Tibalo te-roulette · Kusetjentiswa · emaminithi 8

I-Kelly criterion ne-roulette

Umtsetfo wa-Kelly utjela umbheji lonenzuzo kutsi abheje malini. Ku-roulette unika imphendvulo lecacile: lutfo.

Imphendvulo lemfisha

Linani la-Kelly = inzuzo / ematfuba. Nangabe inzuzo ingaphansi kwelicandza, ifomula ibuyisa incenye lengaphansi kwelicandza, lokusho kutsi ungabheji. Lomtsetfo usewusito ekucondzeni kutsi kungani badlali labebasebentisa emasondvo lachemile babheja ngendlela lababheja ngayo, nekutsi kungani bonkhe labanye kufanele babheje ngekwesabelomali.

incenye ya-Kelly

f* = (bp − q) / b

kulokubovu

(1 × 18/37 − 19/37) / 1 = −1/37

kuchazwa

ungabheji lutfo

emgodzini we-1/30

≈ +0.6% wemali yekubheja

Umtsetfo

John Kelly (1956) wabuta kutsi umgembuli lonenzuzo leyaziwako kufanele abheje malini kute akhulise imali yekubhejaimaliImali yekubhejaImali yonkhe lebekelwe kudlala. Kuphatsa imali yekubheja kusho kunquma kutsi ungafaka engcupheni lengakanani kuko kubheja ngakunye nakuyo iseshini ngayinye.Fundza konkhe → kakhulu esikhatsini lesidze. Imphendvulo, ekubhejeni lokukhokha b ku-1 nelitfubatibaloLitfubaLitfuba lekutsi umphumela wenteke, kusukela ku-0 kuya ku-1 noma ku-0% kuya ku-100%. Inombolo yinye: 1/37 = 2.70%.Fundza konkhe → lekuwina p kanye nelitfuba lekulahlekelwa q = 1 − p, kubheja incenye f* = (bp − q) / b yemali yekubheja. Nangabe f* ingetulu kwelicandza, bheja leyo ncenye; nangabe ingulicandza nobe ingaphansi kwalo, ungabheji. Kelly abesebenta e-Bell Labs, futsi liphepha lakhe, “A new interpretation of information rate”, labeka lenkinga embonweni wetekwatiswa wa-Claude Shannon: umgembuli lotfola emaseluleko ngelucingo lolunemsindvo, ngematfuba lalungile, angakhulisa imali yakhe yekubheja kuphela ngesivinini lucingo loluletsa ngaso lwati. Nga-1961 Leo Breiman wafakazela kutsi kubheja nga-Kelly, esikhatsini lesidze, kugcina kuphambili kwanobe nguliphi lisu lelehlukile futsi kufinyelela umgomo lobekiwe cishe ngesikhatsi lesifishane kakhulu.

Umgembuli uva emaseluleko ngelucingo lolunemsindvo futsi ubheja incenye yemali yakhe yekubheja.

Kubheja nga-Kelly ku-roulette

Ku-lokubovukubhejaBovuKubheja lokulingana nemali etinombolweni letingu-18 letibovu. NgesiFulentji: rouge.Fundza konkhe →: b = 1, p = 18/37, q = 19/37; f* = (18/37 − 19/37)/1 = −1/37. Ku-straight upkubhejaI-straight upInombolo yinye, kukhokha 35:1.Fundza konkhe →: b = 35, p = 1/37, q = 36/37; f* = (35/37 − 36/37)/35 = −1/1295. Konkhe kubheja lokujwayelekile kunika incenye ya-Kelly lengaphansi kwelicandza, ngobe konkhe kubheja kunenzuzo lengaphansi kwelicandza, futsi linani lelikhulisa kakhulu ngulicandza. Kubheja nga-Kelly ku-roulette yindlela yesayensi yekusho loko lokushiwo likhasi lenzuzo yelikhasino: alikho linani kubheja lokunalokulindzelekile lokungaphansi kwelicandza lokukhulisa ngalo imali yekubheja.

