Kelly Criterion e Ruleet
Kelly criterion ina sikkina fijoowo jogiiɗo ɓural ko o foti waɗde pari. E ruleet jaabawol mum ina laaɓi: hay huunde.

Pari Kelly = ɓural / kot. So ɓural ngal ko ɓuri les seero, formil ngol ina rutta feccere ɓurnde les seero, ɗum firti hoto waɗ pari. Kelly criterion ina nafa tawon ngam faamde ko waɗi fijooɓe taarorɗe ooñiiɗe ndenndii pariiji mum hono no ɓe ndenndiri, e ko waɗi woɗɓe ɓee fof ina poti ndenndude pari e bujee.
Kelly criterion
John Kelly (1956) naamnii no fijoowo kaalis jogiiɗo ɓural anndaangal foti ndenndude pariiji mum ngam ɓeydude kaalis parikaalisKaalis pariKaalis fof ko seŋaa ngam fijde. Toppitagol kaalis pari ko ñaawde ko foti waɗeede e kala pari e kala jonnde.Tar fof → makko e juuta ko ɓuri fof. Jaabawol ngol, ngam pari yoɓoyta b e 1, e porobabilitematematikPorobabiliteSahaa njeñtudi, immorde 0 haa 1 walla 0% haa 100%. Limoore wootere: 1/37 = 2,70%.Tar fof → dañde p e porobabilite majjude q = 1 − p, ko waɗde pari feccere f* = (bp − q) / b kaalis pari. f* ɓurɗo seero firti waɗ pari e feccere nde; seero walla ko ɓuri les seero firti hoto waɗ pari. Kelly ina golloo ka Bell Labs, binndol makko, “A new interpretation of information rate”, waɗi caɗeele ɗee nder teori kabaaru Claude Shannon: fijoowo kaalis heɓoowo kabaruuji e laawol jogiingol bayle, e kot potɗi, waawataa ɓeydude kaalis pari mum ko ɓuri yaawngal laawol ngol ina rondoo kabaaru. E 1961 Leo Breiman hollii pari Kelly, e juuta, ina timma ina ɓuri kala dabare woɗnde ceertunde e mum, ina yettina faandaare tabitinaande e ko ɓadii sahaa ɓurɗo famɗude.

Pari Kelly e ruleet
Ngam boɗeerepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof →: b = 1, p = 18/37, q = 19/37; f* = (18/37 − 19/37)/1 = −1/37. Ngam limoore wooterepariLimoore wootereLimoore wootere tan, ina yoɓa 35:1.Tar fof →: b = 35, p = 1/37, q = 36/37; f* = (35/37 − 36/37)/35 = −1/1295. Pari ndenndaandi kala ina rokka feccere Kelly ɓurnde les seero, sabu pari kala ina jogii ɓural ɓurngal les seero, pari ɓurndi moƴƴude ngam ɓeydagol ko seero. Pari Kelly e ruleet ko laawol formil ngam wiyde ko hello ɓural kasino wiyata: alaa ɗowluɗi ɗi pari jogiindi fodaande ɓurnde les seero waawi ɓeydude kaalis pari.
To Kelly nafi
Fijooɓe taarorɗe ooñiiɗe ina njogii ɓural e caɗeele ndenndugol pari. Jagger, García-Pelayo en e Eudaemons en fof ina poti taƴde ko ɓe waɗata pari e ɓural mum ɓe ƴeewtii, waɗde pari seeɗa ina majjina ɓural ngal, waɗde pari keewɗo ina waawi majjinde kaalis fof ado ɓural ngal yiyeede. Ngam suudukuutorɗeSuuduGootel e cuuɗi 37 limoraaɗi e rotoor. Ina noddee kadi: wenndu, kopp.Tar fof → yaltotoondu laabi 1 e nder 30, Kelly ina wiya 0,57% kaalis pari e taarol kala e limoore nde: e $10 000, hono $57 e taarol, ngam ɓeydagol ko ina heewi wonde hono 0,054% e taarol, walla ×1,7 e nder taarle 1 000. Dañal hakkundeejo ko laabi ɗiɗi ɗum, 0,11% e taarol, kono Kelly ina faandii kaalis pari ko ina heewi wonde, wonaa hakkundeejo oo, mo jokkondire seeɗa e baraka ɓeydata. Feccere Kelly ko ko ɓuri suɓeede e golle sabu hiisa ɓural ngal alaa hoolaare.
