. Mukaona manambala k, imatenga 37/(37 − k).
Phatikizani kudikira konse: 37/37 + 37/36 + 37/35 + … + 37/1 = 37 × (1 + 1/2 + 1/3 + … + 1/37) ≈ 37 × 4.20 = kuzungulira 155.5.
Zambiri mwa zimenezo ndi kumapeto. Nambala yomaliza yokha imatenga kuzungulira 37 pa avareji, ndipo zisanu zomaliza pafupifupi 85. Pa gudumu la ku America chiwerengero chomwecho chimapereka pafupifupi 161. Limeneli ndi vuto la wosonkhanitsa makuponi; avareji yomweyo imatuluka m’kuwerengera kwanthawi zonse.
Pa kuzungulira 37 kwa gudumu la ku Ulaya, kuzungulira kumodzi pa kabowo kalikonse, muyenera kuyembekezera kuona manambala osiyana angati?
Onetsani yankho
Yankho Pafupifupi 23.6. Pafupifupi gawo limodzi mwa atatu la manambala, pafupifupi 13, satuluka konse.
Tengani nambala imodzi, mwachitsanzo 17. Pa kuzungulira kulikonse imalephera kutuluka ndi kuthekera kwa 36/37, choncho imaphonya kuzungulira konse 37 ndi kuthekera kwa (36/37)³⁷ ≈ 0.363.
Nambala iliyonse ili ndi kuthekera kofanana, choncho pa avareji manambala 37 × 0.363 ≈ 13.4 sapezeka ndipo 37 − 13.4 ≈ 23.6 amatuluka, ambiri a iwo kawiri kapena kuposerapo.
Osewera roulette amatcha zimenezi lamulo la magawo atatu. Si lamulo, koma masamu chabe a zobwerezedwa: m’zotsatizana zazitali ngati gudumu, pafupifupi gawo limodzi mwa atatu la manambala silituluka, pa gudumu lachilungamo monga pa lina lililonse. Pa tibowo 38 gawolo ndi (37/38)³⁸ ≈ 0.363 nalonso; pa gudumu lalikulu limakhazikika pafupi ndi 1/e ≈ 0.368.
Mnzanu akukusonyezani mindandanda iwiri ya mitundu 50, zofiirabetchaZofiiraBetcha la even-money pa manambala 18 ofiira. Mu Chifalansa: rouge.Werengani yonse → kapena zakudabetchaZakudaBetcha la even-money pa manambala 18 akuda. Mu Chifalansa: noir.Werengani yonse →, iliyonse ikunenedwa kuti yachokera ku gudumu popanda zirogudumuZiroKabowo kamodzi kobiriwira kamene betcha la even-money, dazeni kapena mzati siliphimba; gwero la phindu la kasino. Imatchedwanso: ziro imodzi, 0.Werengani yonse →. Umodzi umasintha mtundu ka 25 ndipo zotsatizana zake zazitali kwambiri ndi zisanu ndi chimodzi. Wina umasintha ka 35 ndipo sukhala ndi zotsatizana zoposa zitatu. Ndi uti umene unapekedwa?
Onetsani yankho
Yankho Wachiwiri. Mndandanda weniweni umasintha pafupifupi ka 24 kapena 25. Wokhala ndi kusintha 35 umapezeka pafupifupi kamodzi pa mindandanda 500, ndipo wopanda zotsatizana zoposa zitatu pafupifupi kawiri pa 100.
Mtundu watsopano uliwonse umabwereza womaliza kapena umasintha, theka ndi theka, choncho mipata 49 yosintha imapereka kusintha 24.5 pa avareji, kuonjezera kapena kuchotsa pafupifupi 3.5. Makumi atatu ndi asanu ndi masitepe atatu otere pamwamba pa avareji; gudumu lachilungamo limapereka kusintha kochuluka chonchi pafupifupi kamodzi pa mindandanda 500.
Zotsatizana zimanena nkhani yomweyo. Mndandanda weniweni wa 50 umakhala ndi zotsatizana za zinayi kapena kuposerapo pafupifupi 98% ya nthawi, ndipo zotsatizana zake zazitali kwambiri kawirikawiri zimakhala zisanu kapena zisanu ndi chimodzi.
Anthu amene apemphedwa kupeka mndandanda wachisawawa amasintha kwambiri, chifukwa zotsatizana za zinayi kapena zisanu zimaoneka kwa iwo ngati kakonzedwe. Taylor (2021) akusonyeza chizindikiro chomwecho m’mindandanda ya kuponya ndalama yopekedwa ndi ophunzira: kusawerengeka kwenikweni kumakhala ndi zotsatizana zambiri kuposa momwe anthu amayembekezera.
Buku la nkhani za makasino likusimba za wosewera amene nambala yake inatuluka kasanu motsatizana ndipo likuzitcha mbiri yosaswedwa. Kodi zimenezo ndi zosowa bwanji pa gudumu la ku Ulaya? Ndipo zingachitike kangati kwinakwake m’kasino imodzi yokhala ndi matebulo 20, lililonse likuzungulira ka 40 pa ola, usana ndi usiku?
Onetsani yankho
Yankho Nambala yotchulidwa kasanu motsatizana: 1 pa 69 miliyoni. Nambala iliyonse kutuluka kanayi kenanso itatuluka koyamba: 1 pa 1.87 miliyoni. Kasino imeneyo imazungulira pafupifupi nthawi 7 miliyoni pa chaka, choncho iyenera kuona zotsatizana za zisanu katatu kapena kanayi pa chaka.
Nambala yotchulidwa imatuluka ndi kuthekera kwa 1/37 pa kuzungulira kulikonse, choncho kasanu motsatizana kuli ndi kuthekera kwa (1/37)⁵ = 1 pa 69,343,957. Koma palibe amene amatchula nambalayo pasadakhale. Chilichonse chimene chituluka poyamba, kuzungulira kanayi kotsatira kuyenera kuchibwereza: (1/37)⁴ = 1 pa 1,874,161.
Matebulo 20 × kuzungulira 40 × maola 24 × masiku 365 = kuzungulira 7,008,000 pa chaka. Kuzungulira kulikonse kungayambitse zotsatizana, choncho kasino imayembekezera 7,008,000/1,874,161 ≈ zotsatizana 3.7 za zisanu pa chaka.
Palibe mbiri yovomerezeka ya mtundu umenewu, ndipo siikufunika: chochitika chosowa patebulo limodzi ndi chochitika chanthawi zonse m’kasino yonse, ndipo nkhani zimasimbidwa za tebulo pamene zinachitika. Nkhaniyi, mu Goldman (2007), ikuchitika pa gudumu la ziro ziwiri, pamene manambala ndi 1 pa 79 miliyoni ndi 1 pa 2.09 miliyoni.
Nthabwala yopumitsa
Zotsatizana zazitali ndi mmene zachisawawa zimaonekera.
Magwero
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.