Izibalo ze-roulette · Ukusetyenziswa · imizuzu eyi-13

Umngcipheko wokuphelelwa yimali

Q: Ingaba ukunyuswa kweebheji kuyawunciphisa umngcipheko wokuphelelwa yimali?

I-Martingale iyawunciphisa kwiiseshoni ezimfutshane kwaye iwunyuse kakhulu kwezinde. Ukubheja ngokulinganayo ngeyunithi enkulu yindlela enyanisekileyo yokuwunciphisa.

Amathuba okuphulukana nayo yonke imali yakho yokudlala phambi kokufikelela kwinjongo.

Impendulo emfutshane

Kwiibheji zemali elinganayo, umngcipheko wokuphelelwa yimali ulandela ifomula ye-gambler’s ruin. Ngemali yokudlala ye-$500, iibheji ze-$10 nenjongo ye-$600, ufikelela kwinjongo malunga nama-57% exesha kwaye uphelelwa yimali ngamanye amaxesha.

ifomula

gambler’s ruin

p (imali elinganayo)

18/37

q/p

1.0556

esona siphumo sidala

Pascal–Fermat, 1656

Umbuzo

Une-a yeeyunithiimaliIyunithiIbheji esisiseko esetyenziswa yinkqubo okanye ngumdlali. Ukunyuswa kweebheji kuchazwa ngeeyunithi ukuze kusebenze kuyo nayiphi na itafile.Funda yonke → zemali yokudlalaimaliImali yokudlalaIsixa esipheleleyo esibekelwe ukudlala. Ulawulo lwemali yokudlala kukugqiba ukuba ingakanani kuyo oyibeka emngciphekweni kwibheji nganye nakwiseshoni nganye.Funda yonke → kwaye ufuna ukufikelela kwi-a + b yeeyunithi, ubheja iyunithi enye ngexesha kwibheji yemali elinganayoibhejiIbheji yemali elinganayoObomvu/omnyama, angalinganiyo/alinganayo, aphezulu/aphantsi. Amanani ali-18, ihlawula u-1:1.Funda yonke → enamathubaizibaloAmathubaIthuba lesiphumo, ukusuka ku-0 ukuya ku-1 okanye ku-0% ukuya ku-100%. Inani elinye: 1/37 = 2.70%.Funda yonke → okuphumelela p = 18/37 namathuba okulahlekelwa q = 19/37. Ngawaphi amathuba okuba ufikelele kwinjongo phambi kokuba ufike kwiqanda? Impendulo yasetyenzwa nguPascal, Fermat noHuygens ngeminyaka yee-1650 kwaye yenye yezona ziphumo zindala kwamathuba.

Blaise Pascal: intsomi yevili le-roulette

Ifomula ye-gambler’s ruin

P(ukufikelela kwinjongo) = (1 − (q/p)ᵃ) / (1 − (q/p)ᵃ⁺ᵇ). Umngcipheko wokuphelelwa yimaliizibaloUmngcipheko wokuphelelwa yimaliAmathuba okulahlekelwa yimali yokudlala yonke phambi kokufikelela kwinjongo okanye kwinani lemijikelo.Funda yonke → ngunye thabatha oko. Xa q/p = 19/18 ≈ 1.0556, umlinganiselo ukhula ngokukhawuleza okukhulu ngokwenani leeyunithi, ngoko ifomula iyazohlwaya kakhulu iiyunithi ezincinci: okukhona kufuneka iibheji ezininzi ukufikelela kwinjongo, kokukhona irhafu ye-2.70% ihlawulwa kaninzi endleleni.

imali yokudlalaiyunithiinjongoiibheji ukuya kwinjongop(ukufikelela kwinjongo)umngcipheko wokuphelelwa yimali

$500$10$60010≈ 57%≈ 43%

$500$50$6002≈ 79%≈ 21%

$500$10$1,00050≈ 6%≈ 94%

$500$100$1,0005≈ 43%≈ 57%

$500$500$1,000148.6%51.4%

$100$10$20010≈ 37%≈ 63%

Iibheji zemali elinganayo, ibheji efanayo, akukho la partage. Isibali somngcipheko wokuphelelwa yimali senza izibalo zawo nawaphi na amanani.

