Okongezelelweyo · Imfundo · imizuzu eyi-7

I-roulette kunye nemfundo yezibalo

Ivili le-roulette lenza amathuba abe lula ukuwacinga. Nantsi indlela yokulisebenzisa esifundweni ngaphandle kokukhuthaza ukungcakaza.

Impendulo emfutshane

Iziphumo ezingamashumi amathathu anesixhenxe ezinamathuba alinganayo, iintlawulo ezimiselweyo, ukuzimela, okulindelekileyo okungalunganga okwaziwayo kunye nerekhodi ende yabantu abaphazamayo. I-roulette ibonisa okulindelekileyo, ukwahlukaizibaloUkwahlukaUmlinganiselo wokuba iziphumo zisasazeke kangakanani zijikeleze ixabiso elilindelekileyo. Kuphezulu kwibheji yenani elinye, kuphantsi kwiibheji zemali elinganayo.Funda yonke →, umthetho wamanani amakhuluizibaloUmthetho wamanani amakhuluUmndilili weziphumo ezizimeleyo usondela kwixabiso elilindelekileyo njengoko inani lemizamo likhula.Funda yonke →, impazamo yomngcakazi, uvavanyo lwe-hypothesis kunye nengxaki yomhla wokuzalwa ngcono kuneengqekembe okanye iidayisi.

isithuba seesampuli

37, ezilinganayo

iingcamango ezigutyungelweyo

≥ 8

izixhobo kule sayithi

zasimahla, kwibhrawuza

isifundo seqanda

EV = −1/37, qho

Kutheni i-roulette

Ingqekembe ineziphumo ezibini kwaye idayisi ezithandathu; zombini zincinci kakhulu ukubonisa ingxaki yomhla wokuzalwaizibaloIngxaki yomhla wokuzalwaBangaphi abantu abafunekayo phambi kokuba ababini mhlawumbi babe nomhla wokuzalwa omnye, okanye mingaphi imijikelo phambi kokuba inani mhlawumbi liphinde liphume. Kwivili elinezikhewu ezingama-37, imijikelo esi-8 yanele ukunika ithuba elingaphezulu kwesiqingatha.Funda yonke → okanye uvavanyo lwe-chi-squareilebhuUvavanyo lwe-chi-squareUvavanyo lwezibalo-manani oluthelekisa ukuphuma okubonwayo kwisikhewu ngasinye nokulindelekileyo u-n/37. Lusetyenziselwa ukugweba ukuba ivili lithambekile na.Funda yonke → ngomdla. Ipakethe yamakhadi inenkumbulo. I-roulette ineziphumo ezingama-37 ezinamathuba alinganayo, iintlawuloimaliIntlawuloOko ibheji ephumeleleyo ikubuyisayo, okuxelwa njengo-“X ku-1” ngaphezulu kwebheji ebuyisiweyo.Funda yonke → ezimiselweyo ezenza okulindelekileyo kube kukubala komgca omnye, ukuzimela ngokoyilo lomzimba, kunye nenzuzo yekhasino encinci ngokwaneleyo ukuba izifihle kwiseshoni nenkulu ngokwaneleyo ukuba ilawule unyaka. Ikwaneenkulungwane ezimbini zeempazamo ezibhaliweyo zokuhlalutywa.

Ingqekembe, idayisi namakhadi zinikezela kwiziphumo ezingama-37 ze-roulette ezinamathuba alinganayo.

Uvavanyo lwe-chi-square

Ulandelelwano lwezifundo

isifundoingcamangoumzekelo we-rouletteisixhobo kule sayithi

1amathuba njengokubalap(ibheji) = n/37Isibali se-odds ze-roulette

2okulindelekileyoEV = (n/37)(36/n − 1) − (37 − n)/37 = −1/37Umakhi weebheji

3ukuzimela nomthetho wokuphindaphinda(18/37)² kubomvu obubiniAmathuba oluhlu lweziphumo kwi-roulette

4okuncedisayo kunye “nobuncinane kanye”1 − (36/37)³⁷ = 63.7%Amathuba kwi-roulette

5ukwahluka nokutenxa okuqhelekileyoσ = 5.84 (inani elinye) ngokuchasene no-1.00 (obomvu), i-EV efanayoUkwahluka

6umthetho wamanani amakhulu (nento ongayithethiyo)umndilili uyasondela; iyonke iyahlukanaUkusondela ngokuhamba kwexesha

7impazamo yomngcakaziabamnyama abangama-26, 1913Impazamo yomngcakazi

8ukuhamba okungacwangciswanga nokuphelelwa yimaliifomula ye-gambler’s ruinIsibali somngcipheko wokuphelelwa yimali

9uvavanyo lwe-hypothesisi-chi-square kwizikhewu ezingama-37Umhlalutyi wokuthambekela kwevili

10ingxaki yomhla wokuzalwaukuphinda kwimijikelo esi-8, 56%Ingxaki: ivili lomhla wokuzalwa

11ulinganiso lwe-Monte Carloiiseshoni ezili-10,000 ngomzuzwanaIsilinganisi sesicwangciso

12kutheni iinkqubo zisilelaubume bomgca bokulindelekileyo (linearity)Ungayoyisa i-roulette?

