Tibalo te-roulette · Inkinga yetibalo · emaminithi 7

Inkinga: Kutsatsa sikhatsi lesingakanani kute kuphume licandza

Q: Licandza liphuma kakhulu yini kulamanye emasondvo?

Hhayi kulelingachemile. Esondvweni lelichemile nobe nguwuphi umgodzi ungaba njalo, futsi kungadzinga tinkhulungwane tekujikeleta kute kwatiwe.

Licandza liphuma kanye ekujikeleteni lokungu-37 ngesilinganiso. Ulindza sikhatsi lesingakanani ngempela, futsi loko kwentani kumbheji wekulingana nemali?

Imphendvulo lemfisha

Kulindza licandza kulandzela i-geometric distribution: silinganiso kujikeleta lokungu-37, i-median ngu-25, futsi kulindza kunye kulokungemashumi lamabili kudlula kujikeleta lokungu-110. Eseshini yekujikeleta lokungu-200 umbheji wekulingana nemali ulindzela emacandza langu-5.4 futsi utawubona nobe ngumaphi kusuka ku-1 kuya ku-10.

kulindza ngesilinganiso

kujikeleta lokungu-37

i-median yekulindza

kujikeleta lokungu-25

p(alikho licandza ekujikeleteni lokungu-100)

6.5%

emacandza ekujikeleteni lokungu-200

5.4 ± 2.3

Inkinga

LicandzalisondvoLicandzaUmgodzi munye loluhlata longambonjwa kubheja lokulingana nemali, kwelidazini noma kwelikholamu; umtfombo wenzuzo yelikhasino. Kuphindze kutsiwe: licandza linye, 0.Fundza konkhe → linelitfubatibaloLitfubaLitfuba lekutsi umphumela wenteke, kusukela ku-0 kuya ku-1 noma ku-0% kuya ku-100%. Inombolo yinye: 1/37 = 2.70%.Fundza konkhe → la-1/37 ekujikeleteni ngakunye. (a) Lingakanani litfuba lekutsi lingaphumi licandza ekujikeleteni lokungu-37 lokulandzelako? (b) Iyini i-median yekulindza? (c) Eseshini yekujikeleta lokungu-200 yekulingana nemali, umdlali kufanele alindzele emacandza langakanani, futsi luhla lunjani?

Tisombululo

(a) (36/37)³⁷ = 36.3%. Ngetulu kwencenye yinye kulokutsatfu yetikhatsi, kujikeleta lokungu-37 kuyendlula ngaphandle kwelicandza nelilodvwa, lokuyibalo lefanako nekutsi “kuwina kanye ngalokuncane ku-straight upkubhejaI-straight upInombolo yinye, kukhokha 35:1.Fundza konkhe → ekujikeleteni lokungu-37” kungu-63.7% kuphela. (b) Kulindza W kulandzela i-geometric distribution; p(W > k) = (36/37)ᵏ; i-median ngu-k lapho loku kwehla ngaphansi kwa-0.5, lokungu-k ≈ 25. Hafu yekulindza kujikeleta lokungu-25 nobe lokufishane, kantsi hafu kudze; silinganiso sa-37 sikhushulwa ngumsila lomudze. (c) Emacandza ekujikeleteni lokungu-200 alandzela i-binomial distribution lenesilinganiso sa-200/37 = 5.4 kanye nekuphambuka lokujwayelekiletibaloKuphambuka lokujwayelekileImphandze yesikwele yekugucugucuka (variance); libanga lelivamile lemphumela kusuka enanini lelilindzelekile.Fundza konkhe → kwa-√(200 × (1/37) × (36/37)) ≈ 2.3. Luhla lwa-95% lucishe lube ngu-1 kuya ku-10.

kulindza licandzalitfuba

ngekhatsi kwekujikeleta lokungu-1024.0%

ngekhatsi kwekujikeleta lokungu-2549.6%

ngekhatsi kwekujikeleta lokungu-3763.7%

ngekhatsi kwekujikeleta lokungu-5074.6%

ngekhatsi kwekujikeleta lokungu-10093.5%

ngetulu kwekujikeleta lokungu-110≈ 5%

ngetulu kwekujikeleta lokungu-2000.4%

p(W ≤ k) = 1 − (36/37)ᵏ. Silinganiso 37, i-median 25.

