Ukwahluka
Kutheni ibheji yenani elinye nebheji kobomvu ezine-lahleko elindelekileyoizibaloIlahleko elindelekileyoIxabiso elilindelekileyo liphindwe ngesixa esipheleleyo esibhejiweyo; isixa esiphakathi esilahlekayo kwiseshoni okanye kwixesha elithile.Funda yonke → efanayo zivakala ngathi yimidlalo eyahlukeneyo.
Ukwahluka kulinganisa ukuba iziphumo zisasazeke kangakanani ngeenxa zonke zexabiso elilindelekileyo. Kwiyunithi nganye ebhejiweyo kumalunga nama-34 kwinani elinye kwaye kumalunga ne-1 kobomvu.
Ifomula yebheji enye
Kwibheji ehlawula u-W ku-1 ngamathubaizibaloAmathubaIthuba lesiphumo, ukusuka ku-0 ukuya ku-1 okanye ku-0% ukuya ku-100%. Inani elinye: 1/37 = 2.70%.Funda yonke → p, isiphumo kwiyunithiimaliIyunithiIbheji esisiseko esetyenziswa yinkqubo okanye ngumdlali. Ukunyuswa kweebheji kuchazwa ngeeyunithi ukuze kusebenze kuyo nayiphi na itafile.Funda yonke → nganye ngu-+W ngamathuba p kunye no-−1 ngamathuba 1 − p. Ixabiso elilindelekileyoizibaloIxabiso elilindelekileyoIsiphumo esiphakathi kwibheji nganye ekuhambeni kwexesha elide. −1/37 yebheji kuyo yonke ibheji eqhelekileyo yaseYurophu.Funda yonke → ngu-pW − (1 − p) = −1/37. UkwahlukaizibaloUkwahlukaUmlinganiselo wokuba iziphumo zisasazeke kangakanani zijikeleze ixabiso elilindelekileyo. Kuphezulu kwibheji yenani elinye, kuphantsi kwiibheji zemali elinganayo.Funda yonke → ngu-E[X²] − EV² = pW² + (1 − p) − (1/37)². Kwi-bheji yenani elinyeibhejiInani elinyeInani elinye, ihlawula u-35:1.Funda yonke →: (1/37)(1225) + 36/37 − 0.0007 ≈ 34.08. KobomvuibhejiObomvuIbheji yemali elinganayo kumanani ali-18 abomvu. NgesiFrentshi: rouge.Funda yonke →: 18/37 + 19/37 − 0.0007 ≈ 0.999.
Kuthetha ntoni kwiseshoni
Ukwahluka kuyadibana kwimijikelo ezimeleyoizibaloImijikelo ezimeleyoUmjikelo ngamnye unamathuba afanayo nokuba imbali injani na. Isiseko sazo zonke izibalo kule sayithi.Funda yonke →, ngoko kwimijikelo engu-N kwibheji emisiweyo ukwahluka kwesixa esipheleleyo ngu-N × ibheji² × σ², kwaye ukutenxa okuqhelekileyoizibaloUkutenxa okuqhelekileyo (standard deviation)Ingcambu yesikwere yokwahluka; umgama oqhelekileyo wesiphumo ukusuka kwixabiso elilindelekileyo.Funda yonke → ngu-σ × ibheji × √N. Imijikelo eli-100 nge-$10: ukutenxa okuqhelekileyo kumalunga ne-$584 kwiibheji zenani elinye kunye ne-$100 kobomvu, ngeenxa zonke zesiphumo esilindelekileyo esifanayo esi-−$27. Omnye umdlali ubona iziphumo zijija ngamakhulu; omnye ubona ukutyibilika okuthambileyo. Bobabini bahlawula ixabiso elinye.
Ukwahluka neenkqubo
Ukunyuswa kweebhejiisicwangcisoUkunyuswa kweebhejiNawuphi na umthetho otshintsha ibheji ngokweziphumo zangaphambili. Ukunyuswa okubi kuyinyusa emva kwelahleko, okuhle emva kokuphumelela.Funda yonke → akuyitshintshi i-EV kwiyunithi nganye ebhejiweyo, kodwa kutshintsha zombini isixa esibhejiweyo nobume bokusasazeka. I-MartingaleisicwangcisoMartingaleUkunyuswa kweebheji okuphindaphinda ibheji emva kokulahlekelwa ngakunye. Bona icandelo lezicwangciso ukuze wazi oko ikwenzayo nengakwenziyo.Funda yonke → ithoba ukwahluka kweeseshoni ezininzi (uphumelelo oluninzi oluncinci) kwaye yongeza umsila otyebileyo (ilahleko enkulu enqabileyo); ukwahluka kukonke kuzo zonke iiseshoni kuphezulu kunoko kokubheja ngokulinganayoisicwangcisoUkubheja ngokulinganayoUkubheja isixa esifanayo kuwo wonke umjikelo. Isiseko apho konke ukunyuswa kweebheji kuthelekiswa khona.Funda yonke → ngenxa yaloo msila. I-ParoliisicwangcisoParoliUkunyuswa kweebheji okuhle: phindaphinda emva kokuphumelela, uqale kwakhona emva kokulahlekelwa okanye emva kokuphumelela kathathu ngokulandelelana. Kwakhona: i-Martingale ebuyela umva.Funda yonke → yenza okuchaseneyo. Ukukhetha inkqubo kukukhetha ubume bokwahluka; umndilili awukho kwimenyu.
