Porobabilite Jokkondire e Ruleet
Jokkondire juutɗe noone wootere ina heewi. Ɗe njogaaki kadi hay maanaa e taarol garoowol.
Boɗeeje joy jokkondirɗe: 2,7%. Sappo: 0,074%. E jonnde taarle 200, jokkondiral noone wootere jeegom ina ɓura heewde wonde e ko ɗum alaa.
No majjereeji jokkondirɗi ngarirta sahaa kala
Pari njoɓdi fotndi e taarorde seero gooto ina majja taarle 19 e 37. Kala gongol ko porobabilite kala taarle jokkondirɗe limtaaɗe majja, e ko fijoowo Martingale, ɓeydoowo pari laabi ɗiɗi caggal kala majjere, majjini haa ndeen.
| majjereeji jokkondirɗi | sahaa | hedde 1 e | majjinaaɗo haa jooni | pari garoowo |
|---|---|---|---|---|
| 1 | 51,4% | 2 | $1 | $2 |
| 2 | 26,4% | 4 | $3 | $4 |
| 3 | 13,5% | 7 | $7 | $8 |
| 4 | 7,0% | 14 | $15 | $16 |
| 5 | 3,6% | 28 | $31 | $32 |
| 6 | 1,8% | 55 | $63 | $64 |
| 7 | 0,94% | 106 | $127 | $128 |
| 8 | 0,48% | 207 | $255 | $256 |
| 9 | 0,25% | 403 | $511 | $512 |
| 10 | 0,13% | 784 | $1 023 | $1 024 |
| 11 | 0,065% | 1527 | $2 047 | $2 048 |
| 12 | 0,034% | 2974 | $4 095 | $4 096 |
| 13 | 0,017% | 5792 | $8 191 | $8 192 |
| 14 | 0,0089% | 11279 | $16 383 | $16 384 |
| 15 | 0,0046% | 21965 | $32 767 | $32 768 |
Porobabilite ndee ko 19/37 fiilaaɗo e hoore mum laabi foti e majjereeji, limtaaɗi gila e taarol gootol anndaangol. Jonnde juutnde ina jogii taarle keewɗe ɗe jokkondiral ngal waawi fuɗɗaade, ɗum noon e nder kikiiɗe gootol ina ɓuri wonde no feewi ko gongol gootol hollata.
Jokkondiral gootal
PorobabilitematematikPorobabiliteSahaa njeñtudi, immorde 0 haa 1 walla 0% haa 100%. Limoore wootere: 1/37 = 2,70%.Tar fof → wonde taarle k garooje fof ko boɗeejepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof → ko (18/37)ᵏ. Ɗiɗi: 23,7%. Joy: 2,7%. Sappo: 0,074%, hedde 1 e nder 1 350. Noogas: 1 e nder miliyoŋ 1,8. Noogas e jeegom, rekoor Monte-Carlo: 1 e nder miliyoŋaaji 137. Ɗee ko porobabiliteeji jokkondiral ganndaangal fuɗɗoyngal e taarol ganndaangol, ɗum ko naamnal ngal hedde hay gooto naamnotaa.
E jonnde
Naamnal ngal yimɓe njiɗi ko “mbele jokkondiral k ina ummoo e nokku e jonnde am?”, jaabawol ngol kadi ina ɓura (18/37)ᵏ no feewi sabu jonnde taarle 200 ina rokka hedde nokkuuji 200 ɗo jokkondiral waawi fuɗɗaade. Jokkondiral jeegom walla ko ɓuri e noone wootere, boɗeere walla ɓaleerepariƁaleerePari njoɓdi fotndi e limooje 18 ɓaleeje. E Farayse: noir.Tar fof →, ina ummoo e jonnde taarle 200 e hedde 94% sahaaji; jeetati walla ko ɓuri hedde 47%; sappo walla ko ɓuri hedde 14%. Inndu noone ndee ado, sahaaji ɗii ina ustoo, haa hedde 75%, 27% e 7%. Fijoowo jooɗiiɗo jemma fof ina yi’a jokkondire juutɗe kala jemma.
Ko waɗi Martingale ina hirjina ɗum
Kala 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 → ɓeydagol caggal majjere ina jogii juutal jokkondiral ngal helata ɗum: majjere jeegom gila $10 haa keerol $500, sappo ngam FibonaccidabareFibonacciJokkondiral pari jokkiingal tolno 1, 1, 2, 3, 5, 8, 13…: daawal gootal yeeso caggal majjere, daawe ɗiɗi gartude caggal dañal.Tar fof →, joy ngam fiɓde laabi tati e sappo e ɗiɗipariSappo e ɗiɗi1–12, 13–24 walla 25–36, ina yoɓa 2:1.Tar fof →. Porobabilite jokkondiral majjere jeegom e njoɓdi fotndi ko (19/37)⁶ ≈ 1,8% e kala etagol, jonnde taarle 200 kadi ina waawi jogaade etagol 100 hedde, ɗuum waɗi helgol ngol ina wara e hedde jonɗe nay e nder joy ɗe juutal ngal. Porobabilite jokkondire e ruleet ko ɗum waɗi ndeen yaltaare heewaani.
