Izibalo ze-roulette · Ingxaki yezibalo · imizuzu eyi-7

Ingxaki: kuthatha ixesha elingakanani ukuze kuphume iqanda

Q: Ingaba iqanda linokwenzeka ngakumbi kwamanye amavili?

Hayi kwelifanelekileyo. Kwi-vili elithambekileyo nasiphi na isikhewu singaba njalo, kwaye kunokuthatha amawaka emijikelo ukuze kwaziwe.

Iqanda liphuma umjikelo omnye kwengama-37 ngokomndilili. Ulinda ixesha elingakanani ngokwenene, kwaye oko kwenza ntoni kumbheji wemali elinganayo?

Impendulo emfutshane

Ukulinda iqanda kuyi-geometric: umndilili yimijikelo engama-37, umbindi ngama-25, kwaye ukulinda okukodwa kwamashumi amabini kugqitha imijikelo eli-110. Kwiseshoni yemijikelo engama-200 umbheji wemali elinganayo ulindele amaqanda angama-5.4 kwaye uya kubona naphi na ukusuka ku-1 ukuya ku-10.

ukulinda komndilili

imijikelo engama-37

umbindi wokulinda

imijikelo engama-25

p(akukho qanda kwimijikelo eli-100)

6.5%

amaqanda kwimijikelo engama-200

5.4 ± 2.3

Ingxaki

IqandaiviliIqandaIsikhewu esinye esiluhlaza esingagubungelwa yibheji yemali elinganayo, yedazini okanye yekholamu; umthombo wenzuzo yekhasino. Kwakhona: iqanda elinye, 0.Funda yonke → linamathubaizibaloAmathubaIthuba lesiphumo, ukusuka ku-0 ukuya ku-1 okanye ku-0% ukuya ku-100%. Inani elinye: 1/37 = 2.70%.Funda yonke → angama-1/37 ngomjikelo. (a) Ngawaphi amathuba okungabikho qanda kwimijikelo engama-37 elandelayo? (b) Yintoni umbindi wokulinda? (c) Kwiseshoni yemali elinganayo yemijikelo engama-200, mangaphi amaqanda umdlali amele awalindele, kwaye luluphi uluhlu?

Izisombululo

(a) (36/37)³⁷ = 36.3%. Ngaphezu kwesinye kwisithathu sexesha, imijikelo engama-37 iyadlula kungekho qanda konke konke, okuzizibalo ezifanayo nokuba “ubuncinane ukuphuma okukodwa kwi-bheji yenani elinyeibhejiInani elinyeInani elinye, ihlawula u-35:1.Funda yonke → kwimijikelo engama-37” kungama-63.7% kuphela. (b) Ukulinda u-W kuyi-geometric; p(W > k) = (36/37)ᵏ; umbindi ngu-k apho oku kuwela u-0.5, oku ku-k ≈ 25. Isiqingatha sokulinda yimijikelo engama-25 okanye ngaphantsi kwaye isiqingatha side; umndilili wama-37 utsalwa phezulu ngumsila omde. (c) Amaqanda kwimijikelo engama-200 ayi-binomial enomndilili wama-200/37 = 5.4 kunye nokutenxa okuqhelekileyoizibaloUkutenxa okuqhelekileyo (standard deviation)Ingcambu yesikwere yokwahluka; umgama oqhelekileyo wesiphumo ukusuka kwixabiso elilindelekileyo.Funda yonke → okungu-√(200 × (1/37) × (36/37)) ≈ 2.3. Uluhlu lwe-95% malunga no-1 ukuya ku-10.

ukulinda iqandaamathuba

kwimijikelo eli-1024.0%

kwimijikelo engama-2549.6%

kwimijikelo engama-3763.7%

kwimijikelo engama-5074.6%

kwimijikelo eli-10093.5%

ngaphezu kwemijikelo eli-110≈ 5%

ngaphezu kwemijikelo engama-2000.4%

p(W ≤ k) = 1 − (36/37)ᵏ. Umndilili 37, umbindi 25.

