Igipimo cya Kelly na Roulette
Igipimo cya Kelly kibwira umukinnyi ufite inyungu uko yategeka. Kuri roulette gitanga igisubizo gisobanutse: nta na kimwe.
Itega rya Kelly = inyungu / odds. Iyo inyungu ari mbi, formula itanga igice kibi, bisobanura ngo ntutege. Igipimo kiracyafite akamaro mu gusobanukirwa impamvu abakinnyi b'ukubogama bagenaga ingano y'amatega yabo uko babigenzaga, n'impamvu abandi bose bagomba kugena ingano bakurikije ingengo y'imari.
Igipimo
John Kelly (1956) yibajije uko umukinnyi w'urusimbi ufite inyungu izwi yagena ingano y'amatega ye kugira ngo igishoro cyo gukinaamafarangaIgishoro cyo gukinaAmafaranga yose yashyizwe ku ruhande yo gukina. Gucunga igishoro ni ukwemeza ingano yacyo uzashyira mu kaga kuri buri tega no kuri buri mukino.Soma byose → gikure uko bishoboka kose mu gihe kirekire. Igisubizo, ku itega ryishyura b kuri 1 rifite amahirweimibareAmahirweAmahirwe y'igisubizo, kuva kuri 0 kugeza kuri 1 cyangwa kuva kuri 0% kugeza kuri 100%. Umubare umwe: 1/37 = 2,70%.Soma byose → yo gutsinda p n'amahirwe yo gutsindwa q = 1 − p, ni ugutega igice f* = (bp − q) / b cy'igishoro. f* nziza bisobanura gutega icyo gice; zeru cyangwa mbi bisobanura kudatega. Kelly yakoraga muri Bell Labs, kandi inyandiko ye, “A new interpretation of information rate”, yashyize ikibazo mu nyigisho ya Claude Shannon ku makuru: umukinnyi w'urusimbi uhabwa amakuru binyuze ku murongo urimo urusaku, ku odds ziboneye, ashobora gukuza igishoro cye ku muvuduko utarenze uw'amakuru uwo murongo utwara. Mu 1961, Leo Breiman yagaragaje ko gutega ukurikije Kelly, mu gihe kirekire, birangira biri imbere y'izindi ngamba zose zitandukanye nabyo by'ukuri, kandi bikagera ku ntego yashyizweho mu gihe hafi kigufi gishoboka.
Gutega ukurikije Kelly muri roulette
Ku mutukuitegaUmutukuItega ryishyura kimwe ku kindi ku mibare 18 y'umutuku. Mu Gifaransa: rouge.Soma byose →: b = 1, p = 18/37, q = 19/37; f* = (18/37 − 19/37)/1 = −1/37. Kuri straight upitegaStraight upUmubare umwe, yishyura 35:1.Soma byose →: b = 35, p = 1/37, q = 36/37; f* = (35/37 − 36/37)/35 = −1/1295. Buri tega risanzwe ritanga igice cya Kelly kibi, kuko buri tega rifite inyungu mbi, kandi itega rikuza igishoro neza kurusha ayandi ni zeru. Gutega ukurikije Kelly muri roulette ni uburyo bw'imibare bwo kuvuga icyo paji y'inyungu ya kazino ivuga: nta ngano y'itega rifite agaciro gateganyijwe kabi ikuza igishoro.
Aho Kelly yakoreshejwe koko
Abakinnyi b'ukubogama bari bafite inyungu n'ikibazo cyo kugena ingano y'amatega. Jagger, aba García-Pelayo na Eudaemons bose bagombaga guhitamo ingano bategeka ku nyungu bapimye, kandi gutega bike cyane bipfusha ubusa inyungu, mu gihe gutega byinshi cyane bishyira mu kaga ko gushira igishoro mbere y'uko inyungu igaragara. Ku kazuibikoreshoAkazuKamwe mu tuzu 37 twanditseho imibare turi kuri rotor. Nanone: slot, cup.Soma byose → gasohoka incuro 1 mu 30, Kelly ivuga 0,57% by'igishoro kuri buri zunguruka kuri uwo mubare: ufite $10.000, hafi $57 kuri buri zunguruka, ku iterambere risanzwe rya hafi 0,054% kuri buri zunguruka, cyangwa ×1,7 mu mazunguruka 1.000. Inyungu y'impuzandengo ni incuro ebyiri z'iyo, 0,11% kuri buri zunguruka, ariko Kelly igamije igishoro gisanzwe, si icy'impuzandengo, kizamurwa n'impererekane nke z'amahirwe. Kimwe cya kabiri cya Kelly ni cyo gihitwamo kenshi mu bikorwa kuko igereranya ry'inyungu ridashidikanywaho.
