Izibalo ze-roulette · Okusetshenziswayo · imizuzu 8

I-Kelly criterion ne-roulette

I-Kelly criterion itshela umbheji onenzuzo ukuthi kufanele abheje malini. Ku-roulette inikeza impendulo ecacile: lutho.

Impendulo emfushane

Inani elibhejwayo le-Kelly = inzuzo / ama-odds. Uma inzuzo ingaphansi kweqanda, ifomula ibuyisa ingxenye engaphansi kweqanda, okusho ukuthi ungabheji. Le ndlela isewusizo ekuqondeni ukuthi kungani abadlali abasebenzisa ukuchema kwesondo babeka amanani ababewabeka, nokuthi kungani bonke abanye kufanele babeke amanani ngokwesabelomali.

ingxenye ye-Kelly

f* = (bp − q) / b

kokubomvu

(1 × 18/37 − 19/37) / 1 = −1/37

incazelo

ungabheji lutho

egodini elishaya ku-1/30

≈ +0.6% yemali yokubheja

Indlela

U-John Kelly (1956) wabuza ukuthi umgembuli onenzuzo eyaziwayo kufanele abeke amanani amakhulu kangakanani ukuze akhulise kakhulu imali yokubhejaimaliImali yokubhejaInani lonke lemali ebekelwe ukudlala. Ukuphatha imali yokubheja kusho ukunquma ukuthi ingakanani yayo ozoyibeka engcupheni ekubhejeni ngakunye nasesheshini ngayinye.Funda konke → esikhathini eside. Impendulo, ekubhejeni okukhokha u-b ku-1 namathubaizibaloAmathubaIthuba lomphumela, kusukela ku-0 kuya ku-1 noma ku-0% kuya ku-100%. Inombolo eyodwa: 1/37 = 2.70%.Funda konke → okuwina angu-p namathuba okuhlulwa angu-q = 1 − p, ukubheja ingxenye f* = (bp − q) / b yemali yokubheja. Uma u-f* engaphezu kweqanda, bheja leyo ngxenye; uma eyiqanda noma engaphansi kwalo, ungabheji. U-Kelly wayesebenza e-Bell Labs, futhi iphepha lakhe, “A new interpretation of information rate”, labeka le nkinga emcabangweni ka-Claude Shannon wolwazi: umgembuli othola amathiphu ngolayini onomsindo, ngama-odds afanele, angakhulisa imali yakhe yokubheja ngesivinini esingeqi lesho ulayini odlulisa ngaso ulwazi. Ngo-1961 u-Leo Breiman wafakazela ukuthi ukubheja nge-Kelly, esikhathini eside, kugcina kuphambili kunanoma yiliphi elinye isu elihluke ngokuyisisekelo, futhi kufinyelela umgomo obekiwe cishe ngesikhathi esifushane kakhulu.

Umgembuli uzwa amathiphu ngolayini onomsindo bese ebheja ingxenye yemali yakhe yokubheja.

Ukubheja nge-Kelly ku-roulette

Ekubhejeni kokubomvuukubhejaBomvuUkubheja okulingana nemali ezinombolweni eziyi-18 ezibomvu. NgesiFulentshi: rouge.Funda konke →: b = 1, p = 18/37, q = 19/37; f* = (18/37 − 19/37)/1 = −1/37. Ku-straight upukubhejaI-straight upInombolo eyodwa, kukhokha u-35:1.Funda konke → (ukubheja enombolweni eyodwa): b = 35, p = 1/37, q = 36/37; f* = (35/37 − 36/37)/35 = −1/1295. Konke ukubheja okujwayelekile kunikeza ingxenye ye-Kelly engaphansi kweqanda, ngoba konke ukubheja kunenzuzo engaphansi kweqanda, futhi inani elibhejwayo elikhulisa kakhulu liyiqanda. Ukubheja nge-Kelly ku-roulette kuyindlela yezibalo yokusho lokho okushiwo yikhasi lenzuzo yekhasino: alikho inani elibhejwayo lapho ukubheja okunenani elilindelekile elingaphansi kweqanda kukhulisa imali yokubheja.

ukubhejabpf* = (bp − q)/bincazelo

okubomvu, yaseYurophu118/37−0.027ungabheji

okubomvu, i-la partage118/37 (+½ eqandeni)−0.0135ungabheji

i-straight up351/37−0.00077ungabheji

i-straight up egodini elishaya ku-1/30 (isondo elichemile)351/30+0.0057bheja u-0.57% wemali yokubheja

i-straight up egodini elishaya ku-1/25351/25+0.0126bheja u-1.26% wemali yokubheja

