Matematik Ruleet · Miijo aslu · hojomaaji 8

Ɓural Kasino e Ruleet

Feccere kala pari nde kasino jogotoo e hakkundeere.

Jaabawol rabbiɗngol

Ruleet Orop: 2,70% e kala pari aadanteengal, sabu njoɓdi ina hiisaa hono cuuɗi ina 36 kono ko 37 woodi.

Orop
2,70%
Amerik
5,26%
njoɓdi fotndi Farayse
1,35%
e kala $1 000 pariyaaɗo
$27,03

Ko ɗum iwi

Njoɓdi potndi ngam limoore wooterepariLimoore wootereLimoore wootere tan, ina yoɓa 35:1.Tar fof → ina foti wonde 36 e 1, sabu laabi 36 majjere ina ngoodi e kala laawol gootol dañal. Kasino ina yoɓa 35 e 1. InitekaalisInitePari fuɗɗoode mo sistem walla fijoowo gollirta. Jokkondirɗe pari ina cifee e initeeji ngam ɗi kuutoroo e kala taabal.Tar fof → majjunde ndee, feccaande e njeñtuɗi 37 potɗi sahaa, ko 1/37 = 2,70% pari e kala taarol. Ndeen ustaare ina wona e kala njoɓdikaalisNjoɓdiKo pari dañndi ruttata, wiyaa “X e 1” ɓeydaa e pari ruttaaɗo.Tar fof → sabu kala njoɓdi ina huutoroo sariya 36/n − 1: limooje ɗiɗipariLimooje ɗiɗiLimooje ɗiɗi takkondirɗe, ina yoɓa 17:1.Tar fof → ina yoɓa 17 nokku 17,5, sappo e ɗiɗipariSappo e ɗiɗi1–12, 13–24 walla 25–36, ina yoɓa 2:1.Tar fof → 2 nokku 2,083, boɗeerepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof → 1 nokku 1,056. Ceergal ngal ko kala sahaa 1/n inite e kala dañal, e dañe n/37 e kala taarol, ɗuum waɗi kala sahaa ko 1/37 e kala taarol.

Njoɓdi kasino e njoɓdi potndinjoɓdi, e 1
Limoore wootere (1/37)
35:1
Limooje ɗiɗi (2/37)
17:1
Limooje tati (3/37)
11:1
Limooje nay (4/37)
8:1
Limooje jeegom (6/37)
5:1
Sappo e ɗiɗi / kolon (12/37)
2:1
Njoɓdi fotndi (18/37)
1:1
njoɓdi, e 1
017,5035:1
Potndi = 37/n − 1. Yoɓaandi = 36/n − 1. Ceergal ngal, 1/n inite e kala dañal fiɓaa e dañe n/37 e kala taarol, ko 1/37 pari e kala pari.

Ɓural e ko kasino jogii

Ɓural ko majjere fodaandematematikMajjere fodaandeNjaru fodaandu fiyaandu e kaalis pariyaaɗo fof; ko hakkundeere kaalis majjataako nder jonnde walla nder sahaa.Tar fof → e kala inite pariyaande: 2,70% e kala taarol. Ko kasino jogiikaalisKo kasino jogiiGeɗal kaalis ko fijooɓe ngaddi e taabal ngal kasino jogiiyata tigi. Ina ɓuri ɓural kasino sabu kaalis dañaaɗo ina pariyee kadi.Tar fof → ko ko kasino jogii e kaalis mo ngaddu-ɗaa e taabal ngal, ɗum ina ɓura mawnude sabu ina a waɗa pari kadi e kaalis dañaaɗo maa. Soodgol jetoŋjitaabalSoodgol jetoŋjiWaylude kaalis kaayit e jetoŋji e taabal. Ina waɗee hakkunde taarle, kaalis oo ina waɗee e tapi, wonaa rokkeede kurupiye e jungo.Tar fof → $100 pariyaaɗo $10 e kala laawol e taarle 200 ina waɗi kaalis pariyaaɗo fof $2 000 kadi yoɓii hedde $54 ɓural; ko kasino jogii e ndeen soodgol ko 54%. Kasinooji ina njeewta ko kasino jogii; fijooɓe ina foti miijaade e ɓural.