Ukuyifunda

Iiyunithi ezincinci ziyenzakalisa. Ukuzama ukuphinda kabini i-$500 ngeebheji ze-$10 kuphumelela i-6% yexesha; ngebheji enye ye-$500 kuphumelela ama-48.6% exesha. Ukudlala ngesibindi, iibheji ezimbalwa nezinkulu, kwandisa amathuba okufikelela kwinjongo kumdlalo onexabiso elilindelekileyo elibi, kuba kunciphisa inani lamaxesha inzuzo yekhasino isetyenziswa ngawo. Kwakhona kwandisa ukwahlukaizibaloUkwahlukaUmlinganiselo wokuba iziphumo zisasazeke kangakanani zijikeleze ixabiso elilindelekileyo. Kuphezulu kwibheji yenani elinye, kuphantsi kwiibheji zemali elinganayo.Funda yonke → kwento eyenzeka kuwe, kwaye kuphelisa ubusuku ngokukhawuleza. Ithiyori ibizwa ngokuba “ukudlala ngesibindi kungoyena mkhwa ulungileyo” (bold play is optimal) kwaye yangqinwa nguDubins noSavage ngo-1965.

Amathuba okuguqula i-$500 ibe yi-$1,000 kobomvu%

ibheji enye ye-$500

48.6%

iibheji ze-$100

≈ 43%

iibheji ze-$50

≈ 37%

iibheji ze-$20

≈ 21%

iibheji ze-$10

≈ 6%

iibheji ze-$5

≈ 0.5%

024.3048.6%

Okukhona kufuneka iibheji ezininzi, kokukhona inzuzo yekhasino ihlawulwa kaninzi. Ukudlala ngokoyika kuyabiza.

Apho ingxaki yaqala khona

Lo mbuzo mdala kune-roulette. Ngo-1656 uPascal wanika uFermat iphazili: abadlali ababini baphosa iidayisi ezintathu, ngamnye eqala ngeekhawuntara ezili-12; ukuphosa i-11 kushenxisa ikhawuntara ngakwelinye icala, ukuphosa i-14 ngakwelinye. Bobabini bayisombulula, kwaye uHuygens, owayiva ngeleta evela kwisazi sezibalo uPierre de Carcavi, wayiprinta ngo-1657 njengengxaki yesihlanu kwincwadi yokuqala ngamathuba, enempendulo kodwa engenabungqina. Ishumi elinanye linokuphoswa ngeendlela ezingama-27 kwaye ishumi elinesine ngeendlela ezili-15 kuphela, ngoko ikhawuntara nganye ishenxela ngakumdlali wokuqala amaxesha ali-9 kwali-14, kwaye ifomula engentla, ngeekhawuntara ezili-12 ngamnye, imenza abe nokwenzeka malunga namaxesha ali-1,157 ngakumbi ukuphumelela yonke into kunokuphulukana nayo yonke into. Inzuzo yekhasino ye-2.70% incinci kakhulu, kodwa ifomula efanayo ibonisa oko ikwenzayo kwiibheji ezininzi.

Kwiphazili kaPascal, ukuphosa ngakunye kweedayisi ezintathu kushenxisa ikhawuntara enye phakathi kwabadlali.

