Kelly Criterion neRoulette
Kelly criterion inoudza mubheji ane mukana wakanaka kuti angabheja zvakadii. MuRoulette inopa mhinduro yakajeka: hapana.
Mari yeKelly = mukana wakanaka / mikana. Kana mukana wakaipa fomula inodzosa chikamu chakaipa, zvinoreva kuti musabheja. Criterion iyi ichiri kubatsira kunzwisisa kuti sei vatambi vekutsauka kwevhiri vaiyera mabheti avo nenzira yavaiita, uye sei vamwe vese vanofanira kuyera nebhajeti.
Criterion
John Kelly (1956) akabvunza kuti mubheji ane mukana wakanaka unozivikanwa anofanira kuyera sei mabheti kuti akurise mari yekutambamariMari yekutambaMari yose yakachengeterwa kutamba. Kutonga mari yekutamba kuri kusarudza kuti mungaisa pangozi yakawanda sei pabheti rimwe nepasesheni imwe.Verengai zvese → zvakanyanya nekufamba kwenguva. Mhinduro, pabheti rinobhadhara b kusvika ku1 rine mukanamasvomhuMukanaMukana wemhedzisiro, kubva pa0 kusvika pa1 kana 0% kusvika 100%. Nhamba imwe: 1/37 = 2.70%.Verengai zvese → wekukunda p nemukana wekurasikirwa q = 1 − p, ndeyekubheja chikamu f* = (bp − q) / b chemari yekutamba. f* yakanaka zvinoreva kubheja chikamu ichocho; zero kana yakaipa zvinoreva kusabheja. Kelly aishanda kuBell Labs, uye pepa rake, “A new interpretation of information rate”, rakaisa dambudziko iri mudzidziso yeruzivo yaClaude Shannon: mubheji anowana mazano pamutsara une ruzha, pamikana yakaenzana, anogona kukurisa mari yekutamba zvakanyanya pakumhanya kunotakura ruzivo nemutsara. Muna 1961 Leo Breiman akaratidza kuti kubheja kweKelly, nekufamba kwenguva, kunopera kuri mberi kwenzira ipi neipi yakasiyana uye kunosvika pachinangwa chakatarwa munguva inenge pfupi kwazvo.
Kubheja kweKelly muRoulette
PatsvukubhetiTsvukuBheti remubhadharo wakaenzana panhamba 18 tsvuku. ChiFrench: rouge.Verengai zvese →: b = 1, p = 18/37, q = 19/37; f* = (18/37 − 19/37)/1 = −1/37. Pastraight upbhetiStraight upNhamba imwe chete, rinobhadhara 35:1.Verengai zvese →: b = 35, p = 1/37, q = 36/37; f* = (35/37 − 36/37)/35 = −1/1295. Bheti rega rega rakajairika rinopa chikamu cheKelly chakaipa, nekuti bheti rega rega rine mukana wakaipa, uye mari inokurisa zvakanyanya izero. Kubheja kweKelly paRoulette inzira yepamutemo yekutaura zvinotaurwa nepeji rechikamu chekasino: hapana huwandu hunoita kuti bheti rine kutarisira kwakaipa rikurise mari yekutamba.
Apo Kelly yakashanda
Vatambi vekutsauka kwevhiri vaiva nemukana wakanaka nedambudziko rekuyera. Jagger, maGarcía-Pelayo neEudaemons vese vaifanira kusarudza kuti vangabheja zvakadii pamukana wavo wakayerwa, uye kubheja zvishoma kunowondonga mukana wakanaka asi kubheja zvakawandisa kunoisa panjodzi yekupera mari mukana usati waonekwa. PagombamidziyoGombaImwe yemakamuri 37 ane nhamba parotor. Mamwe mazita: slot, cup.Verengai zvese → rinobuda 1 pa30, Kelly inoti 0.57% yemari yekutamba pakutenderera panhamba iyoyo: ne$10,000, anenge $57 pakutenderera, kukura kwakajairika kwe0.054% pakutenderera, kana ×1.7 mukutenderera 1,000. Purofiti yepaavhareji yakapetwa kaviri, 0.11% pakutenderera, asi Kelly inonanga mari yekutamba yakajairika, kwete yepaavhareji, iyo inokwidzwa nemitsara mishoma yerombo. Hafu-Kelly ndiyo sarudzo inowanzoitwa nekuti fungidziro yemukana wakanaka haina chokwadi.