Limooje wulɗe e jaanguɗe
Limto gootol ngol ina huutoree e limooje wooterepariLimoore wootereLimoore wootere tan, ina yoɓa 35:1.Tar fof →. E taarle 300, limoore fodaande e kala limoore ko 8,1; seerndu ndenndaandumatematikSeerndu ndenndaanduRaasin karee wariyaas; ko woɗɗeende aadanteende njeñtudi e njaru fodaandu.Tar fof → ko hedde 2,8. Limoore woɗnde ina holla dañe 15 e goɗnde 2 e sahaa tan, kala sahaa. Tabalo njeñtuɗi jalbinoowo limooje “wulɗe” ina jalbina hoore senndugol normal. Laboratuwaar ina firta no taarle foti ado limoore wulndemiijo juumɗoLimoore wulndeLimoore yaltunde ko ɓuri ko fodaa ko ɓooyaani. E taarorde peewnde, nde anndintaa hay huunde.Tar fof → jogaade hay maanaa (ujunaaji, e taarorde wootere anndaande).
Ceertugol ko ɗum fof
Jokkondiral boɗeeje sappo waɗataa ɓaleere ina ɓura sahaa, waɗataa kadi boɗeere ina ɓura sahaa. Ɗe ɗiɗi fof ko 18/37. Jokkondire ko ngonka jokkondire sahaa, so ɗe ngalaa ko ɗum ɓuri jeertinde: jokkondiral taarle 200 ngal alaa jokkondiral ɓurngal nay juutde ina ɓura no feewi seedeede wonde waylaama e dow ngal jogiingal jokkondiral sappo e ɗiɗi.
Formil
Naamne
Ɓaleeje 26 to Monte-Carlo, 18 Ut 1913, ko ngal anndaangal. Boɗeeje 32 jokkondirɗe ina mbiyaa e kasino Amerik e 1943. Ɗi ɗiɗi fof ina potti e sahaa so ƴeewaama taarle keewɗe ɗe kasinooji ngaɗata.
Ko 18/37 e kala laawol. Waɗ pari e ko feere maa wiyi, walla hay huunde.
Alaa. Ooñol ina yiyee nde cuuɗikuutorɗeSuuduGootel e cuuɗi 37 limoraaɗi e rotoor. Ina noddee kadi: wenndu, kopp.Tar fof → goɗɗi ina ɓura heewde ummaade e ujunaaji taarle, wonaa jokkondire noone.
Weltaare e Matematik
Etu ɗum hoore maa adii. Kala jaabawol ina suuɗii; uddit ɗum so a heblii.
Taarle taarorde Orop njelu ngoni e hakkundeere ngam limooje 37 ɗee fof yaltude kala e majje laabi gooto tal?
Hollu jaabawol ngol
Jaabawol Hono taarle 155 e hakkundeere; medyan ko 147.
Limtu fadde nde limoore hesere wootere e wootere. Taarol adanngol ina holla limoore hesere sahaa fof. So a yi'ii limoore 1, cuuɗikuutorɗeSuuduGootel e cuuɗi 37 limoraaɗi e rotoor. Ina noddee kadi: wenndu, kopp.Tar fof → 36 e nder 37 ko kese, ɗum waɗi limoore hesere garoore ndee ina naamnoo taarle 37/36 e hakkundeere. So a yi'ii limooje k, ina naamnoo 37/(37 − k).
Ɓeydin fadde ɗee: 37/37 + 37/36 + 37/35 + … + 37/1 = 37 × (1 + 1/2 + 1/3 + … + 1/37) ≈ 37 × 4,20 = 155,5 taarle.
Ko ɓuri heewde e majji ko gasirde ndee. Limoore sakkitiinde ndee tan ina naamnoo taarle 37 e hakkundeere, ɗe joy sakkitiiɗe ɗee hono 85. E taarorde Amerik, ɓeydondiral gootal ngal ina addi hono 161. Ɗum ko caɗeele moɓtoowo kupon; hakkundeere wootere nde ina yalta e limngal ganndaangal.
E taarle 37 taarorde Orop, taarol gootol e kala suudu, limooje ceertuɗe njelu fodaa yi'ude?
Hollu jaabawol ngol
Jaabawol Hono 23,6. Hono tataɓal limooje ɗee, hono 13, ɗe njaltataa fey.
Ƴettu limoore wootere, hono 17. E kala taarol porobabilite nde yaltataa ko 36/37, ɗum waɗi nde ina majja taarle 37 ɗee fof e porobabilite (36/37)³⁷ ≈ 0,363.
