Wariyaas
Ko waɗi pari limoore wootere e pari boɗeere jogiiɗi majjere fodaandematematikMajjere fodaandeNjaru fodaandu fiyaandu e kaalis pariyaaɗo fof; ko hakkundeere kaalis majjataako nder jonnde walla nder sahaa.Tar fof → wootere ina keɓtinee hono fijooji ceertuɗi.

Wariyaas ina ƴeewa no njeñtuɗi ina caggitoo e sara njaru fodaandu. E kala inite pariyaande ko hedde 34 e limoore wootere e hedde 1 e boɗeere.
Formil pari gootal
E pari yoɓoyngal W e 1 e porobabilitematematikPorobabiliteSahaa njeñtudi, immorde 0 haa 1 walla 0% haa 100%. Limoore wootere: 1/37 = 2,70%.Tar fof → p, njeñtudi e kala initekaalisInitePari fuɗɗoode mo sistem walla fijoowo gollirta. Jokkondirɗe pari ina cifee e initeeji ngam ɗi kuutoroo e kala taabal.Tar fof → ko +W e porobabilite p e −1 e porobabilite 1 − p. Njaru fodaandumatematikNjaru fodaanduNjeñtudi hakkundeere e kala pari e juuta. −1/37 pari ngam kala pari Orop laawol.Tar fof → ko pW − (1 − p) = −1/37. WariyaasmatematikWariyaasPeeta no njeñtuɗi saŋkitiri e njaru fodaandu. Ina toowi ngam limoore wootere, ina lesɗi ngam pariiji njoɓdi fotndi.Tar fof → ko E[X²] − EV² = pW² + (1 − p) − (1/37)². E limoore wooterepariLimoore wootereLimoore wootere tan, ina yoɓa 35:1.Tar fof →: (1/37)(1225) + 36/37 − 0,0007 ≈ 34,08. E boɗeerepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof →: 18/37 + 19/37 − 0,0007 ≈ 0,999.
Ko ɗum firti e jonnde
Wariyaasji ina ɓeydondira e taarle ceertuɗematematikTaarle ceertuɗeKala taarol ina jogii porobabiliteeji gooti, no ko ɓenni wayiri fof. Ko ɗum woni ɓuuɓre kala hasbugol e lowre ndee.Tar fof →, ɗuum waɗi e taarle N e pari tabitngal wariyaas kawrital ngal ko N × pari² × σ², seerndu ndenndaandumatematikSeerndu ndenndaanduRaasin karee wariyaas; ko woɗɗeende aadanteende njeñtudi e njaru fodaandu.Tar fof → kadi ko σ × pari × √N. Taarle 100 e $10: seerndu ndenndaandu ko hedde $584 e limooje wootere e $100 e boɗeere, e sara njeñtudi fodaandi gootu ndun −$27. Fijoowo gooto ina yi’a njeñtuɗi ina njaaɓoo e teemedde; goɗɗo oo ina yi’a yahdu newngu. Ɓe ɗiɗo fof ina njoɓa coggu gootu ngun.
Wariyaas e sistemji
Jokkondiral paridabareJokkondiral pariKala sariya waylowo pari e njeñtuɗi ɓennuɗi. Jokkondiral caggal majjere ina ɓeyda pari caggal majjere, caggal dañal ina ɓeyda ɗum caggal dañal.Tar fof → waylataa EV e kala inite pariyaande kono ina waylita kaalis pariyaaɗo e mbaadi senndugol ngol. MartingaledabareMartingaleJokkondiral pari ɓeydoowo pari ɗiɗi laabi caggal kala majjere. Ƴeew hello Dabareeji ngam anndude ko ngal waɗata e ko ngal waɗataa.Tar fof → ina ustoo wariyaas jonɗe ɓurɗe heewde (dañe tokooɗe keewɗe) kadi ina ɓeyda geɗal sakkitiingal ɓutto (majjere mawnde nde heewaa); wariyaas kawrital e jonɗe fof ina ɓura pari fotɗidabarePari fotɗiWaɗde pari gooto kala taarol. Ko ɗum kala jokkondiral pari kawrondirtee.Tar fof → sabu ngal geɗal. ParolidabareParoliJokkondiral pari caggal dañal: ɓeydu pari ɗiɗi laabi caggal dañal, ruttu e fuɗɗoode caggal majjere walla caggal dañe tati jokkondirɗe. Ina noddee kadi: Martingale huccitinaangal.Tar fof → ina waɗa ko huccondiri e ɗum. Suɓaade sistem ko suɓaade mbaadi wariyaas; hakkundeere nde suɓotaake.