Ibheji yokwenyani yesibindi

Ngo-Epreli 2004 u-Ashley Revell, umfana oliNgesi, wathengisa phantse yonke into awayenayo, kuquka iimpahla zakhe, waza wathatha i-$135,300 waya nayo e-Plaza eLas Vegas. Emva kweebheji ezincinci wabeka sonke isixa kobomvuibhejiObomvuIbheji yemali elinganayo kumanani ali-18 abomvu. NgesiFrentshi: rouge.Funda yonke →, kanye. IbholaizixhoboIbholaIbhola encinci ephoswa emzileni ngokuchasene nerotha. Iibhola zanamhlanje zenziwe nge-ivorine okanye nge-Teflon, zi-18–21 mm.Funda yonke → yawela ku-7 obomvu kwaye waphuma ne-$270,600. Kwivili eneqandaiviliIqandaIsikhewu esinye esiluhlaza esingagubungelwa yibheji yemali elinganayo, yedazini okanye yekholamu; umthombo wenzuzo yekhasino. Kwakhona: iqanda elinye, 0.Funda yonke → eliphindiweyo lo mjikelo mnye wawungamathuba angama-47.37% kwaye wamxabisa i-$7,121 ngokomndilili, inzuzo yekhasino ye-5.26% kwibheji enye. Ukuba isasazwe kwiibheji ze-$10, injongo efanayo ibiya kuphantse ingabi nathemba. Ukudlala ngesibindi akuyenzi ibheji ilunge; kuyenza ibe mfutshane kangangoko kunokwenzeka.

Yonke imali yokudlala ka-Ashley Revell ixhomekeke kumjikelo omnye wevili eliphindiweyo iqanda.

Umngcipheko wokuphelelwa yimali ngaphandle kwenjongo

Ukuba udlala nje de uphelelwe yimali okanye uyeke emva kwemijikelo eyi-N, umbuzo uba “ngawaphi amathuba okuba imali yam yokudlala ichukumise iqanda kwimijikelo eyi-N?”. Akukho fomula evaliweyo ye-N ngokubanzi kodwa izilinganisi kule sayithi ziyabala: imali yokudlala ye-$500 nge-$10 kobomvu phantse ayize iphele kwimijikelo eli-100 (ngaphantsi kwe-1%), iphela malunga ne-9% yexesha kwimijikelo engama-500, nalunga nama-95% exesha kwimijikelo engama-5,000. Ngaphandle komthetho wokuyeka amathuba asondela kwi-100%, nto leyo iyinguqulelo yexesha elide yenzuzo yekhasinoizibaloInzuzo yekhasinoIsabelo sebheji nganye esigcinwa yikhasino ngokomndilili: 2.70% kwi-roulette yaseYurophu.Funda yonke →.

Iiseshoni ezilishumi, imali yokudlala ye-$500, i-$25 kobomvu, imijikelo engama-200isiphumo xa kuthelekiswa nokuqala

iiseshoni ezi-1,000 × imijikelo eyi-500 · mfusa p10/p25/p75/p90, luhlaza okwesibhakabhaka okukhanyayo umbindi, iisampulu ezi-81 ezifiphele · hambisa isalathisi phezu kwegrafu ukuze ubone ii-quantile kumjikelo

p10 −$500
p25 −$500
umbindi −$500
p75 +$0
p90 +$350

iiseshoni ezi-1,000 × imijikelo eyi-500 · i-y-axis inqunyulwe kwi-1st–99th percentile (iziphelo −$500 ukuya ku-+$1,500) · imijikelo eyi-500 · isiseko $25 · imali elinganayo

Imigca echukumisa ezantsi iphelelwe yimali. Ngeyunithi encinci ibiya kuhlala ixesha elide kwaye iphele kwindawo efanayo.

Ukusondela ngokuhamba kwexesha: umthetho wamanani amakhulu kwi-roulette

Ixesha elingakanani, nokuba uphambili kangakanani

Iziphumo ezimbini ezongezelelweyo zakudala ziphendula imibuzo ebuzwa ngabadlali ngokwenene. Ngaphandle kwenjongo, iibheji ezilinganayo zemali elinganayo zihlala ngokomndilili imijikelo engama-37 kwiyunithi nganye yemali yokudlala kwivili laseYurophu ne-19 kwelaseMelika, kuba umjikelo ngamnye uthatha u-1/37 weyunithi ngokomndilili (u-1/19 kwivili laseMelika): iiyunithi ezili-100 zihlala imijikelo engama-3,700 ngokomndilili, nangona isiqingatha seeseshoni ezinjalo siphela kwimijikelo engama-3,134 (jonga Ubude beseshoni neendleko zayo). Kwaye nokuba imali yokudlala inkulu kangakanani, amathuba kwivili laseYurophu okuba wakhe uphambili ngeeyunithi eziyi-k ngu-(18/19)ᵏ. Loo nto ingama-95% kwiyunithi enye nama-58% kwezilishumi, kodwa akukho mali yokudlala, nokuba inzulu kangakanani, enika amathuba alinganayo okuba wakhe uphambili ngeeyunithi ezili-13; kwivili laseMelika amathuba ngu-(9/10)ᵏ kwaye ehla ngaphantsi kwesiqingatha kwiiyunithi ezi-7.

