Kupatuka Kokhazikika mu Roulette
Kupatuka kokhazikika mu roulette, muzu wa square wa kusinthasinthamasamuKusinthasinthaMuyeso wa kufalikira kwa zotsatira kuzungulira mtengo woyembekezeka. Kwakukulu pa straight up, kochepa pa mabetcha a even-money.Werengani yonse →, ndi mtunda wofala pakati pa zotsatira ndi zoyembekezeka zake.
Pa $1 iliyonse yobetchedwa, σ ndi 5.84 pa straight up ndi 1.00 pa zofiira. Chulukitsani ndi ndalama zobetcha ndi muzu wa square wa chiwerengero cha kuzungulira kuti mupeze gawo la masewera.
Lamulo losavuta
Pafupifupi magawo awiri pa atatu a masewera amathera mkati mwa σ imodzi ya zoyembekezeka ndipo 95% mkati mwa ziwiri. Pa kuzungulira 100 kwa zofiirabetchaZofiiraBetcha la even-money pa manambala 18 ofiira. Mu Chifalansa: rouge.Werengani yonse → pa $10 (zoyembekezeka −$27, σ = $100) magawo ambiri amagwera pakati pa −$127 ndi +$73, ndipo pafupifupi onse pakati pa −$227 ndi +$173. Zotsatira kunja kwa malire amenewo si umboni wa chilichonse kupatula kuti gawo limodzi pa makumi awiri limachita zimenezo.
N’chifukwa chiyani √N
Kutayika koyembekezekamasamuKutayika koyembekezekaMtengo woyembekezeka kuchulukitsa ndi ndalama zonse zobetchedwa; kuchuluka kwapakati kwa ndalama zotayika mu gawo la masewera kapena nthawi inayake.Werengani yonse → kumakula molingana ndi N; kufalikira kumakula molingana ndi √N. Pa N yaing’ono kufalikira kumapambana ndipo magawo ali ngati kuponya ndalama ndi kupendekera pang’ono. Pa N yaikulu kutayika kumapitirira kufalikira. Pamene zimadutsana, pamene kutayika koyembekezeka kukufanana ndi kupatuka kokhazikikamasamuKupatuka kokhazikikaMuzu wa sikweya wa kusinthasintha; mtunda wanthawi zonse wa zotsatira kuchokera ku mtengo woyembekezeka.Werengani yonse → kumodzi, ndi pa N = (σ/phindu la kasino)² = (1/0.027)² ≈ kuzungulira 1,370 pa even money ndi (5.84/0.027)² ≈ 46,800 pa ma straight upbetchaStraight upNambala imodzi, amalipira 35:1.Werengani yonse →. Pansi pa manambala amenewo, mwayi umasankha; pamwamba pake, phindu la kasino ndilo limasankha.
Kuchigwiritsa ntchito
Kuti muone ngati gawo la masewera linali lachilendo, werengerani (zotsatira − EV)/σ. Wobetcha $10 pa zofiira amene amaliza kuzungulira 100 pa +$150 ali pa (150 + 27)/100 = 1.77σ, zotsatira za kamodzi pa 25: mwayi, osati chodabwitsa. Wobetcha straight up pa +$150 yomweyo ali pa 0.3σ: usiku wamba. Zotsatira zofanana za madola zimatanthauza zinthu zosiyana pa mabetcha osiyana.
Cholakwika chokhazikika cha gawo (standard error)
Masamu omwewo amakuuzani kuchuluka kwa kuzungulira kofunikira kuti muone phindu la kasino mu zambiri. Cholakwika chokhazikika cha gawo la kupambana loonedwa ndi √(p(1 − p)/N). Pa zofiira ndi N = 1,000: √(0.4865 × 0.5135 / 1000) ≈ 1.6%. Kusiyana pakati pa ndalama yachilungamo yoponya ndi zofiira ndi 1.35%, choncho pambuyo pa kuzungulira 1,000 simungathebe kuzisiyanitsa motsimikiza. Pambuyo pa 10,000 cholakwika chokhazikika ndi 0.5% ndipo mungathe. Ichi ndichonso chifukwa chake kuzindikira kupendekera kwa gudumu kumafuna kuzungulira kochuluka chotere.