- p10 −$500
- p25 −$500
- medyan −$500
- p75 +$40
- p90 +$1 120
Dabare Ruleet Pari FotɗiDabare Ruleet Paroli (Martingale Huccitinaangal)
Ko waɗi ɗum ina jogii maanaa ngam fijoowo
Ko wariyaas waɗata jonɗe gaɗaaɗe ina anndaaka e juutɗe ina anndee. E σ = $100 e EV = −$27 e taarle 100, ɓural ngal ko nayaɓal bayle sahaa, jonnde dañal kadi ko huunde aadanteende. E taarle 10 000 EV ko −$2 700 tawa σ ko $1 000; ɓural ngal jooni ina hedde laabi tati bayle sahaa, jokkondiral dañal kadi ko huunde tati-sigma. Wariyaas ko giɗo fijoowo e sahaa gaɗaaɗo, ko giɗo kasino e juuta.
Wariyaas jokkondiral pariiji
E pariiji keewɗi e taarol gootol, njeñtuɗi ina njowondiri (dañal e 17 ko dañal e ɓaleerepariƁaleerePari njoɓdi fotndi e limooje 18 ɓaleeje. E Farayse: noir.Tar fof → e sappo e ɗiɗipariSappo e ɗiɗi1–12, 13–24 walla 25–36, ina yoɓa 2:1.Tar fof → ɗimmere), ɗuum waɗi wariyaasji ɓeydondirtaa tan. Kuutorgal Mahoowo Pari ina hiisa senndugol potngol e kala jetoŋjikaalisJetoŋMaande hollirde kaalis tabitiiɗo, waɗetee e tapi ngam waɗde pari. Ina wiyee kadi: check.Tar fof → ɓe njoɗɗiɗaa so limtii njeñtuɗi 37 ɗii fof, ɗum tan woni laawol goongaangol.
Formil
Naamne
Alaa. Kala pari ina jogii njaru fodaandu wootu ndun. Wariyaas ɓurɗo toowde ina firta jaaɓooje ɓurɗe yaajde e sara mayru.
Pariiji njoɓdi fotndipariPari njoɓdi fotndiBoɗeere/ɓaleere, peccotaake/peccotoonde, mawɗe/tokooseeje. Limooje 18, ina yoɓa 1:1.Tar fof →, e σ ≈ 1 e kala inite. Ina ɓura lesde e la partagesariyaLa partageSariya Farayse: so seero yalti, feccere pari njoɓdi fotndi ina ruttee. Ina feccita ɓural kasino e pariiji ɗii haa 1,35%.Tar fof →, nde moƴƴintoo hakkundeere nde kadi.
Dañal fodaangal ko gootal e kala dolaar; wariyaas ina laatoo tan e no naafore kasino ina jaaɓoo, kasino kadi ina jogii fijooɓe ujunaaji ngam fotnude ɗum.
Weltaare e Matematik
Etu ɗum hoore maa adii. Kala jaabawol ina suuɗii; uddit ɗum so a heblii.
Fijooɓe ɗiɗo ina mbaɗa pari $1 e kala taarol taarle 100 e taarorde Orop, gooto sahaa fof e boɗeerepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof →, goɗɗo oo sahaa fof e 17. Hol ɓurɗo waawde wonde e dañal e gasirde?
Hollu jaabawol ngol
Jaabawol Fijoowo 17 oo: 50,9%, e yeeso 35,5% ngam boɗeere. Ɓe ɗiɗo fof ina majjina $2,70 e hakkundeere.
Boɗeere: fijoowo oo ina woni e dañal so dañii 51 walla ko ɓuri e nder 100, kala e majje e porobabilitematematikPorobabiliteSahaa njeñtudi, immorde 0 haa 1 walla 0% haa 100%. Limoore wootere: 1/37 = 2,70%.Tar fof → 18/37. Senndugol binomiyal ina addi 35,5%, dañe 50 tigi, nokku fotde, 7,7% goɗɗo.
Limoore 17: kala dañal ina rutta $36, ɗum waɗi dañe ɗiɗi (−$28) yonaani, tati (+$8) ina yonii. Porobabilite hawrugol tati walla ko ɓuri e taarle 100 e 1/37 ko 50,9%.
Fijoowo limoore wootere ina ɓuri wonde e dañal, kono njeñtuɗi ɗee ina ɓuri diwde: hawrugol gootol ɓeydaangol walla ustaangol ina dirna njeñtudi ndii $36, fijooɓe ngonɓe e majjere ina ɓuri woɗɗude sahaa heewɗo. Bollman (2024) ina rokka limooje Amerik ɗee, 26,5% e 49,2%.
Ƴeewndo weltinoowo

Majjere fodaande wootere. Gooto e maɓɓe ina wiya ma ɗum e daande toownde.
Iwdi
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.