Kelly Criterion ne Roulette
Kelly criterion ebuulira omusibi wa zzaala alina enkizo omuwendo gw'alina okusiba. Ku roulette eddamu kyangu: tosiba kintu.
Ssente za zzaala eza Kelly = enkizo / emikisa. Enkizo bw'eba wansi wa zeero, ensengekera ekuwa ekitundu ekiri wansi wa zeero, ekitegeeza nti tosiba zzaala. Wabula enkola eno ekyayamba okutegeera lwaki abazannyi abaanoonya okusosola kwa nnamuziga baasalawo obunene bwa zzaala zaabwe bwe batyo, n'ensonga lwaki abalala bonna balina okusalawo obunene okusinziira ku nteekateeka y'ensimbi zaabwe.
Enkola eno
John Kelly (1956) yabuuza engeri omuzannyi alina enkizo emanyiddwa gy'alina okusalawo obunene bwa zzaala okukuza ennyo ssente z'okuzannyisassenteSsente z'okuzannyisaOmugatte gwa ssente ezaawulibwa ku lw'okuzannya. Okuddukanya ssente z'okuzannyisa kwe kusalawo omuwendo gw'oteeka mu kabi ku buli zzaala ne mu buli kiseera ky'okuzannya.Soma byonna → mu bbanga eddene. Eky'okuddamu, ku zzaala esasula b ku 1 n'obusobokaokubalaObusobokaObusoboka bw'ekivaamu, okuva ku 0 okutuuka ku 1 oba 0% okutuuka ku 100%. Ennamba emu: 1/37 = 2.70%.Soma byonna → bw'okuwangula p n'obusoboka bw'okufiirwa q = 1 − p, kwe kusiba ekitundu f* = (bp − q) / b ku ssente z'okuzannyisa. f* bw'eba waggulu wa zeero, siba ekitundu ekyo; bw'eba zeero oba wansi wa zeero, tosiba. Kelly yakolanga mu Bell Labs, era olupapula lwe, “A new interpretation of information rate”, lwateeka ekizibu kino mu ndowooza ya Claude Shannon ku mawulire: omuzannyi afuna amagezi ku layini erimu amaloboozi, ku mikisa egy'obwenkanya, asobola okukuza ssente ze ku kigero ekisinga obunene ekyenkana n'amawulire layini g'etambuza. Mu 1961 Leo Breiman yalaga nti okusiba okwa Kelly, mu bbanga eddene, kumaliriza nga kusinga enteekateeka yonna ey'enjawulo mu bukulu era kutuuka ku kigendererwa ekiteereddwawo mu kiseera ekimpi kumpi okusinga.
Okusiba okwa Kelly mu roulette
Ku mmyufuzzaalaEmmyufuZzaala ya emu ku emu ku nnamba 18 emmyufu. Mu Lufalansa: rouge.Soma byonna →: b = 1, p = 18/37, q = 19/37; f* = (18/37 − 19/37)/1 = −1/37. Ku straight upzzaalaStraight upEnnamba emu yokka, esasula 35:1.Soma byonna →: b = 35, p = 1/37, q = 36/37; f* = (35/37 − 36/37)/35 = −1/1295. Buli zzaala eya bulijjo ewa ekitundu kya Kelly ekiri wansi wa zeero, kubanga buli zzaala erina enkizo ekukontana nayo, era ssente za zzaala ezisinga okukuza ziba zeero. Okusiba okwa Kelly ku roulette ngeri ya kubala ey'okwogera ekyo olupapula lw'enkizo ya kaasino kye lwogera: tewali bunene zzaala ey'ekisuubirwa ekiri wansi wa zeero bw'esobola okukuza ssente z'okuzannyisa.
Kelly we yakozesebwa ddala
Abazannyi abaanoonya okusosola kwa nnamuziga baalina enkizo era n'ekizibu ky'obunene bwa zzaala. Jagger, aba García-Pelayo n'aba Eudaemons bonna baalina okusalawo omuwendo gw'okusiba ku nkizo gye baapima, era okusiba ekitono kwonoona enkizo so ng'okusiba ekingi kuleeta akabi k'okumalwako ssente nga enkizo tennalabika. Ku kinnyaebikozesebwaEkinnyaKimu ku bisenge 37 ebiriko ennamba ku rotor. Era biyitibwa: slot, cup.Soma byonna → ekijja omulundi 1 ku 30, Kelly agamba 0.57% ku ssente z'okuzannyisa ku buli kwetooloola ku nnamba eyo: n'$10,000, nga $57 buli kwetooloola, ekireeta okukula okwa bulijjo okwa nga 0.054% buli kwetooloola, oba ×1.7 mu kwetooloola 1,000. Amagoba ag'ekigero gakubisaamu emirundi ebiri, 0.11% buli kwetooloola, naye Kelly agenderera ssente ezisinga okubaawo, si ez'ekigero, ezizimbulukusibwa emitendera mitono egy'omukisa. Ekitundu kya Kelly (half-Kelly) kye kitera okulondebwa mu nkola kubanga okubalirira kw'enkizo tekukakafu.
