Izibalo ze-roulette · Ukusetyenziswa · imizuzu eyi-8

I-Kelly criterion kunye ne-roulette

I-Kelly criterion ixelela umbheji onenzuzo ukuba makabheje malini. Kwi-roulette inika impendulo ecacileyo: nto.

Impendulo emfutshane

Ibheji ye-Kelly = inzuzo / ii-odds. Ngenzuzo engalunganga ifomula ibuyisa iqhezu elingalunganga, nto leyo ethetha ukuba ungabheji. Le criterion isaluncedo ekuqondeni ukuba kutheni abadlali bokuthambekela babelinganisa iibheji zabo ngendlela abenza ngayo, nokuba kutheni bonke abanye kufuneka balinganise ngohlahlo-lwabiwo-mali.

Iqhezu le-Kelly

f* = (bp − q) / b

kobomvu

(1 × 18/37 − 19/37) / 1 = −1/37

intsingiselo

ungabheji nto

kwisikhewu se-1/30

≈ +0.6% yemali yokudlala

I-criterion

UJohn Kelly (1956) wabuza ukuba umngcakazi onenzuzo eyaziwayo kufuneka alinganise njani iibheji ukuze andise ukukhula kwexesha elide kwemali yokudlalaimaliImali yokudlalaIsixa esipheleleyo esibekelwe ukudlala. Ulawulo lwemali yokudlala kukugqiba ukuba ingakanani kuyo oyibeka emngciphekweni kwibheji nganye nakwiseshoni nganye.Funda yonke →. Impendulo, kwibheji ehlawula u-b ku-1 enamathubaizibaloAmathubaIthuba lesiphumo, ukusuka ku-0 ukuya ku-1 okanye ku-0% ukuya ku-100%. Inani elinye: 1/37 = 2.70%.Funda yonke → okuphumelela angu-p namathuba okulahlekelwa angu-q = 1 − p, kukubheja iqhezu f* = (bp − q) / b lemali yokudlala. U-f* olungileyo uthetha ukuba ubheje elo qhezu; iqanda okanye ongalunganga uthetha ukuba ungabheji. UKelly wayesebenza eBell Labs, kwaye iphepha lakhe, “A new interpretation of information rate”, labeka ingxaki kwithiyori yolwazi kaClaude Shannon: umngcakazi ofumana iingcebiso ngomgca onengxolo, nge-odds ezifanelekileyo, unokwandisa imali yokudlala ubuninzi ngesantya umgca othwala ngaso ulwazi. Ngo-1961 uLeo Breiman wangqina ukuba ukubheja nge-Kelly, ngexesha elide, kuphela kuphambili kwaso nasiphi na isicwangciso esahlukileyo ngokusisiseko kwaye kufikelela kwinjongo emiselweyo malunga nexesha elifutshane kakhulu.

Umngcakazi uva iingcebiso ngomgca onengxolo kwaye abheje inxalenye yemali yakhe yokudlala.

Ukubheja nge-Kelly kwi-roulette

Kwi-bomvuibhejiObomvuIbheji yemali elinganayo kumanani ali-18 abomvu. NgesiFrentshi: rouge.Funda yonke →: b = 1, p = 18/37, q = 19/37; f* = (18/37 − 19/37)/1 = −1/37. Kwi-bheji yenani elinyeibhejiInani elinyeInani elinye, ihlawula u-35:1.Funda yonke →: b = 35, p = 1/37, q = 36/37; f* = (35/37 − 36/37)/35 = −1/1295. Yonke ibheji eqhelekileyo inika iqhezu le-Kelly elingalunganga, kuba yonke ibheji inenzuzo engalunganga, kwaye ibheji efanelekileyo yokukhula liqanda. Ukubheja nge-Kelly kwi-roulette yindlela esesikweni yokuthetha oko kuthethwa liphepha lenzuzo yekhasino: akukho bukhulu apho ibheji enokulindelekileyo okungalunganga ikhulisa imali yokudlala.