Ko heewi wonde e hakkundeere
Hakkunde kaalis pari ko heewi wonde e hakkundeejo oo ko yaajɗo. Ƴettu suudu yaltotoondu laabi 1 e nder 25, ɓural 44%, limoore nde Thorp rokki ngam kuuɓal makko. Kelly ina waɗa e mayru pari 1,26% kaalis pari. Caggal taarle 1 000 kaalis pari ko heewi wonde ɓeydiima hono laabi 11,5, tawa hakkundeejo oo, mo jokkondire seeɗa e baraka keewɗo ɓanti, ɓeydiima hono laabi 249. Waɗde pari ɓurɗo Kelly ina ɓeyda hakkundeere ndee ina ustoo njeñtudi ko heewi wonde: e pari Kelly laabi ɗiɗi, kaalis pari ko heewi wonde ina ɓeydoo laabi ɗiɗi tan, e pari Kelly laabi ɗiɗi e feccere ina ustoo, hay so tawii pari kala ina jogii tawon ɓural 44%. Waɗde pari ɓurɗo famɗude coggu mum ko seeɗa: feccere pari ndee ina hettina hono tataɓe nay e nder ɓeydagol ngol.
So ɓural ngal ko sikke
Kelly ina sikki ɓural ngal ko anndaangal. E taabal ngal ko hiisaangal, hiisa ngal kadi ko heewi ina ɓuri toownude. Misal Epstein, mahaaɗo e 44% Thorp, ko limoore yaltii laabi 49 e nder taarle 1 225 taarorde seerotaarordeSeeroSuudu haako wootere nde hay pari njoɓdi fotndi, sappo e ɗiɗi walla kolon kuuɓataa; ko ɗum woni iwdi ɓural kasino. Ina noddee kadi: seero gooto, 0.Tar fof → ɗiɗi: laabi 1 e nder 25, ɓural 44%, pari Kelly 1,26%. Kono taarorde seero ɗiɗi peewnde ina jogii limooje 38, ko ɓuri yaltude e majje ina yettoo 49 walla ko ɓuri e nder taarle 1 225 hono laabi gooto e nder jeenay. Limoore ɓurnde yaltude e kala binndol ko nde baraka ɓuri wallude kadi, ɗum noon hay suudu ooñiindu goonga ina wayi e binndol ko ɓuri no woni: ɗum ko “bone dañoowo”. So tawii suudu ndu ooñaani, pari Kelly ko pari majjotoondi 5,26% e hakkundeere tan. Jaabawol ɗe ɓuri heewde ko waɗde pari feccere Kelly e jokkude limde haa ɓural ngal hiswa e binndol kesol (ƴeew No Taarorde Ruleet Ooñiinde Anndirtee).
Yimɓe jogiiɓe ɓural
Anndude ɓural ngal wonaa huutoraade ngal no moƴƴi. Haghani e Dewey (2016) rokkii yimɓe 61 $25 kala gooto ngam waɗde pari feccere waktu e kaalis mo ɓe mbiyaa ina yalta yeeso 60% sahaa, tawa kaalis dañaaɗo ina haaɗi e $250 (fijooɓe anndi keerol ngol tan nde ɓe njettii ɗum). Kelly ina wiya waɗ pari 20% kaalis pari e yeeso sahaa kala, winndooɓe ɓee ina hiisa pariiji tabitɗi 10–20% ina njettoo keerol ngol hono 95% sahaa. Fijooɓe 21% tan njettii ɗon. 28% majjinii kaalis mum fof, 18 e nder 61 ɓee waɗii fof mum pari e weddugol gootol, hono tataɓal timmini les $25 ɗo ɓe puɗɗorii, njoɓdikaalisNjoɓdiKo pari dañndi ruttata, wiyaa “X e 1” ɓeydaa e pari ruttaaɗo.Tar fof → hakkundeeri ndii ko $91. Yimɓe joy tan e nder 61 ɓee nanno Kelly criterion. So a jogii ɓural, ɗowluɗi pariiji ɗii ina taƴa so a hettinii ngal; so a jogaaki ngal, hono e taarorde peewnde, alaa ɗowluɗi wallata.