iiyunithi ophambili ngazo, nangaliphi na ixeshaYaseYurophuYaseMelika

194.7%90.0%

576.3%59.0%

1058.2%34.9%

1349.5%25.4%

2033.9%12.2%

506.7%0.5%

1000.45%0.003%

Iibheji zemali elinganayo, ibheji efanayo, imali yokudlala enkulu ngokwaneleyo ukuba ingaze iphele. Amathuba ngu-(18/19)ᵏ kwivili elineqanda elinye no-(9/10)ᵏ kwelineqanda eliphindiweyo.

Ubude beseshoni neendleko zayo Ivili nemithetho ye-roulette yaseMelika

Imali yokudlala yamathuba alinganayo

Jika umbuzo: kufuneka uze nemali engakanani ukuze ube namathuba alinganayo ubuncinane okuphumelela isixa esithile phambi kokuphulukana nayo yonke into? Kwinzuzo encinci, ayininzi. Kwenkulu ngakumbi imali yokudlala efunekayo inyuka kakhulu, kwaye emva kwenqanaba elithile akukho mali yokudlala yaneleyo, kuba nengapheliyo inika amathuba angaphantsi kwalinganayo okuba wakhe ufikelele phambili kangako. UTaylor (2021) ukubeka ngenye indlela: kwivili laseMelika, ukuze ube namathuba alinganayo okufikelela kwiiyunithi ezili-100 kufuneka uqale nge-94, ubeke emngciphekweni i-94 ukuze uphumelele i-6. Kwivili laseYurophu ubuya kudinga i-88.

ukuphumelelaYaseYurophuYaseMelika

iyunithi e-122

iiyunithi ezi-233

iiyunithi ezi-345

iiyunithi ezi-468

iiyunithi ezi-5712

iiyunithi ezi-6921

iiyunithi ezi-712akukho mali yokudlala yaneleyo

iiyunithi ezi-815akukho mali yokudlala yaneleyo

iiyunithi ezili-1024akukho mali yokudlala yaneleyo

iiyunithi ezili-1246akukho mali yokudlala yaneleyo

iiyunithi ezili-13 nangaphezuluakukho mali yokudlala yaneleyoakukho mali yokudlala yaneleyo

Imali yokudlala encinci kakhulu, ngeeyunithi, enika ubuncinane amathuba alinganayo okuphumelela isixa phambi kokuphulukana nemali yokudlala, ngeebheji ezilinganayo zemali elinganayo. Ubalo lwethu kwifomula engentla.

Isifundo esisebenzayo

Gqiba ukuba uzama ukwenza ntoni. Ukuba injongo yinzuzo ethile, bheja kakhulu kwaye kambalwa. Ukuba injongo bubusuku obude, bheja kancinci kwaye wamkele ukuba inzuzo yekhasino iya kuthatha i-2.70% yayo kwisixa esipheleleyo esibhejiweyoimaliIsixa esipheleleyo esibhejiweyoIsixa esipheleleyo esibhejiweyo kwiseshoni okanye kwixesha elithile, kubalwa nemali ephumeleleyo ephinda ibhejwe. Kwakhona: handle, action.Funda yonke → esikhulu. Ukuba injongo zombini, enye into kufuneka inikezele, kwaye idla ngokuba yinjongo.

Ifomula

P(injongo) = (1 − (q/p)ᵃ) / (1 − (q/p)ᵃ⁺ᵇ)

umngcipheko wokuphelelwa yimali = 1 − P(injongo)

q/p = 19/18 kwimali elinganayo

umndilili wemijikelo ukuya ekuphelelweni yimali, ngaphandle kwenjongo = 37 × iiyunithi

P(wakhe uphambili ngeeyunithi eziyi-k) = (18/19)ᵏ

Imibuzo

Ingaba ukunyuswa kweebheji kuyawunciphisa umngcipheko wokuphelelwa yimali?