ibhejibpf* = (bp − q)/bintsingiselo

obomvu, yaseYurophu118/37−0.027ungabheji

obomvu, la partage118/37 (+½ kwiqanda)−0.0135ungabheji

inani elinye351/37−0.00077ungabheji

inani elinye kwisikhewu se-1/30 (elithambekileyo)351/30+0.0057bheja i-0.57% yemali yokudlala

inani elinye kwisikhewu se-1/25351/25+0.0126bheja i-1.26% yemali yokudlala

Apho i-Kelly yayisebenza khona

Abadlali bokuthambekela babenenzuzo kunye nengxaki yobukhulu bebheji. UJagger, ooGarcía-Pelayo kunye nee-Eudaemons bonke kwafuneka bagqibe ukuba babheje malini kwinzuzo yabo abayilinganisileyo, kwaye ukubheja kancinci kuchitha inzuzo ngelixa ukubheja kakhulu kubeka emngciphekweni wokuphelelwa yimali ngaphambi kokuba inzuzo ibonakale. Kwi-sikhewuizixhoboIsikhewuEsinye sezikhewu ezingama-37 ezinamanani kwirotha. Kwakhona: slot, cup.Funda yonke → esiphuma ka-1 kwi-30, i-Kelly ithi i-0.57% yemali yokudlala ngomjikelo kwelo nani: nge-$10,000, malunga ne-$57 ngomjikelo, ukukhula okuqhelekileyo malunga ne-0.054% ngomjikelo, okanye ×1.7 kwimijikelo eli-1,000. Inzuzo yomndilili iphindwe kabini kunoko, i-0.11% ngomjikelo, kodwa i-Kelly ijolise kwimali yokudlala eqhelekileyo, hayi eyomndilili, ekhukhumaliswa luthotho oluncinci lwethamsanqa. I-Half-Kelly lukhetho oluqhelekileyo olusebenzayo kuba uqikelelo lwenzuzo aluqinisekanga.

Ibheji ye-Kelly njenge-% yemali yokudlala kwibheji yenani elinye, ngesantya sokwenyani sesikhewu%

1/37 (efanelekileyo)

0% · ungabheji

1/35

0.08%

1/33

0.26%

1/30

0.57%

1/25

1.26%

1/20

2.0%

012.0%

Kwanokuthambekela okukhulu kufuna iibheji ezincinci: intlawulo inde kwaye ukwahluka kuphezulu.

Abadlali be-roulette abadumileyo The Eudaemons

Okuqhelekileyo nomndilili

Umsantsa phakathi kwemali yokudlala eqhelekileyo neyomndilili ubanzi. Thatha isikhewu esiphuma ka-1 kwi-25, inzuzo ye-44%, inani elinikwa nguThorp ngesixhobo sakhe. I-Kelly ibheja i-1.26% yemali yokudlala kuso. Emva kwemijikelo eli-1,000 imali yokudlala eqhelekileyo ikhule malunga namaxesha ali-11.5, ngelixa umndilili, otsalwa phezulu luthotho oluncinci lwethamsanqa elikhulu, ukhule malunga namaxesha angama-249. Ukubheja ngaphezu kwe-Kelly kunyusa umndilili kwaye kuhlisa isiphumo esiqhelekileyo: kwibheji ephindwe kabini ye-Kelly imali yokudlala eqhelekileyo iphindeka kabini kuphela, kwaye ngamaxesha amabini nesiqingatha ebheji ye-Kelly iyancipha, nangona yonke ibheji isenenzuzo ye-44%. Ukubheja kancinci kubiza kancinci: isiqingatha sebheji sigcina malunga nesithathu kwisine sokukhula.

ibheji, isabelo se-Kellyibheji, % yemali yokudlalaimali yokudlala eqhelekileyo emva kwemijikelo eli-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

Isikhewu esinye esiphuma ka-1 kwi-25, sihlawulwa u-35 ku-1. Okuqhelekileyo kuthetha umbindi, u-e ophakanyiselwe kumaxesha ali-1,000 okukhula ngomjikelo.