Yakajairika neyepaavhareji
Mukaha pakati pemari yekutamba yakajairika neyepaavhareji wakakura. Torai gomba rinobuda 1 pa25, mukana wakanaka we44%, nhamba inopiwa naThorp yemudziyo wake. Kelly inobheja 1.26% yemari yekutamba pariri. Mushure mekutenderera 1,000 mari yekutamba yakajairika yakura kanenge ka11.5, apo avhareji, ichikwidzwa nemitsara mishoma yerombo guru, yakura kanenge ka249. Kubheja kupfuura Kelly kunokwidza avhareji uye kunoderedza mhedzisiro yakajairika: pamari yakapetwa kaviri yeKelly mari yekutamba yakajairika inopetwa kaviri chete, uye pakapetwa kaviri nehafu kweKelly inoderera, kunyange bheti rega rega richine mukana wakanaka we44%. Kubheja zvishoma kunodhura zvishoma: hafu yemari inochengeta zvikamu zvinenge zvitatu pazvina zvekukura.
Kana mukana wakanaka uri fungidziro
Kelly inofunga kuti mukana wakanaka unozivikanwa. Patafura unofungidzirwa, uye fungidziro kazhinji yakakwira zvikuru. Muenzaniso waEpstein, wakavakirwa pa44% yaThorp, inhamba yakabuda ka49 mukutenderera 1,225 kwevhiri rezerovhiriZeroGomba rimwe chete rakasvibira risingafukidzwi nebheti remubhadharo wakaenzana, redozeni kana rekoramu; ndiko kunobva chikamu chekasino. Mamwe mazita: zero imwe, 0.Verengai zvese → mbiri: 1 pa25, mukana wakanaka we44%, mari yeKelly ye1.26%. Asi vhiri rakaenzana rine zero mbiri rine nhamba 38, uye inobuda zvikuru pakati padzo inosvika 49 kana kupfuura mukutenderera 1,225 kanenge kamwe pakapfumbamwe. Nhamba inobuda zvikuru murekodhi ipi neipi ndiyo yakabatsirwa zvikuru nerombo, saka kunyange gomba rinotsauka chaizvo rinoita seriri nani murekodhi pane zvariri: winner’s curse. Kana gomba iroro risingatsauki chaizvo, mari yeKelly ingori bheti rinorasikirwa 5.26% paavhareji. Mhinduro dzakajairika kubheja chikamu cheKelly nekuramba muchiverenga kusvikira mukana wakanaka wapona murekodhi itsva (onai Maonero eKutsauka kweVhiri reRoulette).
Vanhu vane mukana wakanaka
Kuziva mukana wakanaka hakuna kufanana nekuushandisa zvakanaka. Haghani naDewey (2016) vakapa vanhu 61 $25 mumwe nemumwe kuti vabheje kwehafu yeawa pamari yesimbi yavakaudzwa kuti inobuda musoro 60% yenguva, zvakakundwa zvakaganhurirwa pa$250 (vatambi vakaziva nezvemuganho pavakausvika chete). Kelly inoti bhejai 20% yemari yekutamba pamusoro nguva dzese, uye vanyori vanofungidzira kuti mabheti akadzikama e10–20% aizosvika pamuganho kanenge 95% yenguva. 21% chete yevatambi ndivo vakasvikako. 28% vakapera mari, 18 pa61 vakabheja zvese pakukanda kamwe, vanenge chikamu chimwe pazvitatu vakapedza vari pasi pe$25 yavakatanga nayo, uye mubhadharomariMubhadharoZvinodzoserwa nebheti rakunda, zvinotaurwa se“X kusvika ku1” pamusoro pemari yakabhejwa inodzoserwa.Verengai zvese → wepaavhareji waive $91. Vashanu chete pa61 vakanga vambonzwa nezveKelly criterion. Kana mune mukana wakanaka, huwandu hwemabheti hunosarudza kana muchauchengeta; musina, sepavhiri rakaenzana, hapana huwandu hunobatsira.
Zvekushandisa pachinzvimbo
Pasina mukana wakanaka, kuyera mubvunzo webhajeti, kwete wekukura: mari yakabhejwa = zvamunoda kushandisa pakutenderera, zvichibva pabhajeti yeawa nekumhanya kwetafura (peji rekutonga mari yekutamba). Chipo chaKelly kumutambi akajairika kujeka kwemhinduro yayo: zero. Zvese zvamunobheja pamusoro pezero mutengo wekutamba, wakasarudzwa nemi, kwete wakagadziriswa nefomula ipi neipi.