Lapho i-Kelly yayisebenza khona

Abadlali abasebenzisa ukuchema kwesondo babenenzuzo kanye nenkinga yokukhetha amanani. U-Jagger, umndeni wakwa-García-Pelayo nama-Eudaemons bonke kwakudingeka banqume ukuthi babheje malini enzuzweni yabo abayilinganisile, futhi ukubheja okuncane kakhulu kumosha inzuzo kanti ukubheja okukhulu kakhulu kubeka engozini yokuphelelwa yimali ngaphambi kokuthi inzuzo ibonakale. EgodiniokokusebenzaIgodiEsinye sezikhala ezingu-37 ezinezinombolo ku-rotor. Kubuye kuthiwe: slot, cup.Funda konke → elishaya kanye kokungu-30, i-Kelly ithi u-0.57% wemali yokubheja ngokujikeleza ngakunye kuleyo nombolo: uma une-$10,000, cishe u-$57 ngokujikeleza, ngokukhula okuvamile okucishe kube ngu-0.054% ngokujikeleza, noma ×1.7 ngokujikeleza okungu-1,000. Inzuzo emaphakathi iphindwe kabili kulokho, u-0.11% ngokujikeleza, kodwa i-Kelly ihlose imali yokubheja evamile, hhayi emaphakathi, ekhuliswa wuchungechunge olumbalwa lwenhlanhla. I-Half-Kelly iyisinqumo esivamile ngoba isilinganiso senzuzo asiqinisekile.

Inani elibhejwayo le-Kelly njengo-% wemali yokubheja ku-straight up, ngezinga leqiniso legodi%

1/37 (isondo elifanele)

0% · ungabheji

1/35

0.08%

1/33

0.26%

1/30

0.57%

1/25

1.26%

1/20

2.0%

012.0%

Ngisho nokuchema okukhulu kudinga amanani amancane: inkokhelo inde futhi ukuguquguquka kuphezulu.

Abadlali be-roulette abadumile Ama-Eudaemons

Okuvamile nokumaphakathi

Igebe phakathi kwemali yokubheja evamile nemaphakathi libanzi. Thatha igodi elishaya kanye kokungu-25, inzuzo engu-44%, inani elinikezwa ngu-Thorp ngedivayisi yakhe. I-Kelly ibheja u-1.26% wemali yokubheja kulo. Ngemuva kokujikeleza okungu-1,000 imali yokubheja evamile isikhule cishe izikhathi ezingu-11.5, kanti emaphakathi, ekhuliswe wuchungechunge olumbalwa lwenhlanhla enkulu, isikhule cishe izikhathi ezingu-249. Ukubheja ngaphezu kwe-Kelly kukhuphula isilinganiso futhi kwehlisa umphumela ovamile: uma ubheja kabili inani le-Kelly, imali yokubheja evamile iphindeka kabili kuphela, futhi uma ubheja izikhathi ezimbili nengxenye inani le-Kelly iyancipha, nakuba konke ukubheja kusenenzuzo engu-44%. Ukubheja okuncane akulahlekisi kakhulu: ingxenye yenani igcina cishe izingxenye ezintathu kwezine zokukhula.

inani elibhejwayo, ingxenye ye-Kellyinani elibhejwayo, % wemali yokubhejaimali yokubheja evamile ngemuva kokujikeleza okungu-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

Igodi elilodwa elishaya u-1 kokungu-25, elikhokha u-35 ku-1. Okuvamile kusho i-median (inani elisesiphakathi), u-e ophakanyiselwe emandleni alingana no-1,000 ephindwe ngokukhula ngokujikeleza ngakunye.