Xa inzuzo iyingqikelelo

I-Kelly ithatha ukuba inzuzo iyaziwa. Etafileni iyaqikelelwa, kwaye uqikelelo ludla ngokuba phezulu kakhulu. Umzekelo ka-Epstein, owakhelwe kwi-44% kaThorp, linani elaphuma amaxesha angama-49 kwimijikelo eli-1,225 yevili eneqandaiviliIqandaIsikhewu esinye esiluhlaza esingagubungelwa yibheji yemali elinganayo, yedazini okanye yekholamu; umthombo wenzuzo yekhasino. Kwakhona: iqanda elinye, 0.Funda yonke → eliphindiweyo: ka-1 kwi-25, inzuzo ye-44%, ibheji ye-Kelly ye-1.26%. Kodwa ivili elifanelekileyo eneqanda eliphindiweyo linamanani angama-38, kwaye elona lixakekileyo kuwo lifikelela kuma-49 nangaphezulu kwimijikelo eli-1,225 malunga kanye kumaxesha alithoba. Elona nani lixakekileyo kuyo nayiphi na irekhodi likwalilo elincedwe kakhulu lithamsanqa, ngoko nesikhewu esithambeke ngokwenene sibonakala singcono kwirekhodi kunokuba sinjalo: isiqalekiso somphumeleli (winner’s curse). Ukuba eso sikhewu ngokwenene asithambekanga, ibheji ye-Kelly yibheji nje elahlekelwa yi-5.26% ngokomndilili. Iimpendulo eziqhelekileyo kukubheja iqhezu le-Kelly nokuqhubeka ubala de inzuzo isinde kwirekhodi entsha (jonga Indlela yokufumanisa ukuthambekela kwevili le-roulette).

Abantu abanenzuzo

Ukwazi inzuzo akufani nokuyisebenzisa kakuhle. UHaghani noDewey (2016) banika abantu abangama-61 i-$25 umntu ngamnye ukuze babheje isiqingatha seyure kwingqekembe ababexelelwe ukuba iphuma intloko ama-60% exesha, iimpumelelo zinqunyelwe kwi-$250 (abadlali bawazi umda kuphela xa befika kuwo). I-Kelly ithi bheja i-20% yemali yokudlala entloko qho, kwaye ababhali baqikelela ukuba iibheji ezizinzileyo ze-10–20% bezinokufikelela kumda malunga ne-95% yexesha. Ngama-21% kuphela abadlali abafika apho. Ama-28% aphelelwa yimali, abali-18 kwabangama-61 babheja yonke into ekuphoseni okukodwa, malunga nesinye kwisithathu bagqiba ngaphantsi kwe-$25 abaqale ngayo, kwaye intlawuloimaliIntlawuloOko ibheji ephumeleleyo ikubuyisayo, okuxelwa njengo-“X ku-1” ngaphezulu kwebheji ebuyisiweyo.Funda yonke → yomndilili yayiyi-$91. Babahlanu kuphela kwabangama-61 ababekhe beva nge-Kelly criterion. Xa unenzuzo, ubukhulu beebheji bugqiba ukuba uyayigcina na; ngaphandle kwayo, njengakwivili elifanelekileyo, akukho bukhulu bunceda.

Umdlali omnye ubheja yonke into ekuphoseni okukodwa ngelixa ummelwane wakhe ebheja iqhezu elincinci.

Into omawuyisebenzise endaweni yoko

Ngaphandle kwenzuzo, ubukhulu bebheji ngumbuzo wohlahlo-lwabiwo-mali, hayi owokukhula: ibheji = oko uzimisele ukukuchitha ngomjikelo, okufunyanwa kuhlahlo-lwabiwo-mali lweyure nakwisantya setafile (iphepha lolawulo lwemali yokudlala). Igalelo le-Kelly kumdlali oqhelekileyo kukucaca kwempendulo yayo: iqanda. Yonke into oyibhejayo ngaphezu kweqanda ixabiso lokudlala, elikhethwe nguwe, hayi elilungiswe yiyo nayiphi na ifomula.

Inqaku nge-Kelly eyiqhezu kunye “nolawulo lwemali”

Iinkqubo ezithengiswa njenge-“Kelly ye-roulette” ezicebisa ipesenti emiselweyo yemali yokudlala kwibheji nganye kukubheja ngokulinganayoisicwangcisoUkubheja ngokulinganayoUkubheja isixa esifanayo kuwo wonke umjikelo. Isiseko apho konke ukunyuswa kweebheji kuthelekiswa khona.Funda yonke → ngebheji encipha. Zilahlekelwa yi-2.70% yesixa esipheleleyo esibhejiweyoimaliIsixa esipheleleyo esibhejiweyoIsixa esipheleleyo esibhejiweyo kwiseshoni okanye kwixesha elithile, kubalwa nemali ephumeleleyo ephinda ibhejwe. Kwakhona: handle, action.Funda yonke → kwaye, ngenxa yokuba ibheji iyancipha njengoko ulahlekelwa, zenza ukuphelelwa yimali kucothe kunokuba kungabikho. Yindlela efanelekileyo yokwenza uhlahlo-lwabiwo-mali luhlale ixesha elide; ayisiyo-Kelly, ebiya kuthi yima.