I-MartingaleisicwangcisoMartingaleUkunyuswa kweebheji okuphindaphinda ibheji emva kokulahlekelwa ngakunye. Bona icandelo lezicwangciso ukuze wazi oko ikwenzayo nengakwenziyo.Funda yonke → iyawunciphisa kwiiseshoni ezimfutshane kwaye iwunyuse kakhulu kwezinde. Ukubheja ngokulinganayoisicwangcisoUkubheja ngokulinganayoUkubheja isixa esifanayo kuwo wonke umjikelo. Isiseko apho konke ukunyuswa kweebheji kuthelekiswa khona.Funda yonke → ngeyunithi enkulu yindlela enyanisekileyo yokuwunciphisa.

Kuthekani ngeebheji zenani elinye?

Ifomula engentla yeyemali elinganayo. Kwiibheji ezinokwahluka okuphezulu ukuphelelwa yimali kunokwenzeka ngakumbi ngeebheji ezincinci kwaye injongo ifikelelwa ngendlela engalinganiyo; sebenzisa isibali.

Kutheni u-q/p elelona nani libalulekileyo?

Inyathelo ngalinye elisiya kwinjongo alinakwenzeka kangako kancinci kunenyathelo ngalinye elisiya ekuphelelweni yimali; umlinganiselo uyaphindaphindeka ngokwenani lamanyathelo.

Ukonwaba ngezibalo

Qala uzizame ngokwakho. Isisombululo ngasinye sisongiwe; sivule xa ukulungele.