kubhejabpf* = (bp − q)/blokushiwo

lokubovu, yaseYurophu118/37−0.027ungabheji

lokubovu, i-la partage118/37 (+½ elicandzeni)−0.0135ungabheji

i-straight up351/37−0.00077ungabheji

i-straight up emgodzini we-1/30 (lochemile)351/30+0.0057bheja 0.57% wemali yekubheja

i-straight up emgodzini we-1/25351/25+0.0126bheja 1.26% wemali yekubheja

Lapho Kelly abesebenta khona

Badlali labebasebentisa kuchema kwelisondvo bebanenzuzo kanye nenkinga yelinani. Jagger, labakaGarcía-Pelayo kanye nema-Eudaemons bonkhe kwadzingeka bancume kutsi babheje malini kulenzuzo yabo lebeyilinganisiwe, futsi kubheja lokuncane kakhulu kumosha inzuzo kantsi kubheja lokukhulu kakhulu kubeka engotini yekuphelelwa yimali ngaphambi kwekutsi inzuzo ivele. EmgodzinitinsitaUmgodziLesinye setikhala letingu-37 letinetinombolo ku-rotor. Kuphindze kutsiwe: slot, cup.Fundza konkhe → lophuma 1 ku-30, Kelly utsi 0.57% wemali yekubheja ekujikeleteni ngakunye kuleyo nombolo: nga-$10,000, cishe $57 ekujikeleteni, nekukhula lokujwayelekile lokucishe kube ngu-0.054% ekujikeleteni ngakunye, nobe ×1.7 ekujikeleteni lokungu-1,000. Inzuzo ngesilinganiso iphindvwe kabili kunaleyo, 0.11% ekujikeleteni, kodvwa Kelly uhlose imali yekubheja lejwayelekile, hhayi leyesilinganiso, lekhushulwa luchungechunge lolumbalwa lwenhlanhla. Hafu ya-Kelly kukhetsa lokuvamile ngobe kulinganiselwa kwenzuzo akucinisekile.

Linani la-Kelly njenga-% wemali yekubheja ku-straight up, ngekuphuma kwemgodzi kwangempela%

1/37 (lelungile)

0% · ungabheji

1/35

0.08%

1/33

0.26%

1/30

0.57%

1/25

1.26%

1/20

2.0%

012.0%

Nanoma kuchema lokukhulu kudzinga emanani lamancane: inkhokhelo inkhulu futsi kugucugucuka kukhulu.

Badlali be-roulette labadvumile Ema-Eudaemons

Lokujwayelekile nesilinganiso

Umehluko emkhatsini wemali yekubheja lejwayelekile naleyesilinganiso mkhulu. Tsatsa umgodzi lophuma 1 ku-25, inzuzo ya-44%, sibalo Thorp lasinika lisu lakhe. Kelly ubheja 1.26% wemali yekubheja kuwo. Ngemuva kwekujikeleta lokungu-1,000 imali yekubheja lejwayelekile ikhule cishe kayi-11.5, kantsi silinganiso, lesikhushulwe luchungechunge lolumbalwa lwenhlanhla lenkhulu, sikhule cishe kayi-249. Kubheja ngetulu kwa-Kelly kukhuphula silinganiso futsi kwehlisa umphumela lojwayelekile: nangabe ubheja kabili linani la-Kelly imali yekubheja lejwayelekile iphindvwa kabili kuphela, futsi nangabe ubheja kabili nencenye linani la-Kelly iyancipha, nanoma konkhe kubheja kusenenzuzo ya-44%. Kubheja lokuncane akubiti kakhulu: hafu yelinani igcina cishe tincenye letintsatfu kulokune tekukhula.

linani, incenye ya-Kellylinani, % wemali yekubhejaimali yekubheja lejwayelekile ngemuva kwekujikeleta lokungu-1,000

½0.63%× 6.7

11.26%× 11.5

1½1.89%× 7.4

22.51%× 2.2

2½3.14%× 0.38

33.77%× 0.04

Umgodzi munye lophuma 1 ku-25, lokhokhwa 35 ku-1. Lokujwayelekile kusho i-median, e lephakanyiswe ku-1,000 kuphindvwe kukhula ekujikeleteni ngakunye.

Nangabe inzuzo kucagela

Kelly ucabanga kutsi inzuzo iyaziwa. Etafuleni iyalinganiselwa, futsi kulinganiselwa kanyenti kungetulu kakhulu. Sibonelo sa-Epstein, lesakhelwe ku-44% wa-Thorp, yinombolo leyaphuma kayi-49 ekujikeleteni lokungu-1,225 kwelisondvo lelinelicandzalisondvoLicandzaUmgodzi munye loluhlata longambonjwa kubheja lokulingana nemali, kwelidazini noma kwelikholamu; umtfombo wenzuzo yelikhasino. Kuphindze kutsiwe: licandza linye, 0.Fundza konkhe → lelikabili: 1 ku-25, inzuzo ya-44%, linani la-Kelly la-1.26%. Kodvwa lisondvo lelingachemile lelinelicandza lelikabili linetinombolo letingu-38, futsi lena lephuma kakhulu kuto ifinyelela ku-49 nobe ngetulu ekujikeleteni lokungu-1,225 cishe kanye kulokuyimfica. Inombolo lephuma kakhulu kunobe nguyiphi irekhodi futsi yileyo lesitwe kakhulu yinhlanhla, ngako nanoma umgodzi lochemile ngempela ubukeka uncono erekhodini kunalokuyiwo: sicalekiso semnqobi. Nangabe lowo mgodzi empeleni ungachemile, linani la-Kelly limane libe kubheja lokulahlekelwa 5.26% ngesilinganiso. Timphendvulo letivamile kubheja incenye ya-Kelly nekuchubeka ubala kuze inzuzo isinde erekhodini lelisha (buka “Kutfola kanjani kuchema kwelisondvo le-roulette”).