Isicwangciso sokubheja ngokulinganayo kwi-roulette

Ifomula

f* = (b·p − q) / b

obomvu: f* = −1/37 · inani elinye: f* = −1/1295

isikhewu esithambekileyo ngesantya r: f* = (35r − (1 − r)) / 35

Imibuzo

Ingaba i-Kelly ikhe ithi bheja kwi-roulette?

Kuphela ngenzuzo elinganisiweyo evela kwivili elithambekileyoilebhuIvili elithambekileyoIvili elineziphene ezenza ezinye izikhewu zibe namathuba angaphezulu kwe-1/37. Alifumaneki lula, linokubonwa kuphela ngamawaka emijikelo erekhodiweyo.Funda yonke → okanye kwisixhobo sexesha. Hayi kwivili elifanelekileyo.

Kutheni i-half-Kelly?

Kuba uqikelelo lwenzuzo lunempazamo, kwaye ukubheja kakhulu kubiza ngaphezu kokubheja kancinci. I-Half-Kelly inika isithathu kwisine sokukhula ngesinye kwisine sokwahlukaizibaloUkwahlukaUmlinganiselo wokuba iziphumo zisasazeke kangakanani zijikeleze ixabiso elilindelekileyo. Kuphezulu kwibheji yenani elinye, kuphantsi kwiibheji zemali elinganayo.Funda yonke →.

Ingaba i-Kelly iyafana nolawulo lwemali yokudlala?

Hayi. I-Kelly ilungisa ukukhula xa ukho inzuzo. Ulawulo lwemali yokudlala lulawula inkcitho xa ingekho.