Une-$100 kwaye ufuna i-$1,000, ubheja kobomvuibhejiObomvuIbheji yemali elinganayo kumanani ali-18 abomvu. NgesiFrentshi: rouge.Funda yonke → kuphela. Isicwangciso sokuqala: bheja i-$1 ngexesha. Isicwangciso sesibini: bheja yonke into onayo de udlule i-$500, emva koko kwanele nje ukufikelela kwi-$1,000. Sesiphi isicwangciso esingcono, kwaye ngomlinganiselo ongakanani?
Bonisa isisombululo
Impendulo Isicwangciso sesibini, kakhulu. Sifikelela kwi-$1,000 malunga ne-9.0% yexesha, kufutshane ne-10% efanelekileyo. Isicwangciso sokuqala siphumelela malunga nezihlandlo ezi-7 kwi-10²².
Kumdlalo ofanelekileyoizibaloUmdlalo onobulungisaUmdlalo apho kungekho cala linenzuzo: yonke ibheji inexabiso elilindelekileyo eliliqanda.Funda yonke → ubuya kufikelela kwi-$1,000 usuka kwi-$100 kanye kwezilishumi nokuba wenze ntoni, kuba ixabiso eliphakathi lemali yakho lihlala li-$100.
Inzuzo yekhasino ithatha i-2.70% yayo yonke ibheji, ngoko okukhona ubheja kancinci xa kudityanisiwe, kokukhona uhlala kufutshane nenye kwezilishumi. Isicwangciso sesibini sigqiba umcimbi ngeebheji ezimbalwa: i-$100 iba yi-$200, $400, $800, kwaye emva koko i-$200 yanele. Siphumelela malunga ne-9.0% yexesha. Isicwangciso sokuqala sithatha amawaka eebheji ngaphambi kokuba uhambo luphele, kwaye inzuzo yekhasino, encinci kwibheji nganye, idibana ibe kukuphelelwa yimali okuphantse kuqinisekile.
Lesi sisiphumo se-Dubins–Savage kwindlela yaso elula (Epstein, 2013): kumdlalo othanda ikhasino, bheja kangangoko kufuneka, izihlandlo ezimbalwa kangangoko unako.
Une-$500 kwaye ufuna i-$1,000, umisa kwangoko xa unayo. Ukhetha uhlobo olunye lwebheji kwaye uyiphinde de iphumelele kanye okanye imali iphele. Loluphi uhlobo olunika elona thuba lingcono?
Bonisa isisombululo
Impendulo Ibheji enye ye-$500 kobomvu: 48.6%. Sonke isicwangciso esisasaza imali kwiibheji ezincinci senza kubi ngakumbi.
Khetha isixa sebheji ngasinye ukuze impumelelo enye yanele: i-$30 kwinani elinyeibhejiInani elinyeInani elinye, ihlawula u-35:1.Funda yonke → izuza i-$1,050, i-$60 kumanani amabiniibhejiAmanani amabiniAmanani amabini angabamelwane, ihlawula u-17:1.Funda yonke → izuza i-$1,020, njalo njalo. Emva koko bala ithuba lokuba ubuncinane ibheji enye iphumelele ngaphambi kokuba imali iphele. Iibheji ezilishumi elinesithandathu ze-$30 zenani elinye zonke ziyaphosa ngethuba (36/37)¹⁶ = 64.5%, ngoko zifikelela kwi-$1,000 kwi-35.5% yexesha.
Itheyibhile ibonisa ibheji nganye. Obomvu wenza ngcono kuba ufika apho ngebheji enye, ngoko inzuzo yekhasino ihlawulwa kanye, kwi-$500. Imiqolo emibiniibhejiImiqolo emibiniAmanani amathandathu kwimiqolo emibini engabamelwane, ihlawula u-5:1. NgesiFrentshi: sixain.Funda yonke → iza kwindawo yesibini kuba ifuna ezintathu kuphela. Ibheji enye yedaziniibhejiIdazini1–12, 13–24 okanye 25–36, ihlawula u-2:1.Funda yonke → yeyona imbi, ithuba le-12/37; nokuba idlalwa ngeeyunithiimaliIyunithiIbheji esisiseko esetyenziswa yinkqubo okanye ngumdlali. Ukunyuswa kweebheji kuchazwa ngeeyunithi ukuze kusebenze kuyo nayiphi na itafile.Funda yonke → ze-$250 de ube ne-$1,000 nangaphezulu, idazini ifika apho kuphela kwi-46.4% yexesha.
U-Bollman (2024) wakha itheyibhile efanayo yevili laseMelika. Umqolo wakhe wedazini unempazamo: kufuneka ufundeke u-12/38 = 31.6%.
ibhejiisixa sebheji × inani leebhejiithuba lokufikelela kwi-$1,000
Inani elinye$30 × 1635.5%
Amanani amabini$60 × 835.9%
Umqolo$90 × 534.5%
Ikona$125 × 436.7%
Imiqolo emibini$166, $166, $16841.2%
Idazini$500 × 132.4%
Obomvu$500 × 148.6%
Ubheja iyunithi enye kobomvu, umjikelo emva komjikelo, ngemali yokudlalaimaliImali yokudlalaIsixa esipheleleyo esibekelwe ukudlala. Ulawulo lwemali yokudlala kukugqiba ukuba ingakanani kuyo oyibeka emngciphekweni kwibheji nganye nakwiseshoni nganye.Funda yonke → engaze iphele. Emva komjikelo wokuqala uphambili ngeyunithi enye okanye usemva ngeyunithi enye. Lithini ithuba lokuba uya kuphinda ulingane ngqo?