- p10 −$500
- p25 −$500
- umbindi −$500
- p75 +$40
- p90 +$1,120
Isicwangciso sokubheja ngokulinganayo kwi-rouletteIsicwangciso se-Paroli kwi-roulette (i-Martingale ebuyela umva)
Kutheni kubalulekile kumdlali
Ukwahluka yinto eyenza iiseshoni ezimfutshane zingaqikeleleki kwaye ezinde ziqikeleleke. Nge-σ = $100 kunye ne-EV = −$27 kwimijikelo eli-100, inzuzo yekhasino yikota yengxolo kwaye iseshoni ephumelelayo yinto eqhelekileyo. Kwimijikelo eli-10,000 i-EV yi-−$2,700 kwaye i-σ yi-$1,000; ngoku inzuzo yekhasino iphantse iphindwe kathathu kunengxolo kwaye uthotho oluphumelelayo yisiganeko se-sigma ezintathu. Ukwahluka ngumhlobo womdlali kwixesha elifutshane, kwaye ngowekhasino kwixesha elide.
Ukwahluka kwendibaniselwano
Kwiibheji ezininzi kumjikelo omnye, iziphumo ziyanxulumana (ukubetha ku-17 kukwakukubetha komnyamaibhejiOmnyamaIbheji yemali elinganayo kumanani ali-18 amnyama. NgesiFrentshi: noir.Funda yonke → nakwi-daziniibhejiIdazini1–12, 13–24 okanye 25–36, ihlawula u-2:1.Funda yonke → yesibini), ngoko ukwahluka akudibani nje ngokulula. Isixhobo esithi Umakhi weebheji sibala ukusasazeka okuchanekileyo kwalo naliphi na iqela leetshiphuimaliItshiphuUphawu olumele isixa esimiselweyo, olubekwa kwibhodi yokubheja ukwenza ibheji. Kwakhona: check.Funda yonke → ngokubala zonke iziphumo ezingama-37, nto leyo iyeyona ndlela ichanekileyo yokwenza oko.
Ifomula
Imibuzo
Hayi. Yonke ibheji inexabiso elilindelekileyo elifanayo. Ukwahluka okuphezulu kuthetha ukujija okubanzi ngeenxa zonke zalo.
Iibheji zemali elinganayoibhejiIbheji yemali elinganayoObomvu/omnyama, angalinganiyo/alinganayo, aphezulu/aphantsi. Amanani ali-18, ihlawula u-1:1.Funda yonke →, nge-σ ≈ 1 kwiyunithi nganye. Kuphantsi nangakumbi nge-la partageumthethoLa partageUmthetho wesiFrentshi: xa kuphuma iqanda, isiqingatha sebheji yemali elinganayo siyabuyiswa. Sisika inzuzo yekhasino kwezo bheji ibe sisiqingatha, yi-1.35%.Funda yonke →, ekwaphucula nomndilili.
Inzuzo elindelekileyo iyafana kwidola nganye; ukwahluka kuchaphazela kuphela ukuba ingeniso yekhasino ingalinganiyo kangakanani, kwaye ikhasino inamawaka abadlali ukuyilinganisa.
Ukonwaba ngezibalo
Qala uzizame ngokwakho. Isisombululo ngasinye sisongiwe; sivule xa ukulungele.
Abadlali ababini ngamnye ubheja i-$1 ngomjikelo kwimijikelo eli-100 kwivili laseYurophu, omnye uhlala kobomvuibhejiObomvuIbheji yemali elinganayo kumanani ali-18 abomvu. NgesiFrentshi: rouge.Funda yonke →, omnye uhlala ku-17. Ngubani onethuba elingakumbi lokuba phambili ekupheleni?
Bonisa isisombululo
Impendulo Umdlali oku-17: 50.9%, xa kuthelekiswa ne-35.5% yobomvu. Bobabini balahlekelwa yi-$2.70 ngomndilili.
Obomvu: umdlali uphambili ngeempumelelo ezingama-51 nangaphezulu kwezili-100, nganye ngamathubaizibaloAmathubaIthuba lesiphumo, ukusuka ku-0 ukuya ku-1 okanye ku-0% ukuya ku-100%. Inani elinye: 1/37 = 2.70%.Funda yonke → ali-18/37. Ukusasazeka kwe-binomial kunika i-35.5%, kwaye iimpumelelo ezingama-50 ngqo, ukulinganisa, enye i-7.7%.
Inani 17: impumelelo nganye ibuyisa i-$36, ngoko iimpumelelo ezimbini (−$28) azanele kwaye ezintathu (+$8) zanele. Ithuba leempumelelo ezintathu nangaphezulu kwimijikelo eli-100 ngo-1/37 yi-50.9%.
Umdlali wenani elinye uphambili rhoqo, kodwa iziphumo zinamaqhuma ngakumbi: impumelelo enye ngaphezulu okanye ngaphantsi itshintsha isiphumo nge-$36, kwaye abadlali abasemva badla ngokuba semva ngakumbi. U-Bollman (2024) unika amanani aseMelika, 26.5% kunye ne-49.2%.
Uncumo
Ilahleko elindelekileyo efanayo. Enye yazo ikuxelela ngayo ngelizwi elikhulu.
Imithombo
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.