Igisanzwe n'impuzandengo
Ikinyuranyo hagati y'igishoro gisanzwe n'icy'impuzandengo ni kinini. Fata akazu gasohoka incuro 1 mu 25, inyungu ya 44%, umubare Thorp atanga ku gikoresho cye. Kelly itega 1,26% by'igishoro kuri ako kazu. Nyuma y'amazunguruka 1.000, igishoro gisanzwe kiba cyarakuze hafi incuro 11,5, mu gihe icy'impuzandengo, kizamurwa n'impererekane nke z'amahirwe menshi cyane, kiba cyarakuze hafi incuro 249. Gutega birenze Kelly bizamura impuzandengo bikagabanya igisubizo gisanzwe: ku itega ringana n'incuro ebyiri iya Kelly, igishoro gisanzwe cyikuba kabiri gusa, naho ku ncuro ebyiri n'igice z'itega rya Kelly kiragabanuka, nubwo buri tega rigifite inyungu ya 44%. Gutega bike bihombya gake: kimwe cya kabiri cy'itega kigumana hafi bitatu bya kane by'iterambere.
Iyo inyungu ari igitekerezo gusa
Kelly ifata ko inyungu izwi. Ku meza iragereranywa, kandi igereranya ubusanzwe riba riri hejuru cyane. Urugero rwa Epstein, rushingiye kuri 44% ya Thorp, ni umubare wasohotse incuro 49 mu mazunguruka 1.225 y'uruziga rwa zeruuruzigaZeruAkazu kamwe k'icyatsi katafatwa n'itega ryishyura kimwe ku kindi, irya dazeni cyangwa iry'inkingi; ni ho inyungu ya kazino ikomoka. Nanone: zeru imwe, 0.Soma byose → ebyiri: incuro 1 mu 25, inyungu ya 44%, itega rya Kelly rya 1,26%. Ariko uruziga rutabogamye rwa zeru ebyiri rufite imibare 38, kandi uwusohoka kurusha iyindi ugera ku ncuro 49 cyangwa zirenga mu mazunguruka 1.225 hafi rimwe mu icyenda. Umubare usohoka kurusha iyindi mu nyandiko iyo ari yo yose ni na wo amahirwe yafashije kurusha iyindi, bityo n'akazu kabogamye koko kagaragara mu nyandiko neza kurusha uko kari: umuvumo w'uwatsinze (winner’s curse). Niba ako kazu mu by'ukuri katabogamye, itega rya Kelly ni itega gusa rihomba 5,26% ku mpuzandengo. Ibisubizo bisanzwe ni ugutega igice cya Kelly no gukomeza kubara kugeza inyungu ihagaze no mu nyandiko nshya (reba Uko Watahura Ukubogama k'Uruziga rwa Roulette).
Abantu bafite inyungu
Kumenya inyungu si kimwe no kuyikoresha neza. Haghani na Dewey (2016) bahaye abantu 61 buri wese $25 ngo batege mu gice cy'isaha ku giceri babwiwe ko kigwa ku ruhande rw'umutwe 60% by'igihe, intsinzi zifite imbibi za $250 (abakinnyi bamenyaga izo mbibi ari uko bazigezeho). Kelly ivuga gutega 20% by'igishoro ku mutwe buri gihe, kandi abanditsi bagereranya ko amatega ahoraho ya 10–20% yagera ku mbibi hafi 95% by'igihe. 21% gusa by'abakinnyi ni bo bahageze. 28% bashize igishoro, 18 muri 61 bateze byose ku gutera igiceri kumwe, hafi kimwe cya gatatu barangije bari munsi ya $25 batangiranye, kandi ubwishyuamafarangaUbwishyuIbyo itega ryatsinze rigarura, bivugwa nka “X kuri 1” hiyongereyeho itega rigarurwa.Soma byose → bw'impuzandengo bwari $91. Batanu gusa muri 61 bari barumvise igipimo cya Kelly. Ufite inyungu, ingano y'amatega ni yo igena niba uyigumana; utayifite, nko ku ruziga rutabogamye, nta ngano ifasha.