Bonisa isisombululo
Impendulo Ama-36 kwangama-37, 97.3%. Kwivili laseMelika ngama-36 kwangama-38, 94.7%.
Ukuba umjikelo wokuqala uyaphumelela (izihlandlo ezili-18 kwezingama-37), uphambili ngeyunithi enye, kwaye inzuzo yekhasino itsala yonke iseshoni engapheliyo ezantsi, ngoko kungekudala uya kuphinda udlule ekulinganeni: oko kuqinisekile. Ukuba uyalahlekelwa (izihlandlo ezili-19 kwezingama-37), kufuneka unyuke ngeyunithi enye, kwaye ithuba lokuba phambili ngeyunithi enye ngu-18/19 (jonga itheyibhile engentla).
Kunye: 18/37 + 19/37 × 18/19 = 18/37 + 18/37 = 36/37.
Ngokubanzi ithuba ngu-1 thabatha umahluko phakathi kwamathuba okuphumelela nokulahlekelwa kumjikelo: 1 − 1/37 kwivili laseYurophu, 1 − 2/38 kwelaseMelika. Kumdlalo ongenalo iqandaiviliIqandaIsikhewu esinye esiluhlaza esingagubungelwa yibheji yemali elinganayo, yedazini okanye yekholamu; umthombo wenzuzo yekhasino. Kwakhona: iqanda elinye, 0.Funda yonke → umahluko awukho kwaye ithuba ngu-1: amanqaku ahlala ebuyela ekulinganeni. U-Epstein (2013) unika umthetho jikelele.
Iphazili ka-Pascal yowe-1656: abadlali ababini baphosa iidayisi ezintathu, ngamnye eqala ngeekhawuntara ezili-12. Yonke i-11 isa ikhawuntara kumdlali wokuqala, yonke i-14 isa enye kowesibini; ezinye iziphoso azibalwa. Kunokwenzeka kangakanani ukuba umdlali wokuqala aphumelele zonke ezingama-24? Kwaye ukuba endaweni yoko ubheja iyunithi e-1 kobomvu kumjikelo ngamnye ngokuchasene nomhlobo osebenza njengebhanki, iiyunithi ezili-12 umntu ngamnye, kunokwenzeka kangakanani ukuba uphumelele zonke ezingama-24?
Bonisa isisombululo
Impendulo Umdlali wokuqala uphumelela malunga nezihlandlo ezi-1,157 kwi-1,158. Wena, kobomvu, uphumelela zonke iiyunithi ezingama-24 malunga ne-34% yexesha kuphela.
Iidayisi ezintathu zenza i-11 ngeendlela ezingama-27 kunye ne-14 ngeendlela ezili-15, ngoko ikhawuntara nganye ehambayo iya kumdlali wokuqala izihlandlo ezingama-27 kwezingama-42, izihlandlo ezi-9 kwezili-14. Icala ngalinye liqala ngezili-12, ithuba lokuthatha yonke into ngu-1/(1 + r¹²), apho u-r engumlinganiselo wethuba lelinye icala kwelakho.
Kumdlali wokuqala u-r = 5/9, kwaye (5/9)¹² ≈ 0.00086, ngoko ithuba limalunga no-0.99914: ii-odds zika-9¹² ku-5¹², okanye u-282,429,536,481 ku-244,140,625, malunga ne-1,157 ku-1. U-Huygens washicilela kanye loo manani ngowe-1657.
Kobomvu, u-r = 19/18 ngenxa yeqanda, kwaye (19/18)¹² ≈ 1.913: ithuba lakho ngu-1/2.913 ≈ 34.3%. Ingqekembe ibinganika i-50%. Inzuzo yekhasino eyi-2.70% kwibheji nganye idibana, kwiibheji ezininzi ezifunekayo, ibe ngumahluko wamanqaku ali-16.

Uncumo

$Ukudlala ngesibindi kungoyena mkhwa ulungileyo. Kwakhona kuphela ngokukhawuleza.$

Ukudlala ngesibindi kungoyena mkhwa ulungileyo. Kwakhona kuphela ngokukhawuleza.

Imithombo

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, uhlelo lwesi-3, 1968. Gambler’s ruin, isahluko XIV.
Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed. Academic Press, 2013.
Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021.
Carcavi, P. de. Ileta eya kuHuygens, 28 Septemba 1656, ngengxaki uPascal awayinika uFermat. Œuvres complètes de Christiaan Huygens, vol. 1, 1888, pp. 492–494.
Huygens, C. De Ratiociniis in Ludo Aleae. 1657. Eyona ngxoxo yokuqala eprintiweyo ngexabiso elilindelekileyo.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Isahluko 13, i-roulette.
Reuters. “Briton bets it all on roulette spin, and wins.” Epreli 2004.
Las Vegas Sun. “Man wagers life’s worth.” 12 Epreli 2004.

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