Chinyorwa pamusoro pefractional Kelly ne“kutonga mari”
Masisitimu anotengeswa se“Kelly yeRoulette” anokurudzira pesenti yakatarwa yemari yekutamba pabheti rega rega ikubheja kwakaenzananziraKubheja kwakaenzanaKubheja mari imwe chete pakutenderera kwega kwega. Chiyero chinoenzaniswa nacho progression yega yega.Verengai zvese → nemari inoderera. Anorasikirwa 2.70% yemari yose yakabhejwamariMari yose yakabhejwaMari yese yakabhejwa musesheni kana munguva yakati, kusanganisira mari yakakundwa yakabhejwazve. Mamwe mazita: handle, action.Verengai zvese → uye, nekuti mari inoderera sezvamunorasikirwa, anoita kuti kupera mari kunonoke pane kuti kusaitika. Inzira ine musoro yekuita kuti bhajeti igare; haisi Kelly, iyo yaizoti mirai.
Fomula
Mibvunzo
Chete nemukana wakanaka wakayerwa kubva pavhiri rinotsaukaongororoVhiri rinotsaukaVhiri rine zvikanganiso zvemuviri zvinoita kuti mamwe makomba ave nemukana unopfuura 1/37. Hazviwanzoitika, uye zvinoonekwa chete nekutenderera kwezviuru kwakanyorwa.Verengai zvese → kana mudziyo wekuyera nguva. Kwete pavhiri rakaenzana.
Nekuti fungidziro yemukana wakanaka ine kukanganisa, uye kubheja zvakawandisa kunodhura kupfuura kubheja zvishoma. Hafu-Kelly inopa zvikamu zvitatu pazvina zvekukura pachikamu chimwe pazvina chemusiyanomasvomhuMusiyanoChiyero chekuti mhedzisiro yakapararira zvakadii kutenderedza kukosha kunotarisirwa. Wakakwirira pastraight up, wakaderera pamabheti emubhadharo wakaenzana.Verengai zvese →.
Kwete. Kelly inogadzirisa kukura kana paine mukana wakanaka. Kutonga mari yekutamba kunodzora kushandisa kana pasina.
Kutamba neMasvomhu
Edzai izvi imi pachenyu pekutanga. Mhinduro yega yega yakapetwa; ivhurei kana magadzirira.
Muchina wekufanotaura waThorp naShannon waipa mukana pamusoro wenge 44%. Panhamba imwe yakafanotaurwa, Kelly anoti bhejai 1.26% yemari yekutambamariMari yekutambaMari yose yakachengeterwa kutamba. Kutonga mari yekutamba kuri kusarudza kuti mungaisa pangozi yakawanda sei pabheti rimwe nepasesheni imwe.Verengai zvese →. Ko dai mukana iwoyo we44% wauya pabheti rimwe rakaparadzirwa panhamba shanu dzakavakidzana?
Ratidza mhinduro
Mhinduro Ipapo Kelly anoti 7.1% yemari yekutamba, uye mari yekutamba inokura kanenge katanhatu nekukurumidza: anenge 1.25 miriyoni pamabheti 1,000, kana zvichienzaniswa nekanenge ka11.5.
Straight upbhetiStraight upNhamba imwe chete, rinobhadhara 35:1.Verengai zvese → ine mukana pamusoro we44% inokunda nemukana we0.04, nekuti 36 × 0.04 = 1.44. Mari yekubheja yaKelly mukana pamusoro wakakamurwa nemikana: 0.44/35 = 1.26%. Kukura kwakajairwa pabheti i0.04 × ln(1 + 35 × 0.0126) + 0.96 × ln(1 − 0.0126) ≈ 0.00244, saka mabheti 1,000 anowanza mari yekutamba nekanenge e^2.44 ≈ 11.5.
Paradzirai mari imwe yekubheja panhamba shanu uye bheti rinokunda nemukana we0.20 uye rinobhadhara 36/5 for 1, kureva 6.2 kusvika ku1: richiri mukana pamusoro we44%, nekuti 0.2 × 7.2 = 1.44. Mari yekubheja yaKelly inova 0.44/6.2 = 7.10%, uye kukura pabheti 0.01404, anenge ka5.75 kupfuura. Pamabheti 1,000 ndiko e^14.04, anenge 1.25 miriyoni.