Kala limoore jogii porobabilite gootal ngal, ɗum waɗi e hakkundeere 37 × 0,363 ≈ 13,4 limooje ina majji, 37 − 13,4 ≈ 23,6 ina njalta, heewɗe e majje laabi ɗiɗi walla ko ɓuri.
Fijooɓe ruleet ina noddira ɗum sariya tataɓe. Ɗum wonaa sariya, ko limngal fillitagol tan: e jokkondiral juutngal hono taarorde ndee, hono tataɓal limooje ɗee ina njooɗoo, e taarorde peewnde hono e goɗnde fof. E cuuɗi 38 geɗal ngal ko (37/38)³⁸ ≈ 0,363 kadi; e taarorde mawnde ina tabita takko 1/e ≈ 0,368.
Sehil maa ina holla ma doggol ɗiɗi nooneeji 50, boɗeerepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof → walla ɓaleerepariƁaleerePari njoɓdi fotndi e limooje 18 ɓaleeje. E Farayse: noir.Tar fof →, kala e majji ina wiyee ko iwi e taarorde ɗe 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 → accaama. Gootol ngol ina waylita noone laabi 25, jokkondiral mum ɓurngal juutde ko jeegom. Goɗngol ngol ina waylita laabi 35, ɓurtaani tati fey. Hol ngol tafaa?
Hollu jaabawol ngol
Jaabawol Ɗimmol ngol. Doggol goonga ina waylita hono laabi 24 walla 25. Ngol waylitii laabi 35 ina yalta hono laabi gooto e nder doggi 500, ngol alaa jokkondiral ɓurngal tati hono laabi ɗiɗi e nder 100.
Kala noone hesere ina fillita ko adii walla ina waylita, feccere e feccere, ɗum waɗi kaawe 49 waylitagol ina ndokka waylitagol 24,5 e hakkundeere, ɓeydi walla ustii hono 3,5. Capanɗe tati e joy ko tappe tati ɗee ɓurɗe hakkundeere ndee; taarorde peewnde ina addi waylitagol ngol keewngol hono laabi gooto e nder doggi 500.
Jokkondire ɗee ina mbiya ko gootum. Doggol goonga nooneeji 50 ina jogii jokkondiral nay walla ko ɓuri hono 98% sahaa, jokkondiral mum ɓurngal juutde ko ɓuri heewde ko joy walla jeegom.
Yimɓe ɗe njamaa tafde doggol sahaa ina mbaylita ko ɓuri, sabu jokkondiral nay walla joy ina wona e gite maɓɓe ko feere. Taylor (2021) ina holla maande wootere nde e doggi werle kaalis ɗe almuɓɓe tafi: sahaa goonga ina heewi jokkondire ko ɓuri ko yimɓe sikki.
Deftere taariki kasino ina yeewta fijoowo mo limoore mum yalti laabi joy e jokkondiral, ina noddira ɗum rekoor. Ko honno ɗum hewtortoo e taarorde Orop? Hol no ɗum foti waɗirde nde kala e nder kasino gooto joginɗo taabalji 20, kala e majji ina taarna laabi 40 e kala waktu, ñalawma e jemma?
Hollu jaabawol ngol
Jaabawol Limoore innaande yaltude laabi joy e jokkondiral: 1 e nder 69 miliyoŋ. Kala limoore yaltude laabi nay goɗɗe caggal nde yalti adii: 1 e nder 1,87 miliyoŋ. Kasino oo ina taarna hono 7 miliyoŋ laabi e hitaande, ɗum waɗi ina foti yi'ude jokkondiral joy laabi tati walla nay e hitaande.
Limoore innaande ina yalta e porobabilite 1/37 e kala taarol, ɗum waɗi joy e jokkondiral ina jogii porobabilite (1/37)⁵ = 1 e nder 69 343 957. Kono alaa mo inndata limoore ndee adii. Ko yalti adii fof, taarle nay garooje ɗee ina poti fillitaade: (1/37)⁴ = 1 e nder 1 874 161.
Taabalji 20 × taarle 40 × waktuuji 24 × ñalɗi 365 = taarle 7 008 000 e hitaande. Kala taarol ina waawi fuɗɗude jokkondiral, ɗum waɗi kasino oo ina fodaa 7 008 000/1 874 161 ≈ 3,7 jokkondire joy e hitaande.
Alaa rekoor laawɗinaaɗo e ɗum, ɗum alaa nafoore: huunde seeɗa e taabal gootal ko huunde ñalawmaare e kasino fof, taariki ɗee ina yeewtee e taabal ngal ɗum waɗi heen. Taariki oo, e Goldman (2007), ina waɗi e taarorde seero ɗiɗi, ɗo limooje ɗee ngoni 1 e nder 79 miliyoŋ e 1 e nder 2,09 miliyoŋ.
Ƴeewndo weltinoowo
Jokkondire juutɗe ko no sahaa mbaaditiri.
Iwdi
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.