Ukufundisa ngaphandle kokufundisa ukungcakaza

Sebenzisa imali yokudlala nomdlalo wedemo, ongenazo iibheji zokwenyani. Qala ngexabiso elilindelekileyoizibaloIxabiso elilindelekileyoIsiphumo esiphakathi kwibheji nganye ekuhambeni kwexesha elide. −1/37 yebheji kuyo yonke ibheji eqhelekileyo yaseYurophu.Funda yonke → uze uqhubeke ubuyela kulo: wonke umthambo uphela ngo-“kwaye ixabiso elilindelekileyo ngu-−1/37 webheji”. Sebenzisa iinkqubo njengemizekelo echasayo kunokuba zibe ziindlela: umthambo kukufumana isiphene, kwaye isilinganisi senza isiphene sibonakale ngemizuzwana. Quka imbali yabantu abalahlekelwayo. Isifundo kukuba izibalo ziyaphumelela, nto leyo echasene nentengiso.

Imithambo esebenzayo

Yenza abafundi baqikelele ukuba mingaphi imijikelo de kubekho ukuphinda, emva koko baqhube umdlalo wedemo amaxesha alishumi (ingxaki yomhla wokuzalwa). Yenza babhale “inkqubo” kumhleli wezicwangciso baze baqhube iiseshoni ezili-10,000 (ubume bomgca bokulindelekileyo). Yenza babale amathubaizibaloAmathubaIthuba lesiphumo, ukusuka ku-0 ukuya ku-1 okanye ku-0% ukuya ku-100%. Inani elinye: 1/37 = 2.70%.Funda yonke → othotho luka-1913 emva koko lothotho olwenzeka kwindawo ethile kwiminyaka engamashumi amahlanu yaseMonte Carlo (umahluko phakathi kwesiganeko esithile nesiganeko esithile nje). Yenza bafumane isikhewuizixhoboIsikhewuEsinye sezikhewu ezingama-37 ezinamanani kwirotha. Kwakhona: slot, cup.Funda yonke → “esithambekileyo” kwimbali yemijikelo efanelekileyo baze baxube idatha (uthelekiso oluninzi).

Ingqondo yabafundi iphazama ngokukhawuleza kangakanani (uqikelelo oluqhelekileyo lweklasi ngokuchasene nenyani)

imijikelo ukuya ekuphindeni: uqikelelo ≈ 19, inyani 8

8 ngokuchasene no-19

p(≥1 ukuphuma kwimijikelo engama-37): uqikelelo 100%, inyani 63.7%

63.7% ngokuchasene ne-100%

p(obomvu emva kobomvu ali-10): uqikelelo “ngaphantsi”, inyani 48.65%

48.65%

iiseshoni ezinenzuzo, Martingale: uqikelelo ≈ 95%, inyani ≈ 78%

78% ngokuchasene ne-95%

isiphumo somndilili, Martingale: uqikelelo “lulungile”, inyani alulunganga

alulunganga

050100

Umsantsa ngamnye sisifundo. Owokugqibela yikhosi.

Ukufunda iimbali zemijikelo ezipapashiweyo Ukubaluleka ngokwezibalo-manani

Kutheni kuhlala engqondweni

Abafundi bakhumbula abamnyamaibhejiOmnyamaIbheji yemali elinganayo kumanani ali-18 amnyama. NgesiFrentshi: noir.Funda yonke → abangama-26, ivili likaJagger, nomzuzu isilinganisi esabonisa ngawo inkqubo yabo ilahlekelwa. Amathuba angabonakaliyo ayalibaleka ngexesha leemviwo; ivili alilibaleki. Umgca wokuziphatha ucacile: fundisa izibalo ezenza umdlalo ube yibheji embi, usebenzisa umdlalo, kwaye abafundi abaya kungcakaza kamva ubuncinane baya kulazi ixabiso.

Abadlali be-roulette abadumileyo

Imibuzo

Ingaba kufanelekile kubafundi abasesikolweni?

Ngemali yokudlala nangesakhelo esicacileyo sokuba inzuzo yekhasinoizibaloInzuzo yekhasinoIsabelo sebheji nganye esigcinwa yikhasino ngokomndilili: 2.70% kwi-roulette yaseYurophu.Funda yonke → sisifundo, iikharikhulam ezininzi sele zisebenzisa iidayisi neelotho; i-roulette luhlobo olunzulu lwento efanayo.

Utitshala kufuneka aqale ngeliphi iphepha?

Inzuzo yekhasino kwi-roulette, emva koko umdlalo wedemo, emva koko Isilinganisi sesicwangciso se-roulette.

Ingaba umdlalo wedemo ukhuselekile eklasini?

Awunayo imali yokwenyani, akukho ii-akhawunti kwaye akukho makhonkco kubaqhubi bamashishini okungcakaza.

Uncumo

Iziphumo ezingamashumi amathathu anesixhenxe, inzuzo yekhasino enye, iinkulungwane ezimbini zeempazamo zokufunda kuzo.

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 ↗