Bantfu labanenzuzo

Kwati inzuzo akufani nekuyisebentisa kahle. Haghani na-Dewey (2016) banika bantfu labangu-61 $25 ngamunye kute babheje sikhatsi lesingangehafu yelihora kuluhlavu lwemali labatjelwa kutsi luphuma ngelikhanda ku-60% wetikhatsi, nemali lewinwako lebeyinemkhawulo wa-$250 (badlali bebati ngemkhawulo kuphela nabawufinyelela). Kelly utsi bheja 20% wemali yekubheja elikhanda njalo, futsi babhali balinganisela kutsi kubheja lokungagucuki kwa-10–20% bekungafinyelela emkhawulweni cishe ku-95% wetikhatsi. Ngu-21% kuphela wabadlali lowafika lapho. Bangu-28% labaphelelwa yimali, labangu-18 kulabangu-61 babheja konkhe ekuphonseni kunye, cishe incenye yinye kulokutsatfu yacedza ingaphansi kwa-$25 lebebacale ngayo, futsi inkhokheloimaliInkhokheloLoko lokubuyiswa kubheja lokuwinile, lokushiwo ngekutsi “X ku-1” ngetulu kwelinani lelibhejiwe lelibuyiswako.Fundza konkhe → ngesilinganiso yaba ngu-$91. Ngulabasihlanu kuphela kulabangu-61 lebebake beva ngemtsetfo wa-Kelly. Nakukhona inzuzo, linani lekubheja lincuma kutsi uyayigcina yini; ngaphandle kwayo, njengasesondvweni lelingachemile, akukho linani lelisitako.

Umdlali munye ubheja konkhe ekuphonseni kunye kantsi makhelwane wakhe ubheja incenye lencane.

Lokufanele ukusebentise esikhundleni salokho

Ngaphandle kwenzuzo, linani lekubheja ngumbuto wesabelomali, hhayi wekukhula: linani lelibhejwako = loko lofuna kukusebentisa ekujikeleteni ngakunye, lokususelwa esabelomalini selihora nasesivinini setafula (likhasi lekulawula imali yekubheja). Lokwengetwa nguKelly kumdlali lojwayelekile kucaca kwemphendvulo yakhe: licandza. Konkhe lokubheja ngetulu kwelicandza yintsengo yekudlala, loyikhetsako wena, lengakhetfwanga yinobe nguyiphi ifomula.

Lokwatiswa nge-fractional Kelly kanye “nekulawula imali”

Tinhlelo letitsengiswa njenga-“Kelly ye-roulette” letincoma liphesenti lelingagucuki lemali yekubheja ekubhejeni ngakunye kubheja ngelinani linyelisuKubheja ngelinani linyeKubheja linani lelifanako kuko konkhe kujikeleta. Lizinga lesisekelo lekucatsaniswa nalo konkhe kwenyuswa kwelinani.Fundza konkhe → nelinani lelinciphako. Tilahlekelwa 2.70% wemali yonkhe lebhejiweimaliImali yonkhe lebhejiweLinani lonkhe lelibhejwe ngesikhatsi seseshini noma ngesikhatsi lesitsite, kubalwa nemali lewiniwe lephindze yabhejwa. Kuphindze kutsiwe: handle, action.Fundza konkhe → futsi, ngobe linani liyancipha njengoba ulahlekelwa, tenta kuphelelwa yimali kwenteke kancane kunekutsi kungenteki. Kuyindlela lenengcondvo yekwenta sabelomali sihlale sikhatsi lesidze; akusiko Kelly, lobekangatsi yima.

Lisu lekubheja ngelinani linye ku-roulette

Lifomula

f* = (b·p − q) / b

lokubovu: f* = −1/37 · i-straight up: f* = −1/1295

umgodzi lochemile ngesilinganiso r: f* = (35r − (1 − r)) / 35

Imibuto

Kelly uke atsi bheja ku-roulette yini?