Chenjezo pa kupindika (skew)
Zotsatira za straight up sizigawidwa mwa normal konse m’gawo lalifupi: magawo ambiri ndi −$10 yosasintha pa kuzungulira kulikonse ndi kudumpha kwa +$350 nthawi zina. Lamulo la ±1σ limafotokoza kufalikira molondola koma mawonekedwe moipa mpaka N ifike m’mazana. Pa mabetcha a even-moneybetchaBetcha la even-moneyZofiira/zakuda, osakhala awiriawiri/awiriawiri, okwera/otsika. Manambala 18, amalipira 1:1.Werengani yonse → kuyerekeza kwa normal kuli bwino kuyambira pa kuzungulira pafupifupi 30.
Fomula
Mafunso
Ndi umboni woti munasewera magawo pafupifupi 40, kapena kuti munali mu gawo lamwayi limodzi pa makumi anayi. Bwerezani.
Imasinthasintha pang’ono pang’ono: cholakwika chokhazikika cha avareji ndi σ/√N. Pofika N = 10,000 ndi 1% ya ndalama zobetcha.
Masamu Osangalatsa
Yesani nokha choyamba. Yankho lililonse labisika; litsegulireni mukakonzeka.
Pa kuzungulira 100 kwa gudumu la ku Ulaya, unitndalamaUnitNdalama zobetcha zoyambira zimene dongosolo kapena wosewera amagwiritsa ntchito. Maprogression amafotokozedwa mu ma unit kuti agwire ntchito pa tebulo lililonse.Werengani yonse → imodzi pa zofiirabetchaZofiiraBetcha la even-money pa manambala 18 ofiira. Mu Chifalansa: rouge.Werengani yonse → ili patsogolo ndi kupambana 51 kapena kuposerapo, ndipo unit imodzi pa straight upbetchaStraight upNambala imodzi, amalipira 35:1.Werengani yonse → ili patsogolo ngati nambala yake yagunda ka 3 kapena kuposerapo. Gwiritsani ntchito mkhota wa belu kuyerekeza kuthekera konse kuwiri, kenako yerekezerani ndi mayankho enieni.
Onetsani yankho
Yankho Zofiira: mkhota wa belu umapereka 35.6% ndipo yankho lenileni ndi 35.5%. Straight up: mkhota wa belu umapereka 55.0% ndipo yankho lenileni ndi 50.9%. Njira yachidule imagwira ntchito pa zofiira ndipo imalephera pa nambala imodzi.
Zofiira: kupambana kuli ndi avareji ya 100 × 18/37 = 48.6, ndi kufalikira kwa √(100 × 18/37 × 19/37) = 5.0. Kukhala patsogolo kumatanthauza 51 kapena kuposerapo; chizindikiro chapakati, 50.5, chili makufalikira 0.37 pamwamba pa avareji, ndipo mkhota wa belu umaika 35.6% pamwamba pa pamenepo. Kuphatikiza kuthekera kwenikweni kwa kupambana 51, 52 … 100 kumapereka 35.5%.
Straight up: kugunda kuli ndi avareji ya 100/37 = 2.70, ndi kufalikira kwa √(100 × 1/37 × 36/37) = 1.62. Kugunda katatu kapena kuposerapo kumatanthauza pamwamba pa 2.5, makufalikira 0.12 pansi pa avareji: 55.0% malinga ndi mkhota wa belu. Kwenikweni, ndi 1 kuchotsa kuthekera kwa kugunda 0, 1 ndi 2, 6.5% + 17.9% + 24.7%, zimene zimasiya 50.9%.
Mkhota wa belu umafunika zotsatira zambiri mbali zonse ziwiri za avareji. Zofiira zili nazo pambuyo pa kuzungulira 100; nambala imene imagunda zosakwana katatu pa avareji ilibe. Mkhotawo umaperekanso 8.7% ku “palibe kugunda”, pamene kuthekera kwenikweni ndi 6.5%. Taylor (2021) amaika binomial ndi mkhota wa belu mbali ndi mbali chimodzimodzi.
Nthabwala yopumitsa
Gawo limodzi pa makumi awiri lili kunja kwa sigma ziwiri. Wina nthawi zonse ali pa mchira.
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.