Ukonwaba ngezibalo

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

Isixhobo sokuqikelela sika-Thorp no-Shannon sanika inzuzo emalunga ne-44%. Kwinani elinye eliqikelelweyo, u-Kelly uthi bheja i-1.26% yemali yokudlalaimaliImali yokudlalaIsixa esipheleleyo esibekelwe ukudlala. Ulawulo lwemali yokudlala kukugqiba ukuba ingakanani kuyo oyibeka emngciphekweni kwibheji nganye nakwiseshoni nganye.Funda yonke →. Kuthekani ukuba le nzuzo ye-44% ifanayo ibikwibheji enye esasazwe kumanani amahlanu angabamelwane?
Bonisa isisombululo
Impendulo Emva koko u-Kelly uthi i-7.1% yemali yokudlala, kwaye imali yokudlala ikhula phantse kathandathu ngokukhawuleza: malunga nezihlandlo eziyi-1.25 yezigidi kwiibheji eziyi-1,000, xa kuthelekiswa nezihlandlo ezimalunga ne-11.5.
Ibheji yenani elinyeibhejiInani elinyeInani elinye, ihlawula u-35:1.Funda yonke → enenzuzo ye-44% iphumelela ngethuba elingu-0.04, kuba 36 × 0.04 = 1.44. Ibheji ka-Kelly yinzuzo eyahlulwe zii-odds: 0.44/35 = 1.26%. Ukukhula okuqhelekileyo kwibheji nganye ngu-0.04 × ln(1 + 35 × 0.0126) + 0.96 × ln(1 − 0.0126) ≈ 0.00244, ngoko iibheji eziyi-1,000 ziphindaphinda imali yokudlala malunga no-e^2.44 ≈ 11.5.
Sasaza ibheji enye kumanani amahlanu kwaye ibheji iphumelela ngethuba elingu-0.20 kwaye ihlawula u-36/5 ku-1, oko kukuthi u-6.2 ku-1: isenenzuzo ye-44%, kuba 0.2 × 7.2 = 1.44. Ibheji ka-Kelly iba ngu-0.44/6.2 = 7.10%, kwaye ukukhula kwibheji nganye ngu-0.01404, malunga nezihlandlo ezi-5.75 ngaphezulu. Kwiibheji eziyi-1,000 oko kungu-e^14.04, malunga nezigidi ezi-1.25.
Inzuzo iyafana; ukuguquguquka kuncinci. Ibheji ephumelela kanye kwezintlanu ingathwala isabelo esikhulu semali yokudlala ngaphandle komngcipheko wokuphelelwa yimali, kwaye ukukhula kuka-Kelly kuyakuvuza oko. U-Thorp (1984) usebenzisa lo mzekelo ukubonisa ukuba kutheni abadlali bokuqikelela bebheja amacandeloiviliIcandeloIsiqwenga esiqhubekayo sezikhewu evilini, esahlukileyo kwiqela elikwibhodi yokubheja.Funda yonke →. Ngokwenyani abamelwaneibhejiAbamelwaneInani kunye nezikhewu ezibini kwicala ngalinye lalo evilini, iitshiphu ezintlanu zenani elinye.Funda yonke → abahlanu banenzuzo ephantsi kancinci kunelona nani lilodwa lingcono (jonga Ukudlala ngenzuzo).
Umdlali ufumene izikhewuizixhoboIsikhewuEsinye sezikhewu ezingama-37 ezinamanani kwirotha. Kwakhona: slot, cup.Funda yonke → ezimbini ezingabamelwane, nganye iphuma i-1 kwezingama-25 endaweni ye-1 kwezingama-37. Ingaba kufuneka abheje amanani amabiniibhejiAmanani amabiniAmanani amabini angabamelwane, ihlawula u-17:1.Funda yonke → phakathi kwazo ngo-17 ku-1, okanye inani ngalinye njengenani elinye? U-Kelly uthi malini, kwaye imali yokudlala ikhula ngokukhawuleza kangakanani xa kuthelekiswa nesikhewu esinye esinjalo?
Bonisa isisombululo
Impendulo Akwenzi mahluko: i-2.59% yemali yokudlala kumanani amabini, okanye i-1.29% kwinani ngalinye. Imali yokudlala eqhelekileyo ikhula malunga nezihlandlo eziyi-155 kwimijikelo eyi-1,000, xa kuthelekiswa nezihlandlo ezili-11.5 ngesikhewu esinye.
Amanani amabini aphumelela ngamathubaizibaloAmathubaIthuba lesiphumo, ukusuka ku-0 ukuya ku-1 okanye ku-0% ukuya ku-100%. Inani elinye: 1/37 = 2.70%.Funda yonke → angu-2/25 = 0.08 kwaye ahlawula u-17 ku-1, ngoko abuyisa u-18 × 0.08 = 1.44 kwiyunithiimaliIyunithiIbheji esisiseko esetyenziswa yinkqubo okanye ngumdlali. Ukunyuswa kweebheji kuchazwa ngeeyunithi ukuze kusebenze kuyo nayiphi na itafile.Funda yonke → nganye ebhejiweyo: inzuzo ye-44%, efana neyesikhewu esinye esithambekileyo. Ibheji ka-Kelly yinzuzo eyahlulwe zii-odds: 0.44/17 = 2.59%.
Iibheji ezimbini zenani elinye ze-1.29% nganye zinika iziphumo ezifanayo ngqo. Xa elinye lamanani liphuma, itshiphuimaliItshiphuUphawu olumele isixa esimiselweyo, olubekwa kwibhodi yokubheja ukwenza ibheji. Kwakhona: check.Funda yonke → enye iphumelela u-35 ku-1 kwaye enye iyalahleka, inzuzo yokwenyani engu-34 × 1.29% = 44% yemali yokudlala, njengoko amanani amabini ehlawula; xa kungaphumi nalinye, zombini ziyalahleka.
Ukukhula ngomjikelo ngu-0.00505, xa kuthelekiswa no-0.00244 wesikhewu esinye, ngoko kwimijikelo eyi-1,000 imali yokudlala eqhelekileyo ikhula u-e^5.046 ≈ 155 izihlandlo kunokuba ibe ngu-e^2.44 ≈ 11.5. Amanani amabini alungileyo axabisa kakhulu ngaphezu kokuphindwa kabini kwelinye, yiyo loo nto abadlali bokuthambekela bebheja amaqela amanani. U-Thorp (1984) wenza olu thelekiso lufanayo.

Uncumo

$Ibheji ye-roulette efanelekileyo yokukhula linani wonke umntu osele elazi.$

Ibheji ye-roulette efanelekileyo yokukhula linani wonke umntu osele elazi.

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, 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. Isahluko 13, i-roulette.
Haghani, V. & Dewey, R. “Rational decision-making under uncertainty: observed betting patterns on a biased coin.” Iphepha lomsebenzi, Okthobha 2016; SSRN 2856963, arXiv:1701.01427.

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