Licandza libita malini kumbheji wekulingana nemali

Licandza ngalinye libita linani linye lelibhejwako, futsi emacandza ayiyo yonkhe inzuzo yelikhasino kulokubovukubhejaBovuKubheja lokulingana nemali etinombolweni letingu-18 letibovu. NgesiFulentji: rouge.Fundza konkhe →: ekujikeleteni lokungu-37 ngesilinganiso kuwina lokungu-18 nekulahlekelwa lokungu-18 kuyacedzana, futsi licandza linye yi-−1/37. Eseshini yekujikeleta lokungu-200 nga-$10, emacandza langu-5.4 lalindzelekile abita $54, lokungu-200 × $10 / 37 ncamashi. Iseshini lenemacandza la-2 ibe nenhlanhla lenhle ya-$34; iseshini lenemacandza la-9 ibe nebunhlanhla lobubi ba-$36, futsi itawuva shengatsi iphambukisiwe. Etafuleni le-la partageumtsetfoLa partageUmtsetfo wesiFulentji: nangabe kuphuma licandza, sigamu selinani lelibhejiwe ekubhejeni lokulingana nemali siyabuyiswa. Kwehlisa inzuzo yelikhasino ngesigamu kulokubheja kuye ku-1.35%.Fundza konkhe → licandza ngalinye libita hafu yelinani lelibhejwako futsi tibalo tiyehla ngehafu.

Emacandza eseshini yekujikeleta lokungu-200% wetiseshini

0–1

2.5%

2–3

18%

4–5

34%

6–7

28%

8–9

13%

10 nobe ngetulu

4.5%

% wetiseshini

01734%

Binomial(200, 1/37). Umbheji wa-$10 kulokubovu ukhokha $10 kulicandza ngalinye; kusabalala kwemacandza kusabalala kwentsengo yebusuku.

Umtsetfo we-La Partage ku-roulette Kutsi i-roulette ye-inthanethi iyakhohlisa yini? Inganekwane

Lokulandzelako

Lingakanani litfuba lemacandza lamabili kulandzelana? (1/37)² = 1/1,369. Elikhasino lelinematafula langu-20 ladlala kujikeleta lokungu-50 ngelihora, loko kucishe kube libhangca linye lemacandza lalandzelanako endzaweni letsite njalo emahoreni langu-1.4. Badlali lababona loko baphetsa ngekutsi lisondvo laphukile; tibalo titsi lilanga lejwayelekile nje, Lesibili.

Kuzame

Silingisi seseshini ye-roulette sibala emacandza eseshini ngayinye. Dlala kujikeleta lokungu-100 emakhulu lambalwa etikhatsi bese ubeka sibalo eshadini: i-histogram lengenhla itawuvela, nemsila wayo lomudze ngesekudla. Umsila ngulapho tindzaba tivela khona.

Lifomula

p(W > k) = (36/37)ᵏ

E[W] = 37 · i-median ≈ 25

emacandza ekujikeleteni lokungu-N ~ Binomial(N, 1/37)

Imibuto

Licandza liphuma kakhulu yini kulamanye emasondvo?

Hhayi kulelingachemile. Esondvweni lelichemilelilabhorethriLisondvo lelichemileLisondvo lapho tici talo temtimba tenta leminye imigodzi ibe nematfuba langetulu kwa-1/37. Kuyindlalane, kutfolakala kuphela ngekujikeleta lokutinkhulungwane lokubhaliwe.Fundza konkhe → nobe nguwuphi umgodzitinsitaUmgodziLesinye setikhala letingu-37 letinetinombolo ku-rotor. Kuphindze kutsiwe: slot, cup.Fundza konkhe → ungaba njalo, futsi kungadzinga tinkhulungwane tekujikeleta kute kwatiwe.

Kufanele ngihlale ngibeka lithokheni elicandzeni njengemshwalensi yini?

Kubheja kwa-2.70% njengako konkhe lokunye. Kugucula simo seseshini (licandza liba kuwina) hhayi indleko.

I-median incane kunesilinganiso ngani?

Ngobe kusabalala kwekulindza akulingani: kulindza lokufishane lokunyenti, lokumbalwa lokudze kakhulu.

Lokuhlekisako

$Silinganiso 37, i-median 25, nemsila lomudze lapho tinganekwane tihlala khona.$

Silinganiso 37, i-median 25, nemsila lomudze lapho tinganekwane tihlala khona.

Imitfombo

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, luhlelo lwesi-3, 1968. Kuphelelwa yimali kwemgembuli, sehluko XIV.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Sehluko 13, i-roulette.

kubuyeketwe nga-2026-09-28imodeli: yaseYurophu, licandza linyeindlela yekusebenta ↗imitfombo ↗