Ko huutoree nden
So alaa ɓural, ndenndugol pari ko naamnal bujee, wonaa naamnal ɓeydagol: pari = ko jaɓɗaa ndonkude e taarol kala, ɓaŋngol e bujee waktu e yaawngal taabal ngal (hello toppitagol kaalis pari). Ko Kelly rokki fijoowo jaɓɗo ko laaɓal jaabawol mum: seero. Kala ko waɗɗaa pari ɓurɗo seero ko coggu fijo, ko aan suɓi ɗum, wonaa formil feewnitiiɗo ɗum.
Konngol e feccere Kelly e “toppitagol kaalis”
Sistemji njeeyeteeɗi hono “Kelly ngam ruleet” waajotooɗi feccere tabitnde kaalis pari e pari kala ko pari fotɗidabarePari fotɗiWaɗde pari gooto kala taarol. Ko ɗum kala jokkondiral pari kawrondirtee.Tar fof → e pari ustotooɗo. Ina majjina 2,70% kaalis pariyaaɗo fofkaalisKaalis pariyaaɗo fofKawrital kaalis pariyaaɗo nder jonnde walla sahaa, limtaa kadi kaalis dañaaɗo pariyaaɗo kadi. Ina noddee kadi: handle, action.Tar fof → kadi, sabu pari oo ina ustoo nde majjataa, ina leelna majjinde kaalis fof, wonaa ina waɗa ɗum ko waawaa waɗde. Ko laawol moƴƴol ngam juutinde bujee; wonaa Kelly, kam ina wiya daro.
Formil
Naamne
Tan so ɓural ƴeewtaangal ina woodi, iwde e taarorde ooñiindelaboratuwaarTaarorde ooñiindeTaarorde nde ŋakkeeli mum ɗi fiisik waɗi cuuɗi goɗɗi ina ɓura yaltude 1/37. Ina woowaa, anndetaake si wonaa e taarle ujunaaje winndaaɗe.Tar fof → walla kuuɓal hiisa sahaa. Wonaa e taarorde peewnde.
Sabu hiisa ɓural ngal ina jogii juumre, waɗde pari keewɗo ina ɓuri coggu waɗde pari seeɗa. Feccere Kelly ina rokka tataɓe nay e nder ɓeydagol ngol e nayaɓal wariyaasmatematikWariyaasPeeta no njeñtuɗi saŋkitiri e njaru fodaandu. Ina toowi ngam limoore wootere, ina lesɗi ngam pariiji njoɓdi fotndi.Tar fof → oo.
Alaa. Kelly ina feewnita ɓeydagol so ɓural ina woodi. Toppitagol kaalis pari ina toppita ndonkugol so ɓural alaa.
Weltaare e Matematik
Etu ɗum hoore maa adii. Kala jaabawol ina suuɗii; uddit ɗum so a heblii.
Kuutorgal hiinnirgal Thorp e Shannon ina rokkayno ɓural hono 44%. E limoore wootere hiinnaande, Kelly ina wiya waɗde pari 1,26% kaalis parikaalisKaalis pariKaalis fof ko seŋaa ngam fijde. Toppitagol kaalis pari ko ñaawde ko foti waɗeede e kala pari e kala jonnde.Tar fof →. Ko honɗum waɗata so ɓural 44% gootal ngal arii e pari gootal senndangal e limooje joy ɗe ndeenondiri?
Hollu jaabawol ngol
Jaabawol Ndeen Kelly ina wiya 7,1% kaalis pari, kaalis pari ina ɓeydoo yaawde hono laabi jeegom: hono 1,25 miliyoŋ laabi e nder pariiji 1 000, e yeeso hono 11,5 laabi.
Pari limoore wooterepariLimoore wootereLimoore wootere tan, ina yoɓa 35:1.Tar fof → joginngal ɓural 44% ina daña e porobabilite 0,04, sabu 36 × 0,04 = 1,44. Pari Kelly ko ɓural ngal senndaa e kot: 0,44/35 = 1,26%. Ɓeydagol aadanteengol e kala pari ko 0,04 × ln(1 + 35 × 0,0126) + 0,96 × ln(1 − 0,0126) ≈ 0,00244, ɗum waɗi pariiji 1 000 ina keewna kaalis pari hono e^2,44 ≈ 11,5.
Sennd pari gootal e limooje joy, pari ngal ina daña e porobabilite 0,20 ina yoɓa 36/5 ngam 1, ɗum ko 6,2 e 1: ɓural ngal ko 44% tan, sabu 0,2 × 7,2 = 1,44. Pari Kelly ina wonta 0,44/6,2 = 7,10%, ɓeydagol e kala pari 0,01404, hono laabi 5,75. E pariiji 1 000 ɗum ko e^14,04, hono 1,25 miliyoŋ.
