Matematik Ruleet · Caɗeele matematik · hojomaaji 7

Caɗeele: Sappo e Ɗiɗi Ɗiɗi e Jetoŋ Gooto

Sappo e ɗiɗi ɗiɗi ina kupi limooje 24. Ɓeydu jetoŋ e seero, a hupii 25. Mbele asurans oo ina nafa?

Jaabawol rabbiɗngol

Alaa. Feccere kala ko −2,70% pari mum, ɗum noon kawtal ngal ko −2,70% pari fof. Caɗeele ɗee ina njaha e ko waɗi, ina hiisa senndugol goonga ngol, ina holla ko waylotoo (mbaadi ndi) e ko waylotaako (coggu ngu).

sappo e ɗiɗi ɗiɗi
24/37 · laaɓɗo +1 walla −2
ɓeydi seero
25/37 hupaaɗe
EV e inite kala
−1/37 e kala no wayri
ekkitinol
EV ina kawtoo

Caɗeele ɗee

A waɗii pari $10 e sappo e ɗiɗipariSappo e ɗiɗi1–12, 13–24 walla 25–36, ina yoɓa 2:1.Tar fof → adannde, $10 e sappo e ɗiɗi ɗimmere e $1 e 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 →. (a) Hol ko ngoni njeñtuɗi waawooɗi e porobabilite mum? (b) Hol ko woni njaru fodaandumatematikNjaru fodaanduNjeñtudi hakkundeere e kala pari e juuta. −1/37 pari ngam kala pari Orop laawol.Tar fof → ndee? (c) Mbele jetoŋkaalisJetoŋMaande hollirde kaalis tabitiiɗo, waɗetee e tapi ngam waɗde pari. Ina wiyee kadi: check.Tar fof → seero oo ina moƴƴina pari ndii?

Jaabawol (a) e (b)

Njeñtuɗi: balkuutorɗeBalBal tokoosal werlaangal e laawol ngol e laawol rotoor ngol. Balli jamaanu hannde ko ivorine walla Teflon, 18–21 mm.Tar fof → e 1–24 (cuuɗikuutorɗeSuuduGootel e cuuɗi 37 limoraaɗi e rotoor. Ina noddee kadi: wenndu, kopp.Tar fof → 24): sappo e ɗiɗi gooto ina yoɓa $20, goɗngo ngoo ina majjina $10, seero ina majjina $1: laaɓɗo +$9. Bal e 25–36 (cuuɗi 12): sappo e ɗiɗi ɗiɗi ɗii fof ina majja, seero ina majja: −$21. Bal e seero (suudu 1): sappo e ɗiɗi ɗii ina majjina $20, seero ina yoɓa $35: +$15. EV = (24 × 9 + 1 × 15 − 12 × 21)/37 = (216 + 15 − 252)/37 = −21/37 ≈ −$0,57 e taarol kala e $21 pariyaaɗo: 2,70%.

njeñtudicuuɗiporobabilitenjeñtudi
1–242464,9%+$9
25–361232,4%−$21
012,7%+$15
fodaandi−$0,57 = 2,70% $21

Jaabawol (c)

Tawa alaa jetoŋ seero: (24 × 10 − 13 × 20)/37 = (240 − 260)/37 = −20/37 ≈ −$0,54 e $20 pariyaaɗo, ɗum kadi 2,70%. Jetoŋ seero oo waylii njeñtudi seero −$20 ndii ngam waɗde +$15 (moƴƴugol $35 laabi gooto e nder 37, ɗum foti $0,95 e taarol kala), ina coggoo $1 e taarle 36 goɗɗe ɗee ($0,97 e taarol kala). Waylo laaɓngo: −$0,03 e taarol kala, ɗum ko 2,70% dolaar ɓeydaaɗo oo. Asurans oo ina coggoo tigi hono kala huunde woɗnde.

Ko waɗi ɗum ina fawii e fof

Njaru fodaandu ina kawtoo. Kala pariiji waɗaaɗi e sahaa gooto, EV mum ina fota e kawtal EV feccere kala, tawa kala e mum ko −1/37 pari mum. Ɗum noon kala kawtal ko −1/37 pari fof. Alaa no jetoŋji ndenndirtee e tapikuutorɗeTapiKaare pariiji winndaande e taabal. Ina noddee kadi: taabal, feetere, sanyo.Tar fof → oo, hay so ɗi keewii, daɗata ɗum; kuutorgal Mahoowo Pari ina tabitina ɗum ngam kala pariiji ɗi mbaawɗaa waɗde. Ko kawtal ngal waylata ko senndugol ngol: no ɗum heewiri dañde, ko foti, e no ko ɓuri bonde wayi.

$21 gooto oo e laabi tati: porobabilite dañde e ko ɓuri bonde
$21 e boɗeere: p(dañde)
48,6% · ko ɓuri bonde −$21
sappo e ɗiɗi ɗiɗi + seero: p(dañde)
67,6% · ko ɓuri bonde −$21
$21 e 17: p(dañde)
2,7% · ko ɓuri bonde −$21
033,8067,6% · ko ɓuri bonde −$21
Tati ɗii fof ina njogii EV −$0,57 e taarol kala. Ina ceerti tan e mbaadi.

Naamnal jokkowal ɓurngal caɗude

Yiytu kawtal pariiji ndenndaaɗi hupooji limooje 37 ɗee fof. Sappo e ɗiɗi tati ($10 kala) ɓeydi $1 e seero: kala e 1–36 ina rokka laaɓɗo −$1 (sappo e ɗiɗi gooto ina yoɓa $20, ɗiɗi goɗɗi ɗii ina majjina $20, seero ina majjina $1), seero kadi ina rokka +$35 − $30 = +$5. EV = (36 × (−1) + 5)/37 = −31/37 e $31 pariyaaɗo: 2,70%. A waawii hoolnaade wonde huunde haawnataa ma abadaa, kono a yoɓat tawon coggu gooto oo ngam ndeen ndimaagu.

Formil

EV(kawtal) = Σ EV(pecce) = −(pari fof)/37

Naamne

Mbele kawtal pariiji ina woodi jogiingal ɓural ɓurngal famɗude?

Alaa, e taabal Orop. E taabal Farayse, pariiji njoɓdi fotndipariPari njoɓdi fotndiBoɗeere/ɓaleere, peccotaake/peccotoonde, mawɗe/tokooseeje. Limooje 18, ina yoɓa 1:1.Tar fof → tan ko 1,35%; ɓeydude kala huunde woɗnde ina ɓeyda ɓural jillaangal ngal.

Waɗde pari e boɗeere e ɓaleere fof nden?

Ina majjina $1 e $1 kala e seero tan, dañataa hay huunde so wonaa ɗum. EV −2,70% tawa alaa nafoore: ɗum ko kawtal gootal ngal alaa nafoore fey.

Ko waɗi nden kawtirtee pariiji?

Ngam suɓaade mbaadi jonnde nde weltoto-ɗaa. Ɗum ko daliilu goonga, ko ngu gootu tan.

Ƴeewndo weltinoowo

Asurans e taabal ruleet ina coggoo tigi ko o hisnata.

Asurans e taabal ruleet ina coggoo tigi ko o hisnata.

Iwdi

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Pecco 13, ruleet.
ƴeewtaa 2026-09-28misal: ruleet Orop, seero gootolaawol golle ↗iwdi ↗