Ekisinga okubaawo n'eky'ekigero
Enjawulo wakati wa ssente ezisinga okubaawo n'ez'ekigero nnene. Twale ekinnya ekijja omulundi 1 ku 25, enkizo ya 44%, omuwendo Thorp gw'awa ku kyuma kye. Kelly asiba 1.26% ku ssente z'okuzannyisa ku kyo. Oluvannyuma lw'okwetooloola 1,000 ssente ezisinga okubaawo ziba zikuze emirundi nga 11.5, so ng'ez'ekigero, ezisikiddwa waggulu emitendera mitono egy'omukisa ennyo, ziba zikuze emirundi nga 249. Okusiba okusinga Kelly kwongera ku kigero ne kukendeeza ku kivaamu ekisinga okubaawo: ku ssente za zzaala ezikubisaamu emirundi ebiri eza Kelly, ssente ezisinga okubaawo zikubisaamu emirundi ebiri zokka, era ku mirundi ebiri n'ekitundu eza Kelly zikendeera, wadde nga buli zzaala ekyalina enkizo ya 44%. Okusiba ekitono tekufiiriza nnyo: ekitundu kya ssente za zzaala kikuuma nga ebitundu bisatu ku bina eby'okukula.
Enkizo bw'eba ya kuteebereza
Kelly atwala nti enkizo emanyiddwa. Ku mmeeza ebalirirwa, era okubalirira okwo kutera okuba okw'awaggulu ennyo. Ekyokulabirako kya Epstein, ekyazimbibwa ku 44% za Thorp, ye nnamba eyajja emirundi 49 mu kwetooloola 1,225 okwa nnamuziga wa zeeronnamuzigaZeeroEkinnya kimu ekya kiragala ekitabikkibwa zzaala ya emu ku emu, eya dazeni oba ey'empagi; y'ensibuko y'enkizo ya kaasino. Era eyitibwa: zeero emu, 0.Soma byonna → bbiri: omulundi 1 ku 25, enkizo ya 44%, ssente za zzaala eza Kelly eza 1.26%. Naye nnamuziga wa zeero bbiri ow'obwenkanya alina ennamba 38, era esinga okujja mu zo etuuka ku mirundi 49 oba okusingawo mu kwetooloola 1,225 nga omulundi gumu ku mwenda. Ennamba esinga okujja mu biwandiiko byonna era y'eyo omukisa gwe gusinze okuyamba, kale ne ekinnya ekisosola ddala kirabika mu biwandiiko nga kirungi okusinga bwe kiri: ekikolimo ky'omuwanguzi (winner’s curse). Singa ekinnya ekyo mu butuufu tekisosola, ssente za zzaala eza Kelly ziba zzaala bwazzi efiirwa 5.26% ku kigero. Eby'okuddamu ebya bulijjo kwe kusiba ekitundu kya Kelly n'okugenda mu maaso n'okubala okutuusa enkizo lw'ewangaala mu biwandiiko ebipya (laba Engeri y'Okuzuula Okusosola kwa Nnamuziga wa Roulette).
Abantu abalina enkizo
Okumanya enkizo si kye kimu n'okugikozesa obulungi. Haghani ne Dewey (2016) baawa abantu 61 buli omu $25 okusiba okumala ekitundu ky'essaawa ku sente gye baabuulirwa nti egwa ku mutwe 60% ku mirundi, ng'amagoba gakomezeddwa ku $250 (abazannyi baamanya ekkomo lino nga balituuseeko). Kelly agamba siba 20% ku ssente z'okuzannyisa ku mutwe buli mulundi, era abawandiisi babalirira nti okusiba okutebenkevu okwa 10–20% kwanditutte ku kkomo nga 95% ku mirundi. 21% zokka ku bazannyi abaatuukayo. 28% baamalibwako ssente, 18 ku 61 baasiba buli kye baalina ku kukuba sente kumu, nga ekitundu kimu ku bisatu baamaliriza wansi wa $25 ze baatandika nazo, era ensasulassenteEnsasulaZzaala ewangudde ky'ekomyawo, ekyogerwa nga “X ku 1” okwongera ku ssente za zzaala ezizzibwayo.Soma byonna → ey'ekigero yali $91. Bataano bokka ku 61 abaali bawuliddeko ku Kelly criterion. Ng'olina enkizo, obunene bwa zzaala bwe busalawo oba onoogikuuma; awatali yo, nga ku nnamuziga ow'obwenkanya, tewali bunene buyamba.