Iqanda libiza malini kumbheji wemali elinganayo

Iqanda ngalinye libiza ibheji enye, kwaye amaqanda yiyo yonke inzuzo yekhasino kobomvuibhejiObomvuIbheji yemali elinganayo kumanani ali-18 abomvu. NgesiFrentshi: rouge.Funda yonke →: kwimijikelo yomndilili engama-37 iimpumelelo ezili-18 neelahleko ezili-18 ziyacimana, kwaye iqanda elinye yi-−1/37. Kwiseshoni yemijikelo engama-200 nge-$10, amaqanda angama-5.4 alindelekileyo abiza i-$54, eyiyo kanye 200 × $10 / 37. Iseshoni enamaqanda ama-2 ibe nethamsanqa elihle le-$34; iseshoni enamaqanda ali-9 ibe nethamsanqa elibi le-$36, kwaye iya kuziva iqhathiwe. Kwitafile ye-la partageumthethoLa partageUmthetho wesiFrentshi: xa kuphuma iqanda, isiqingatha sebheji yemali elinganayo siyabuyiswa. Sisika inzuzo yekhasino kwezo bheji ibe sisiqingatha, yi-1.35%.Funda yonke → iqanda ngalinye libiza isiqingatha sebheji kwaye amanani ahla ngesiqingatha.

Amaqanda kwiseshoni yemijikelo engama-200% yeeseshoni

0–1

2.5%

2–3

18%

4–5

34%

6–7

28%

8–9

13%

10 nangaphezulu

4.5%

% yeeseshoni

01734%

Binomial(200, 1/37). Umbheji we-$10 kobomvu uhlawula i-$10 ngeqanda ngalinye; usasazo lwamaqanda lusasazo lwexabiso lobusuku.

Umthetho we-La Partage kwi-roulette Ingaba i-roulette ye-intanethi iyakopela? Intsomi

Okulandelayo

Ngawaphi amathuba amaqanda amabini elandelelana? (1/37)² = 1/1,369. Kwikhasino eqhuba iitafile ezingama-20 kwimijikelo engama-50 ngeyure, malunga nesibini esinye samaqanda alandelelanayo kwindawo ethile rhoqo kwiiyure ezi-1.4. Abadlali abakubonayo bagqiba ukuba ivili laphukile; izibalo zithi lulwesiBini nje oqhelekileyo.

Zama

Isilinganisi seseshoni ye-roulette sibala amaqanda kwiseshoni nganye. Qhuba imijikelo eli-100 amakhulu ambalwa amaxesha uze uzobe inani: ihistogram engentla iya kuvela, nomsila wayo omde osekunene. Umsila yindawo apho amabali avela khona.

Ifomula

p(W > k) = (36/37)ᵏ

E[W] = 37 · umbindi ≈ 25

amaqanda kwimijikelo engu-N ~ Binomial(N, 1/37)

Imibuzo

Ingaba iqanda linokwenzeka ngakumbi kwamanye amavili?

Hayi kwelifanelekileyo. Kwi-vili elithambekileyoilebhuIvili elithambekileyoIvili elineziphene ezenza ezinye izikhewu zibe namathuba angaphezulu kwe-1/37. Alifumaneki lula, linokubonwa kuphela ngamawaka emijikelo erekhodiweyo.Funda yonke → nasiphi na isikhewuizixhoboIsikhewuEsinye sezikhewu ezingama-37 ezinamanani kwirotha. Kwakhona: slot, cup.Funda yonke → singaba njalo, kwaye kunokuthatha amawaka emijikelo ukuze kwaziwe.

Ingaba kufuneka ndihlale ndibeka itshiphu kwiqanda njenge-inshorensi?

Yibheji ye-2.70% njengazo zonke ezinye. Itshintsha imo yeseshoni (iqanda liba yimpumelelo) hayi iindleko.

Kutheni umbindi mncinci kunomndilili?

Kuba usasazo lokulinda luthambekile: ukulinda okufutshane okuninzi, okumbalwa okude kakhulu.

Uncumo

$Umndilili 37, umbindi 25, nomsila omde apho iintsomi zihlala khona.$

Umndilili 37, umbindi 25, nomsila omde apho iintsomi zihlala khona.

Imithombo

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, uhlelo lwe-3, 1968. Gambler’s ruin, isahluko XIV.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Isahluko 13, i-roulette.

ihlolwe ngo-2026-09-28imodeli: yaseYurophu, iqanda elinyeindlela yokusebenza ↗imithombo ↗