Icyo wakoresha aho
Nta nyungu ufite, kugena ingano ni ikibazo cy'ingengo y'imari, si icy'iterambere: itega = icyo wemera gutanga kuri buri zunguruka, gikomoka ku ngengo y'imari y'isaha n'umuvuduko w'ameza (paji yo gucunga igishoro). Icyo Kelly imarira umukinnyi usanzwe ni igisubizo cyayo gisobanutse: zeru. Ibyo utega byose birenze zeru ni igiciro cyo gukina, wihitiyemo, kitatunganyijwe na formula iyo ari yo yose.
Icyitonderwa ku gice cya Kelly no ku “gucunga amafaranga”
Uburyo bugurishwa nka “Kelly ya roulette” busaba ijanisha rihoraho ry'igishoro kuri buri tega ni ugutega itega rihorahoingambaGutega itega rihorahoGutega amafaranga angana kuri buri zunguruka. Ni yo ngero buri ruhererekane rw'amatega rugereranywa na yo.Soma byose → rigenda rigabanuka. Bihomba 2,70% by'amafaranga yose yategeweamafarangaAmafaranga yose yategeweAmafaranga yose yategewe mu mukino umwe cyangwa mu gihe runaka, harimo n'intsinzi zongeye gutegwa. Nanone: handle, action.Soma byose → kandi, kubera ko itega rigabanuka uko uhomba, bituma gushira igishoro bitinda aho kuba bidashoboka. Ni uburyo bwumvikana bwo gutuma ingengo y'imari imara igihe; si Kelly, yo yavuga ngo hagarara.
Formula
Ibibazo
Gusa iyo hari inyungu yapimwe ivuye ku ruziga rubogamyelaboratwariUruziga rubogamyeUruziga rufite inenge z'umubiri zituma utuzu tumwe tugira amahirwe arenze 1/37. Ni gake, kandi rutahurwa gusa n'amazunguruka ibihumbi byanditswe.Soma byose → cyangwa ku gikoresho cyo kubara igihe. Si ku ruziga rutabogamye.
Kuko igereranya ry'inyungu rifite ikosa, kandi gutega byinshi cyane bihenda kurusha gutega bike cyane. Kimwe cya kabiri cya Kelly gitanga bitatu bya kane by'iterambere ku gice cya kane cy'ihindagurikaimibareIhindagurikaIgipimo cy'uko ibisubizo bikwirakwira kure y'agaciro gateganyijwe. Riri hejuru kuri straight up, hasi ku matega yishyura kimwe ku kindi.Soma byose →.
Oya. Kelly itunganya iterambere iyo hari inyungu. Gucunga igishoro bigenzura ibyo utanga iyo nta nyungu ihari.
Kwishimisha n'Imibare
Banza ubigerageze ubwawe. Buri gisubizo kirapfunyitse; ugifungure igihe witeguye.
Igikoresho cyo guhanura cya Thorp na Shannon cyatangaga inyungu ya hafi 44%. Ku mubare umwe wahanuwe, Kelly avuga gutega 1,26% by'igishoro cyo gukinaamafarangaIgishoro cyo gukinaAmafaranga yose yashyizwe ku ruhande yo gukina. Gucunga igishoro ni ukwemeza ingano yacyo uzashyira mu kaga kuri buri tega no kuri buri mukino.Soma byose →. Byagenda bite iyo iyo nyungu imwe ya 44% iza ku itega rimwe rikwirakwijwe ku mibare itanu ituranye?
Erekana igisubizo
Igisubizo Icyo gihe Kelly avuga 7,1% by'igishoro, kandi igishoro gikura hafi incuro esheshatu vuba: hafi incuro miliyoni 1,25 mu matega 1.000, ugereranyije n'incuro hafi 11,5.
Straight upitegaStraight upUmubare umwe, yishyura 35:1.Soma byose → ifite inyungu ya 44% itsinda ku mahirwe ya 0,04, kuko 36 × 0,04 = 1,44. Itega rya Kelly ni inyungu igabanyijwe na odds: 0,44/35 = 1,26%. Ikura risanzwe kuri buri tega ni 0,04 × ln(1 + 35 × 0,0126) + 0,96 × ln(1 − 0,0126) ≈ 0,00244, bityo amatega 1.000 akuba igishoro hafi e^2,44 ≈ 11,5.