Ky'oyinza okukozesa mu kifo kyayo
Awatali nkizo, okusalawo obunene kibuuzo kya nteekateeka y'ensimbi, si kya kukula: ssente za zzaala = ky'oyagala okusaasaanya ku buli kwetooloola, okusinziira ku nteekateeka y'ensimbi eya buli ssaawa n'embiro z'emmeeza (olupapula lw'okuddukanya ssente z'okuzannyisa). Kelly ky'awa omuzannyi owa bulijjo bwe butangaavu bw'eky'okuddamu kye: zeero. Buli ky'osiba okusukka zeero ye bbeeyi y'okuzannya, gy'olondawo ggwe, si eyalongoosebwa ensengekera yonna.
Ebigambo ku kitundu kya Kelly ne “okuddukanya ssente”
Enkola ezitundibwa nga “Kelly ku roulette” eziragira ekitundu ekitakyuka ku ssente z'okuzannyisa ku buli zzaala ziba zzaala ey'omuwendo gumuenteekateekaZzaala ey'omuwendo gumuOkusiba ssente ze zimu buli kwetooloola. Kye kipimo buli kulinnyisa zzaala kwe kugeraageranyizibwako.Soma byonna → nga ssente za zzaala zikendeera. Zifiirwa 2.70% ku mugatte gwa zzaalassenteOmugatte gwa zzaalaOmugatte gwa ssente zonna ezisibiddwa mu kiseera ky'okuzannya oba mu bbanga, nga mw'otwalidde n'amagoba agaddamu okusibwa. Era guyitibwa: handle, action.Soma byonna → era, kubanga ssente za zzaala zikendeera nga bw'ofiirwa, zireetera okumalwako ssente okujja mpola so si obutabaawo. Ngeri ya magezi ey'okuwangaaza enteekateeka y'ensimbi; si Kelly, eyandigambye nti yimirira.
Ensengekera
Ebibuuzo
Ng'olina enkizo epimiddwa okuva ku nnamuziga asosolalaabuNnamuziga asosolaNnamuziga alina obulema mu mubiri bwe obufuula ebinnya ebimu okujja okusinga 1/37. Tebitera kubaawo, era bizuulibwa wokka n'okwetooloola enkumi n'enkumi okuwandiikiddwa.Soma byonna → oba ku kyuma ekipima ebiseera kyokka. Si ku nnamuziga ow'obwenkanya.
Kubanga okubalirira kw'enkizo kulimu ensobi, era okusiba ekingi kufiiriza okusinga okusiba ekitono. Ekitundu kya Kelly kiwa ebitundu bisatu ku bina eby'okukula ku kimu kya kuna eky'enjawulo y'ebivaamuokubalaEnjawulo y'ebivaamuEkipimo ky'engeri ebivaamu gye bisaasaanamu okwetooloola omuwendo ogusuubirwa. Kinene ku straight up, kitono ku zzaala za emu ku emu.Soma byonna →.
Nedda. Kelly alongoosa okukula ng'enkizo weeri. Okuddukanya ssente z'okuzannyisa kufuga okusaasaanya nga tewali nkizo.
Okwesanyusa n'Okubala
Gezaako bino ggwe kennyini okusooka. Buli kugonjoola kuzingiddwa; kuggulewo ng'oli mwetegefu.
Ekyuma kya Thorp ne Shannon ekyalagula kyawa enkizo nga ya 44%. Ku nnamba emu eyalagulwa, Kelly agamba osibe 1.26% ku ssente z'okuzannyisassenteSsente z'okuzannyisaOmugatte gwa ssente ezaawulibwa ku lw'okuzannya. Okuddukanya ssente z'okuzannyisa kwe kusalawo omuwendo gw'oteeka mu kabi ku buli zzaala ne mu buli kiseera ky'okuzannya.Soma byonna →. Kiba kitya singa enkizo y'emu eya 44% yajja ku zzaala emu esaasaanyiziddwa ku nnamba ttaano eziriraanagana?
Laga okugonjoola
Eky'okuddamu Awo Kelly agamba 7.1% ku ssente z'okuzannyisa, era ssente z'okuzannyisa zikula kumpi emirundi mukaaga mangu: nga emirundi obukadde 1.25 mu zzaala 1,000, so nga awalala nga emirundi 11.5.
Straight upzzaalaStraight upEnnamba emu yokka, esasula 35:1.Soma byonna → erina enkizo ya 44% ewangula n'obusoboka bwa 0.04, kubanga 36 × 0.04 = 1.44. Ssente za zzaala eza Kelly ze nkizo nga egabanyizibwa ku mikisa: 0.44/35 = 1.26%. Okukula okwa bulijjo ku buli zzaala kuli 0.04 × ln(1 + 35 × 0.0126) + 0.96 × ln(1 − 0.0126) ≈ 0.00244, kale zzaala 1,000 zikubisaamu ssente z'okuzannyisa nga e^2.44 ≈ 11.5.