Uma inzuzo iwukuqagela

I-Kelly icabanga ukuthi inzuzo iyaziwa. Etafuleni iyalinganiswa, futhi isilinganiso sivamise ukuba siphezulu kakhulu. Isibonelo sika-Epstein, esakhelwe ku-44% ka-Thorp, siyinombolo eyashaya izikhathi ezingu-49 ekujikelezeni okungu-1,225 kwesondo leqandaisondoIqandaIgodi elilodwa eliluhlaza elingambozwa ukubheja okulingana nemali, okwedazini noma okwekholamu; umthombo wenzuzo yekhasino. Kubuye kuthiwe: iqanda elilodwa, 0.Funda konke → eliphindiwe: kanye kokungu-25, inzuzo engu-44%, inani elibhejwayo le-Kelly elingu-1.26%. Kodwa isondo elifanele leqanda eliphindiwe linezinombolo ezingu-38, futhi leyo ematasa kakhulu kuzo ifinyelela ku-49 noma ngaphezulu ekujikelezeni okungu-1,225 cishe kanye kokuyisishiyagalolunye. Inombolo ematasa kakhulu kunoma yiliphi irekhodi yiyo futhi esizwe kakhulu yinhlanhla, ngakho ngisho negodi elichemile ngempela libukeka lingcono erekhodini kunalokho eliyikho: isiqalekiso somnqobi. Uma lelo godi empeleni lingachemile, inani elibhejwayo le-Kelly limane libe ukubheja okulahlekelwa ngu-5.26% ngokwesilinganiso. Izimpendulo ezivamile ukubheja ingxenye ye-Kelly nokuqhubeka nokubala kuze kube yilapho inzuzo isinda erekhodini elisha (bheka Indlela yokuthola ukuchema kwesondo le-roulette).

Abantu abanenzuzo

Ukwazi inzuzo akufani nokuyisebenzisa kahle. U-Haghani no-Dewey (2016) banika abantu abangu-61 u-$25 ngamunye ukuze babheje isigamu sehora ohlamvini lwemali ababetshelwe ukuthi luwela ngekhanda izikhathi ezingu-60%, nemali ewinwayo inqunywe ku-$250 (abadlali bawazi lo mkhawulo kuphela lapho bewufinyelela). I-Kelly ithi bheja u-20% wemali yokubheja ekhanda njalo, futhi ababhali balinganisa ukuthi ukubheja okuzinzile kuka-10–20% kungafinyelela umkhawulo cishe izikhathi ezingu-95%. Ngu-21% kuphela wabadlali owafika lapho. U-28% waphelelwa yimali, abangu-18 kwabangu-61 babheja yonke into ekuphonseni okukodwa, cishe ingxenye eyodwa kwezintathu yaqeda ngaphansi kuka-$25 ababeqale ngawo, futhi inkokheloimaliInkokheloLokho ukubheja okuwinile okubuyisayo, okushiwo ngokuthi “X ku-1” ngaphezu kwenani elibhejiwe elibuyiswayo.Funda konke → emaphakathi yaba ngu-$91. Abahlanu kuphela kwabangu-61 ababeke bezwa nge-Kelly criterion. Uma unenzuzo, ubukhulu bokubheja kwakho bunquma ukuthi uyayigcina yini; uma ungenayo, njengasesondweni elifanele, abukho ubukhulu obusizayo.

Umdlali oyedwa ubheja yonke into ekuphonseni okukodwa, kanti umakhelwane wakhe ubheja ingxenye encane.

Okufanele ukusebenzise esikhundleni salokho

Ngaphandle kwenzuzo, ukukhetha inani kungumbuzo wesabelomali, hhayi wokukhula: inani elibhejwayo = lokho ozimisele ukukusebenzisa ngokujikeleza ngakunye, okuthathwe esabelomalini sehora nasesivinini setafula (ikhasi lokuphatha imali yokubheja). Okunikelwa yi-Kelly kumdlali ojwayelekile ukucaca kwempendulo yayo: iqanda. Konke okubheja ngaphezu kweqanda kuyintengo yokudlala, oyikhetha wena, hhayi elungiswe yinoma iyiphi ifomula.

Inothi nge-fractional Kelly kanye ne-“money management”

Izinhlelo ezithengiswa njenge-“Kelly for roulette” ezincoma iphesenti elinqunyiwe lemali yokubheja ngokubheja ngakunye ziwukubheja ngenani elingashintshiisuUkubheja ngenani elilodwaUkubheja inani elifanayo kukho konke ukujikeleza. Isisekelo okuqhathaniswa naso konke ukwenyuswa kwenani.Funda konke → ngenani elincipha njalo. Zilahlekelwa ngu-2.70% wemali yonke ebhejiweimaliImali yonke ebhejiweInani lonke elibhejwe phakathi neseshini noma esikhathini esithile, kubalwa nemali ewiniwe ephinde yabhejwa. Kubuye kuthiwe: handle, action.Funda konke → futhi, ngoba inani lincipha njengoba uhlulwa, zenza ukuphelelwa yimali kube kancane kunokuba kungenzeki. Kuyindlela enengqondo yokwenza isabelomali sihlale isikhathi eside; akuyona i-Kelly, yona ebingakutshela ukuthi uyeke.