Ɓural ngal ko gootal; yahdi-ngartaali ɗii ɓuri famɗude. Pari dañata laabi gooto e nder joy ina waawi roondaade geɗal kaalis pari ɓurngal mawnude tawa hulataa majjinde kaalis fof, ɓeydagol Kelly ina yoɓa ɗum. Thorp (1984) ina huutoroo misal oo ngam hollude ko waɗi fijooɓe hiinnooɓe ina mbaɗa pari e geɗe taarordetaarordeGeɗal taarordeCeeɓnde cuuɗi takkondirɗi e taarorde, ceertunde e mooftere e tapi.Tar fof →. E golle, takkoyɗepariTakkoyɗeLimoore e cuuɗi ɗiɗi e kala sera mayre e taarorde, jetoŋji joy limoore wootere.Tar fof → joy ina njogii ɓural famɗungal seeɗa e limoore wootere ɓurnde moƴƴude (ƴeew Fijo Ɓural e Ruleet).
Fijoowo heɓii cuuɗikuutorɗeSuuduGootel e cuuɗi 37 limoraaɗi e rotoor. Ina noddee kadi: wenndu, kopp.Tar fof → ɗiɗi ɗe ndeenondiri ɗe kala e majji yaltata laabi 1 e nder 25 nde wonaa 1 e nder 37. Hol ko foti, waɗde pari limooje ɗiɗipariLimooje ɗiɗiLimooje ɗiɗi takkondirɗe, ina yoɓa 17:1.Tar fof → hakkunde majji e 17 e 1, walla kala limoore e pari limoore wootere? Kelly ina wiya no foti, ɓeydagol kaalis pari ina yaawi no foti so yerondiraa e suudu wootere nii?
Hollu jaabawol ngol
Jaabawol Ceerondiral alaa: 2,59% kaalis pari e limooje ɗiɗi, walla 1,29% e kala limoore. Kaalis pari aadanteeɗo ina ɓeydoo hono laabi 155 e taarle 1 000, e yeeso laabi 11,5 e suudu wootere.
Limooje ɗiɗi ina daña e porobabilitematematikPorobabiliteSahaa njeñtudi, immorde 0 haa 1 walla 0% haa 100%. Limoore wootere: 1/37 = 2,70%.Tar fof → 2/25 = 0,08 ina yoɓa 17 e 1, ɗum waɗi ina rutta 18 × 0,08 = 1,44 e kala initekaalisInitePari fuɗɗoode mo sistem walla fijoowo gollirta. Jokkondirɗe pari ina cifee e initeeji ngam ɗi kuutoroo e kala taabal.Tar fof → pariyaande: ɓural 44%, gootal e suudu ooñiinde wootere. Pari Kelly ko ɓural ngal senndaa e kot: 0,44/17 = 2,59%.
Pariiji limoore wootere ɗiɗi 1,29% kala e majji ina ngaddi njeñtuɗi gooto tigi. So limoore gooto e majje yaltii, jetoŋkaalisJetoŋMaande hollirde kaalis tabitiiɗo, waɗetee e tapi ngam waɗde pari. Ina wiyee kadi: check.Tar fof → gooto ina daña 35 e 1, goɗɗo oo ina majja, laaɓɗum 34 × 1,29% = 44% kaalis pari, hono no limooje ɗiɗi njoɓirta; so hay gooto yaltaani, ɗiɗo ɓee fof ina majja.
Ɓeydagol e kala taarol ko 0,00505, e yeeso 0,00244 e suudu wootere, ɗum waɗi e taarle 1 000 kaalis pari aadanteeɗo ina ɓeydoo e^5,046 ≈ 155 laabi, wonaa e^2,44 ≈ 11,5 laabi. Limooje moƴƴe ɗiɗi ina ɓuri foti fotde laabi ɗiɗi gootol, ɗum ko waɗi fijooɓe ooñol ina mbaɗa pari e mooftirɗe limooje. Thorp (1984) ina waɗa yerondiral gootal ngal.
Ƴeewndo weltinoowo

Pari ruleet ɓurndi moƴƴude ngam ɓeydagol ko limoore nde kala gooto anndi kisa.
Iwdi
- 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.”