Kuphela nakukhona inzuzo lelinganisiwe yelisondvo lelichemilelilabhorethriLisondvo lelichemileLisondvo lapho tici talo temtimba tenta leminye imigodzi ibe nematfuba langetulu kwa-1/37. Kuyindlalane, kutfolakala kuphela ngekujikeleta lokutinkhulungwane lokubhaliwe.Fundza konkhe → nobe yesikhiciti sekubala sikhatsi. Hhayi esondvweni lelingachemile.

Kungani hafu ya-Kelly?

Ngobe kulinganiselwa kwenzuzo kunemaphutsa, futsi kubheja lokukhulu kakhulu kubita kakhulu kunekubheja lokuncane kakhulu. Hafu ya-Kelly inika tincenye letintsatfu kulokune tekukhula ngencenye yinye kulokune yekugucugucukatibaloKugucugucukaSilinganiso sekutsi imiphumela isabalele kangakanani etungeleta linani lelilindzelekile. Kukhulu ku-straight up, kuncane ekubhejeni lokulingana nemali.Fundza konkhe →.

Kelly uyafana yini nekulawula imali yekubheja?

Cha. Kelly ukhulisa kukhula nangabe kukhona inzuzo. Kulawula imali yekubheja kulawula kusebentisa imali nangabe ingekho.

Bumnandi betibalo

Zama loku ngekwakho kucala. Sixazululo ngasinye sifihliwe; sivule nawukulungele.