Mukana pamusoro wakafanana; kukwira nekudzika ndiko kudiki. Bheti rinokunda kamwe chete pashanu rinogona kutakura chikamu chikuru chemari yekutamba pasina njodzi yekupera mari, uye kukura kwaKelly kunopa mubayiro izvozvo. Thorp (1984) anoshandisa muenzaniso uyu kuratidza kuti nei vatambi vekufanotaura vachibheja zvikamu zvevhirivhiriChikamu chevhiriRutivi rwemakomba akatevedzana pavhiri, rwakasiyana neboka riri patafura yekubhejera.Verengai zvese →. Pakuita, vavakidzanibhetiVavakidzaniNhamba nemakomba maviri kurutivi rumwe nerumwe rwayo pavhiri, machipi mashanu e straight-up.Verengai zvese → vashanu vane mukana pamusoro wakaderera zvishoma pane nhamba imwe yakanakisisa (onai Advantage Play).
Mutambi awana makombamidziyoGombaImwe yemakamuri 37 ane nhamba parotor. Mamwe mazita: slot, cup.Verengai zvese → maviri akavakidzana anobuda rimwe nerimwe ka1 pa25 pachinzvimbo che1 pa37. Vanofanira kubheja splitbhetiSplitNhamba mbiri dzakavakidzana, rinobhadhara 17:1.Verengai zvese → iri pakati pawo pa17 kusvika ku1 here, kana nhamba imwe neimwe straight up? Kelly anoti marii, uye mari yekutamba inokura nekukurumidza zvakadii kana zvichienzaniswa negomba rimwe rakadaro?
Ratidza mhinduro
Mhinduro Hazvina musiyano: 2.59% yemari yekutamba pasplit, kana 1.29% panhamba imwe neimwe. Mari yekutamba yakajairwa inokura kanenge ka155 pakutenderera 1,000, kana zvichienzaniswa neka11.5 negomba rimwe.
Split inokunda nemukanamasvomhuMukanaMukana wemhedzisiro, kubva pa0 kusvika pa1 kana 0% kusvika 100%. Nhamba imwe: 1/37 = 2.70%.Verengai zvese → we2/25 = 0.08 uye inobhadhara 17 kusvika ku1, saka inodzosa 18 × 0.08 = 1.44 payunitimariYunitiMari yehwaro inoshandiswa nesisitimu kana nemutambi. Maprogression anotsanangurwa nemayuniti kuitira kuti ashande patafura ipi zvayo.Verengai zvese → yakabhejwa: mukana pamusoro we44%, zvakafanana negomba rimwe rinotsauka. Mari yekubheja yaKelly mukana pamusoro wakakamurwa nemikana: 0.44/17 = 2.59%.
Mabheti maviri e-straight up e1.29% rimwe nerimwe anopa mhedzisiro yakafanana chaizvo. Kana imwe yenhamba ikabuda, chipimariChipiChiratidzo chinomiririra mari yakatarwa, chinoiswa patafura yekubhejera kuita bheti. Rimwe zita: check.Verengai zvese → chimwe chinokunda 35 kusvika ku1 uye chimwe chinorasikirwa, pundutso ye34 × 1.29% = 44% yemari yekutamba, sezvinobhadharwa nesplit; kana pasina inobuda, zvose zviri zviviri zvinorasikirwa.
Kukura pakutenderera i0.00505, kana zvichienzaniswa ne0.00244 pagomba rimwe, saka pakutenderera 1,000 mari yekutamba yakajairwa inokura ne e^5.046 ≈ ka155 pachinzvimbo che e^2.44 ≈ ka11.5. Nhamba mbiri dzakanaka dzinokosha zvikuru kupfuura kaviri imwe, ndosaka vatambi vekutsauka vachibheja mapoka enhamba. Thorp (1984) anoita kuenzanisa ukoku kumwe chete.
Kuseka zvishoma
Mari yeRoulette inokurisa zvakanyanya inhamba inotozivikanwa nemunhu wese.
Zvinyorwa
- Kelly, J. L. “A new interpretation of information rate.”
- Breiman, L. “Optimal gambling systems for favorable games.”
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Haghani, V. & Dewey, R. “Rational decision-making under uncertainty: observed betting patterns on a biased coin.”