Isu lokubheja inani elingaguquki ku-roulette

Ifomula

f* = (b·p − q) / b

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

igodi elichemile ngezinga r: f* = (35r − (1 − r)) / 35

Imibuzo

Ingabe i-Kelly ike ithi kufanele ubheje ku-roulette?

Kuphela uma kunenzuzo elinganisiwe evela esondweni elichemileilebhuIsondo elichemileIsondo elinamaphutha omzimba enza amanye amagodi abe namathuba angaphezu kuka-1/37. Alivamile, futhi litholakala kuphela ngokujikeleza okuyizinkulungwane okubhaliwe.Funda konke → noma kudivayisi yokubala isikhathi. Hhayi esondweni elifanele.

Kungani i-half-Kelly?

Ngoba isilinganiso senzuzo sinephutha, futhi ukubheja okukhulu kakhulu kubiza kakhulu kunokubheja okuncane kakhulu. I-Half-Kelly inikeza izingxenye ezintathu kwezine zokukhula ngengxenye eyodwa kwezine yokuguquguqukaizibaloUkuguquguqukaIsilinganiso sokuthi imiphumela ihlakazeke kangakanani ezungeze inani elilindelekile. Kuphezulu ku-straight up, kuphansi ekubhejeni okulingana nemali.Funda konke →.

Ingabe i-Kelly iyafana nokuphatha imali yokubheja?

Cha. I-Kelly ikhulisa ukukhula uma kunenzuzo. Ukuphatha imali yokubheja kulawula ukusebenzisa imali uma ingekho.

Ubumnandi bezibalo

Zama lezi ngokwakho kuqala. Isixazululo ngasinye sifihliwe; sivule uma usukulungile.