Kwirakwiza itega rimwe ku mibare itanu bituma itega ritsinda ku mahirwe ya 0,20 kandi ryishyura 36/5 kuri 1, ni ukuvuga 6,2 kuri 1: iracyari inyungu ya 44%, kuko 0,2 × 7,2 = 1,44. Itega rya Kelly riba 0,44/6,2 = 7,10%, naho ikura kuri buri tega 0,01404, hafi incuro 5,75 kurushaho. Mu matega 1.000 ibyo ni e^14,04, hafi miliyoni 1,25.
Inyungu ni imwe; ihindagurika ni rito. Itega ritsinda rimwe mu ncuro eshanu rishobora kwikorera umugabane munini w'igishoro nta kwishyira mu kaga ko gushira, kandi ikura rya Kelly rirabihemba. Thorp (1984) akoresha uru rugero yerekana impamvu abakinnyi bahanura batega ibiceuruzigaIgice cy'uruzigaUmuheto w'utuzu dukurikirana ku ruziga, bitandukanye n'itsinda ku mbonerahamwe y'amatega.Soma byose →. Mu bikorwa, abaturanyiitegaAbaturanyiUmubare n'utuzu tubiri kuri buri ruhande rwawo ku ruziga, amajeto atanu ya straight up.Soma byose → batanu bafite inyungu ntoya gato ugereranyije n'umubare umwe mwiza kurusha (reba Gukina Ushaka Inyungu muri Roulette).
Umukinnyi yabonye utuzuibikoreshoAkazuKamwe mu tuzu 37 twanditseho imibare turi kuri rotor. Nanone: slot, cup.Soma byose → tubiri dutuye, buri kamwe gasohoka incuro 1 muri 25 aho kuba 1 muri 37. Yagombye gutega splititegaSplitImibare ibiri yegeranye, yishyura 17:1.Soma byose → hagati yatwo kuri 17 kuri 1, cyangwa buri mubare straight up? Kelly avuga angahe, kandi igishoro gikura vuba bingana iki ugereranyije n'akazu kamwe nk'ako?
Erekana igisubizo
Igisubizo Nta tandukaniro: 2,59% by'igishoro kuri split, cyangwa 1,29% kuri buri mubare. Igishoro gisanzwe gikura hafi incuro 155 mu mazunguruka 1.000, ugereranyije n'incuro 11,5 n'akazu kamwe.
Split itsinda ku mahirweimibareAmahirweAmahirwe y'igisubizo, kuva kuri 0 kugeza kuri 1 cyangwa kuva kuri 0% kugeza kuri 100%. Umubare umwe: 1/37 = 2,70%.Soma byose → ya 2/25 = 0,08 kandi yishyura 17 kuri 1, bityo igarura 18 × 0,08 = 1,44 kuri buri niteamafarangaIniteItega ry'ibanze uburyo cyangwa umukinnyi akoresha. Impererekane z'amatega zisobanurwa mu nite kugira ngo zikoreshwe ku meza ayo ari yo yose.Soma byose → yategewe: inyungu ya 44%, kimwe n'akazu kamwe kabogamye. Itega rya Kelly ni inyungu igabanyijwe na odds: 0,44/17 = 2,59%.
Amatega abiri ya straight up ya 1,29% buri rimwe atanga ibisubizo bimwe neza. Iyo umwe muri iyo mibare usohotse, jetoamafarangaJeto (chip)Jeto ihagarariye amafaranga angana atahinduka, ishyirwa ku mbonerahamwe y'amatega kugira ngo utege. Nanone: check.Soma byose → imwe itsinda 35 kuri 1 indi igatsindwa, igiteranyo nyacyo cya 34 × 1,29% = 44% by'igishoro, nk'uko split yishyura; iyo nta n'umwe usohotse, zombi zitsindwa.
Ikura kuri buri zunguruka ni 0,00505, ugereranyije na 0,00244 ku kazu kamwe, bityo mu mazunguruka 1.000 igishoro gisanzwe gikura e^5,046 ≈ incuro 155 aho kuba e^2,44 ≈ incuro 11,5. Imibare ibiri myiza ifite agaciro kenshi kurusha kabiri k'umwe, ari na yo mpamvu abakinnyi b'ukubogama batega amatsinda y'imibare. Thorp (1984) akora igereranya rimwe.
Akanya k'urwenya
Itega rya roulette rikuza igishoro neza kurusha ayandi ni umubare buri wese asanzwe azi.
Inkomoko
- 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.”