Sisetjentiswa sekubikezela sa-Thorp na-Shannon besinika inzuzo lecishe ibe ngu-44%. Enombolweni yinye lebikezelwe, Kelly utsi bheja 1.26% wemali yekubhejaimaliImali yekubhejaImali yonkhe lebekelwe kudlala. Kuphatsa imali yekubheja kusho kunquma kutsi ungafaka engcupheni lengakanani kuko kubheja ngakunye nakuyo iseshini ngayinye.Fundza konkhe →. Kutawentekani nangabe lenzuzo lefanako ya-44% ifika ngekubheja kunye lokuhlakatwe etinombolweni letisihlanu letakhelene?
Khombisa sixazululo
Imphendvulo Kelly ngako-ke utsi 7.1% wemali yekubheja, futsi imali yekubheja ikhula cishe ngekushesha lokuphindvwe kasitfupha: cishe tikhatsi letingu-1.25 wetigidzi ekubhejeni lokungu-1,000, ngekucatsaniswa nalokucishe kube tikhatsi letingu-11.5.
I-straight upkubhejaI-straight upInombolo yinye, kukhokha 35:1.Fundza konkhe → lenenzuzo ya-44% iwina ngelitfuba la-0.04, ngobe 36 × 0.04 = 1.44. Linani la-Kelly lelibhejwako yinzuzo lehlukaniswe ngematfuba enkhokhelo: 0.44/35 = 1.26%. Kukhula lokujwayelekile ngekubheja ngu-0.04 × ln(1 + 35 × 0.0126) + 0.96 × ln(1 − 0.0126) ≈ 0.00244, ngako kubheja lokungu-1,000 kuphindzaphindza imali yekubheja ngalokucishe kube ngu-e^2.44 ≈ 11.5.
Hlakata linani linye lelibhejwako etinombolweni letisihlanu bese kubheja kuwina ngelitfuba la-0.20 futsi kukhokha 36/5 nga-1, lokungu-6.2 ku-1: kusenenzuzo ya-44%, ngobe 0.2 × 7.2 = 1.44. Linani la-Kelly liba ngu-0.44/6.2 = 7.10%, kantsi kukhula ngekubheja kuba ngu-0.01404, cishe kuphindvwe tikhatsi letingu-5.75. Ekubhejeni lokungu-1,000 loko ngu-e^14.04, cishe tigidzi letingu-1.25.
Inzuzo iyafana; kugucugucuka kuncane. Kubheja lokuwina kanye kulokusihlanu kungatsatsa ingcenye lenkhulu yemali yekubheja ngaphandle kwekufaka engotini yekuphelelwa yimali, futsi kukhula kwa-Kelly kuyakuklomelisa loko. Thorp (1984) usebentisa lesibonelo kukhombisa kutsi kungani badlali bekubikezela babheja tigabalisondvoSigabaIngcenye lelandzelanako yemigodzi elisondvweni, lehlukile kulicembu letinombolo elithebuleni lekubheja.Fundza konkhe →. Ngalokwentekako bomakhelwanekubhejaBomakhelwaneInombolo kanye nemigodzi lemibili ngetinhlangotsi tonkhe letimbili elisondvweni, emathokheni lasihlanu e-straight up.Fundza konkhe → lababisihlanu banenzuzo lephansana kunenombolo yinye lencono kakhulu (buka i-Advantage Play).
Umdlali utfole imigodzitinsitaUmgodziLesinye setikhala letingu-37 letinetinombolo ku-rotor. Kuphindze kutsiwe: slot, cup.Fundza konkhe → lemibili leyakhelene, ngamunye wayo uphuma 1 ku-25 esikhundleni sa-1 ku-37. Kufanele abheje i-splitkubhejaI-splitTinombolo letimbili leyakhelene, kukhokha 17:1.Fundza konkhe → emkhatsini wayo nga-17 ku-1, nobe inombolo ngayinye ngekwe-straight up? Kelly utsi malini, futsi imali yekubheja ikhula ngekushesha lokungakanani ngekucatsaniswa nemgodzi munye lonjalo?
Khombisa sixazululo
Imphendvulo Akwenti mehluko: 2.59% wemali yekubheja ku-split, nobe 1.29% enombolweni ngayinye. Imali yekubheja lejwayelekile ikhula cishe tikhatsi letingu-155 ekujikeleteni lokungu-1,000, ngekucatsaniswa netikhatsi letingu-11.5 nemgodzi munye.
I-split iwina ngelitfubatibaloLitfubaLitfuba lekutsi umphumela wenteke, kusukela ku-0 kuya ku-1 noma ku-0% kuya ku-100%. Inombolo yinye: 1/37 = 2.70%.Fundza konkhe → la-2/25 = 0.08 futsi ikhokha 17 ku-1, ngako ibuyisa 18 × 0.08 = 1.44 liyunithiimaliLiyunithiLinani lelibhejwako lelisisekelo luhlelo noma umdlali lasebenta ngalo. Kwenyuswa kwelinani kuchazwa ngemayunithi kute kusebente kunoma ngumuphi litafula.Fundza konkhe → ngalinye lelibhejwako: inzuzo ya-44%, lefanana nemgodzi munye lochemile. Linani la-Kelly yinzuzo lehlukaniswe ngematfuba enkhokhelo: 0.44/17 = 2.59%.
Kubheja lokubili kwe-straight up kwa-1.29% ngamunye kunika imiphumela lefanako ncamashi. Nangabe nobe nguyiphi inombolo iphuma, lithokheniimaliLithokheniLuphawu lolumele linani lelingagucuki, lolubekwa kulithebula lekubheja kute ubheje. Lelinye ligama: check.Fundza konkhe → linye liwina 35 ku-1 kantsi lelinye liyalahleka, inzuzo lehlantekile ya-34 × 1.29% = 44% wemali yekubheja, njengoba i-split ikhokha; nangabe kute leyiphumako, womabili ayalahleka.
Kukhula ngekujikeleta ngu-0.00505, ngekucatsaniswa na-0.00244 kwemgodzi munye, ngako ekujikeleteni lokungu-1,000 imali yekubheja lejwayelekile ikhula tikhatsi letingu-e^5.046 ≈ 155 esikhundleni setikhatsi letingu-e^2.44 ≈ 11.5. Tinombolo letimbili letinhle tinelinani lelikhulu kakhulu kunekuphindvwa kabili kwayinye, yingako badlali bekuchema babheja emacembu etinombolo. Thorp (1984) wenta kucatsanisa lokufanako.

Lokuhlekisako

$Linani le-roulette lelikhulisa kakhulu yinombolo lesevele yatiwa ngulowo nalowo.$

Linani le-roulette lelikhulisa kakhulu yinombolo lesevele yatiwa ngulowo nalowo.

Imitfombo

Kelly, J. L. “A new interpretation of information rate.” Bell System Technical Journal 35(4), 1956.
Breiman, L. “Optimal gambling systems for favorable games.” Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, 1961.
Thorp, E. O. “Optimal gambling systems for favorable games.” Review of the International Statistical Institute 37(3), 1969.
Thorp, E. O. The Mathematics of Gambling. Gambling Times / Lyle Stuart, 1984.
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.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Sehluko 13, i-roulette.
Haghani, V. & Dewey, R. “Rational decision-making under uncertainty: observed betting patterns on a biased coin.” Liphepha lemsebenti, Imphala 2016; SSRN 2856963, arXiv:1701.01427.

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