Idivayisi yokubikezela ka-Thorp no-Shannon yayinikeza inzuzo yomdlali ecishe ibe ngu-44%. Enombolweni eyodwa ebikezelwe, u-Kelly uthi bheja u-1.26% we-mali yokubhejaimaliImali yokubhejaInani lonke lemali ebekelwe ukudlala. Ukuphatha imali yokubheja kusho ukunquma ukuthi ingakanani yayo ozoyibeka engcupheni ekubhejeni ngakunye nasesheshini ngayinye.Funda konke →. Kuthiwani uma inzuzo efanayo engu-44% itholakala ekubhejeni okukodwa okusabalaliswe ezinombolweni ezinhlanu ezingomakhelwane?
Bonisa isixazululo
Impendulo U-Kelly-ke uthi u-7.1% wemali yokubheja, futhi imali yokubheja ikhula ngejubane elicishe liphindwe kasithupha: cishe izikhathi eziyizigidi ezingu-1.25 ekubhejeni okungu-1,000, uma kuqhathaniswa nezikhathi ezingu-11.5.
I-straight upukubhejaI-straight upInombolo eyodwa, kukhokha u-35:1.Funda konke → enenzuzo yomdlali engu-44% iwina ngamathuba angu-0.04, ngoba 36 × 0.04 = 1.44. Inani lokubheja lika-Kelly liyinzuzo ehlukaniswe ngenkokhelo: 0.44/35 = 1.26%. Ukukhula okujwayelekile ekubhejeni ngakunye kungu-0.04 × ln(1 + 35 × 0.0126) + 0.96 × ln(1 − 0.0126) ≈ 0.00244, ngakho ukubheja okungu-1,000 kuphindaphinda imali yokubheja cishe ngo-e^2.44 ≈ 11.5.
Sabalalisa inani elilodwa ezinombolweni ezinhlanu bese ukubheja kuwina ngamathuba angu-0.20 futhi kukhokha 36/5 ngo-1, okungu-6.2 ku-1: kusenenzuzo engu-44%, ngoba 0.2 × 7.2 = 1.44. Inani lika-Kelly liba ngu-0.44/6.2 = 7.10%, bese ukukhula ekubhejeni ngakunye kuba ngu-0.01404, cishe ngokuphindwe ka-5.75. Ekubhejeni okungu-1,000 lokho kungu-e^14.04, cishe izigidi ezingu-1.25.
Inzuzo iyafana; ukuguquguquka kuncane. Ukubheja okuwina kanye kokuhlanu kungathwala ingxenye enkulu yemali yokubheja ngaphandle kokubeka engozini yokuphelelwa yimali, futhi ukukhula kuka-Kelly kuyakuklomelisa lokho. U-Thorp (1984) usebenzisa lesi sibonelo ukubonisa ukuthi kungani abadlali bokubikezela bebheja ezigabeniisondoIsigabaIngxenye eqhubekayo yamagodi alandelanayo esondweni, ehlukile eqenjini lezinombolo ethebuleni lokubheja.Funda konke →. Empeleni omakhelwaneukubhejaOmakhelwaneInombolo kanye namagodi amabili nhlangothi zombili zayo esondweni, amathokheni amahlanu e-straight up.Funda konke → abahlanu banenzuzo encane kancane kunenombolo eyodwa engcono kakhulu (bheka “Ukudlala ngenzuzo yomdlali ku-roulette”).
Umdlali uthole amagodiokokusebenzaIgodiEsinye sezikhala ezingu-37 ezinezinombolo ku-rotor. Kubuye kuthiwe: slot, cup.Funda konke → amabili angomakhelwane, ngalinye liphuma ka-1 kokungu-25 esikhundleni sika-1 kokungu-37. Kufanele abheje i-splitukubhejaI-splitIzinombolo ezimbili ezingomakhelwane, kukhokha u-17:1.Funda konke → phakathi kwawo ngo-17 ku-1, noma inombolo ngayinye i-straight up? U-Kelly uthi malini, futhi imali yokubheja ikhula ngokushesha kangakanani uma kuqhathaniswa negodi elilodwa elinjalo?
Bonisa isixazululo
Impendulo Akwenzi mehluko: u-2.59% wemali yokubheja ku-split, noma u-1.29% enombolweni ngayinye. Imali yokubheja ejwayelekile ikhula cishe izikhathi ezingu-155 ekujikelezeni okungu-1,000, uma kuqhathaniswa nezikhathi ezingu-11.5 ngegodi elilodwa.
I-split iwina ngamathubaizibaloAmathubaIthuba lomphumela, kusukela ku-0 kuya ku-1 noma ku-0% kuya ku-100%. Inombolo eyodwa: 1/37 = 2.70%.Funda konke → angu-2/25 = 0.08 futhi ikhokha 17 ku-1, ngakho ibuyisa u-18 × 0.08 = 1.44 kulo lonke iyunithiimaliIyunithiInani elibhejwayo eliyisisekelo uhlelo noma umdlali asebenza ngalo. Ukwenyuswa kwenani kuchazwa ngamayunithi ukuze kusebenze kunoma yiliphi itafula.Funda konke → elibhejiwe: inzuzo engu-44%, efanayo neyegodi elilodwa elichemile. Inani lika-Kelly liyinzuzo ehlukaniswe ngenkokhelo: 0.44/17 = 2.59%.
Ukubheja okubili kwe-straight up ngo-1.29% ngakunye kunikeza imiphumela efanayo ncamashi. Uma kuphuma noma iyiphi inombolo, ithokheniimaliIthokheniUphawu olumele inani elinqunyiwe, olubekwa ethebuleni lokubheja ukuze ubheje. Kubuye kuthiwe: check.Funda konke → eyodwa iwina 35 ku-1 kuthi enye ilahleke, inzuzo ehlanzekile engu-34 × 1.29% = 44% wemali yokubheja, njengoba kukhokha i-split; uma kungaphumi neyodwa, zombili ziyalahleka.
Ukukhula ekujikelezeni ngakunye kungu-0.00505, uma kuqhathaniswa no-0.00244 wegodi elilodwa, ngakho ekujikelezeni okungu-1,000 imali yokubheja ejwayelekile ikhula izikhathi ezingu-e^5.046 ≈ 155 kunokuba ikhule izikhathi ezingu-e^2.44 ≈ 11.5. Izinombolo ezimbili ezinhle zibaluleke kakhulu kunokuphindwe kabili kweyodwa, yingakho abadlali abasebenzisa ukuchema kwesondo bebheja amaqembu ezinombolo. U-Thorp (1984) wenza ukuqhathanisa okufanayo.

Okokuhlekisa

$Inani elibhejwayo le-roulette elikhulisa kakhulu yinombolo wonke umuntu asevele eyazi.$

Inani elibhejwayo le-roulette elikhulisa kakhulu yinombolo wonke umuntu asevele eyazi.

Imithombo

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, umqulu 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, uhlelo lwesi-2. Academic Press, 2013.
Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, uhlelo lwesi-2. CRC Press, 2021.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Isahluko 13, i-roulette.
Haghani, V. & Dewey, R. “Rational decision-making under uncertainty: observed betting patterns on a biased coin.” Iphepha lomsebenzi, Okthoba 2016; SSRN 2856963, arXiv:1701.01427.

kubuyekezwe ngo-2026-09-28imodeli: yaseYurophu, iqanda elilodwaindlela yokusebenza ↗imithombo ↗