Saasaanya ssente za zzaala emu ku nnamba ttaano, zzaala ewangula n'obusoboka bwa 0.20 era esasula 36/5 olwa 1, kwe kugamba 6.2 ku 1: ekyali nkizo ya 44%, kubanga 0.2 × 7.2 = 1.44. Ssente za zzaala eza Kelly zifuuka 0.44/6.2 = 7.10%, n'okukula ku buli zzaala 0.01404, nga emirundi 5.75 okusingawo. Mu zzaala 1,000 ekyo kiba e^14.04, nga obukadde 1.25.
Enkizo y'emu; okukyukakyuka kutono. Zzaala ewangula omulundi gumu ku etaano esobola okutwala omugabo omunene ku ssente z'okuzannyisa awatali kabi k'okumalwako ssente, era okukula kwa Kelly kusasula ekyo. Thorp (1984) akozesa ekyokulabirako kino okulaga lwaki abazannyi abalagula basiba ku bitundu bya nnamuzigannamuzigaEkitundu kya nnamuzigaEkitundu ky'ebinnya ebigoberegana ku nnamuziga, nga kyawukana ku kibinja ku mmeeza ya zzaala.Soma byonna →. Mu nkola, ebinnya ebiriraanyezzaalaEbinnya ebiriraanyeEnnamba emu n'ebinnya bibiri ku buli ludda lwayo ku nnamuziga, cipu ttaano eza straight up.Soma byonna → bitaano birina enkizo ntono katono okusinga ennamba emu esinga (laba Okuzannya Roulette n'Enkizo).
Omuzannyi azudde ebinnyaebikozesebwaEkinnyaKimu ku bisenge 37 ebiriko ennamba ku rotor. Era biyitibwa: slot, cup.Soma byonna → bibiri ebiriraanagana nga buli kimu kijja omulundi 1 ku 25 mu kifo kya 1 ku 37. Asibe splitzzaalaSplitEnnamba bbiri eziriraanaganye, esasula 17:1.Soma byonna → wakati waabyo ku 17 ku 1, oba buli nnamba straight up? Kelly agamba ki, era ssente z'okuzannyisa zikula mangu kyenkana wa bw'ozigerageranya n'ekinnya kimu ekyo?
Laga okugonjoola
Eky'okuddamu Tekirina njawulo: 2.59% ku ssente z'okuzannyisa ku split, oba 1.29% ku buli nnamba. Ssente z'okuzannyisa ezisinga okubaawo zikula nga emirundi 155 mu kwetooloola 1,000, so nga n'ekinnya kimu emirundi 11.5.
Split ewangula n'obusobokaokubalaObusobokaObusoboka bw'ekivaamu, okuva ku 0 okutuuka ku 1 oba 0% okutuuka ku 100%. Ennamba emu: 1/37 = 2.70%.Soma byonna → bwa 2/25 = 0.08 era esasula 17 ku 1, kale ezzaayo 18 × 0.08 = 1.44 ku buli yunitissenteYunitiSsente za zzaala ez'entandikwa enkola oba omuzannyi z'akozesa. Okulinnyisa zzaala kunnyonnyolwa mu yuniti kusobole okukola ku mmeeza yonna.Soma byonna → esibiddwa: enkizo ya 44%, nga ey'ekinnya kimu ekisosola. Ssente za zzaala eza Kelly ze nkizo nga egabanyizibwa ku mikisa: 0.44/17 = 2.59%.
Zzaala bbiri eza straight up eza 1.29% buli emu ziwa ebivaamu bye bimu ddala. Ennamba yonna ku zo bw'ejja, cipussenteCipuAkabonero akakiikirira omuwendo ogutakyuka, akateekebwa ku mmeeza ya zzaala okusiba zzaala. Era kayitibwa: check.Soma byonna → emu ewangula 35 ku 1 ate endala efiirwa, ekituufu kya 34 × 1.29% = 44% ku ssente z'okuzannyisa, nga split bw'esasula; bwe watabaawo ejja, zombi zifiirwa.
Okukula ku buli kwetooloola kuli 0.00505, so nga ku kinnya kimu 0.00244, kale mu kwetooloola 1,000 ssente z'okuzannyisa ezisinga okubaawo zikula e^5.046 ≈ emirundi 155 mu kifo kya e^2.44 ≈ emirundi 11.5. Ennamba bbiri ennungi zigasa nnyo okusinga emirundi ebiri egy'emu, y'ensonga lwaki abazannyi abanoonya okusosola basiba ku bibinja by'ennamba. Thorp (1984) akola okugeraageranya kwe kumu.
Eky'okusesa
Ssente za zzaala eza roulette ezisinga okukuza ye nnamba buli muntu gy'amanyi dda.
Ensibuko
- 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.”