firolimoore ruleet aadanteere
Ɓural kasinomajjere fodaande ÷ kaalis pariyaaɗo2,70%
RTP1 − ɓural97,30%
Ko kasino jogiidañal kasino ÷ soodgol jetoŋji20–30% e saal, ina waylitoo
Dañal teoriɓural × pari hakkundeeri × taarleko dokke kasino ndaarata

Ko waɗi kala pari ina jogii ɓural gootal

Ɗum ko suɓaade, wonaa sahaa. Sariya 36/n − 1 tabitinaa ko e teemedannde 18ɓiire, seero ɗiɗifannuSeero ɗiɗiSuudu 00 taarorde Amerik. Woodde mayru ina ɓeyda ɓural kasino immorde 2,70% haa 5,26%.Tar fof → ittaa caggal ɗuum tawa njoɓdi meemaaka. Si njoɓdi ina potnoo ngam cuuɗikuutorɗeSuuduGootel e cuuɗi 37 limoraaɗi e rotoor. Ina noddee kadi: wenndu, kopp.Tar fof → 37, limoore wootere yoɓatno ko 36 e 1 tawa kasino heɓataa hay huunde. Ɓural gootal ngal ina newna: alaa pari ruleet woni “pari ngam majjinaade” e dow goɗngal, si wonaa pari limooje joy Amerik e 7,89%.

Ɓural kasino e pariiji njoɓdi fotndi, e kala mbaadi% pari
Farayse (la partage)
1,35%
Orop
2,70%
Amerik (0, 00)
5,26%
Mini (cuuɗi 13)
7,69%
Seero tati
7,69%
% pari
03,857,69%
Njoɓdi gootu ndun e kala nokku; ko limoore cuuɗi tan waylotoo.

Pari Limooje Joy e Ruleet

Ko ɓural ruleet wonaa

Ɗum wonaa porobabilitematematikPorobabiliteSahaa njeñtudi, immorde 0 haa 1 walla 0% haa 100%. Limoore wootere: 1/37 = 2,70%.Tar fof → majjinde jonnde; jonɗe gaɗaaɗe ɓurɗe heewde ko wariyaasmatematikWariyaasPeeta no njeñtuɗi saŋkitiri e njaru fodaandu. Ina toowi ngam limoore wootere, ina lesɗi ngam pariiji njoɓdi fotndi.Tar fof → taƴata, e hedde 42% jonɗe taarle 100 e njoɓdi fotndi ina timmoo tawa fijoowo ina dañi. Ɗum wonaa njoɓdi e kala jonnde; ina ɓeydoo e kaalis pariyaaɗo fofkaalisKaalis pariyaaɗo fofKawrital kaalis pariyaaɗo nder jonnde walla sahaa, limtaa kadi kaalis dañaaɗo pariyaaɗo kadi. Ina noddee kadi: handle, action.Tar fof →, ɗuum waɗi 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 → ɓurngal waɗde pari ina ɓura yoɓde. Ɗum wonaa huunde nde mbaadi pariiji waawi famɗinde, sabu ɓuraaji pariiji waɗaaɗi e sahaa gootal ina ɓeydondira e nder pariiji majji.

E kaalis

E kala $1 000 pariyaaɗo, majjere fodaande ko $27,03 e ruleet OropfannuRuleet OropTaarorde seero gooto, cuuɗi 37, ɓural kasino 2,70%. Ko modeel ngol lowre ndee ƴettori.Tar fof →, $52,63 e Amerik, $13,51 e pariiji njoɓdi fotndipariPari njoɓdi fotndiBoɗeere/ɓaleere, peccotaake/peccotoonde, mawɗe/tokooseeje. Limooje 18, ina yoɓa 1:1.Tar fof → 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 →. Fijoowo jokkuɗo ngo waɗata pari $500 kala jemma, laabi ɗiɗi e yontere, duuɓi gooto, ina waɗi kaalis pariyaaɗo fof $52 000 kadi yoɓii hedde $1 400 ɓural e taarorde Orop. Limoore ndee ina famɗi e kala taarol kono ina ɓetoyaa e kala hitaande.

Sariya La partage e RuleetRuleet Orop

E kala taarol walla e kala pari taƴaaɗo

Hedde kala pari ruleet ina taƴee e taarol gootol, ɗuum waɗi ɓural mum e kala taarol e ɓural mum e kala pari ko limoore wootere. Pari waawngal heddaade tawa taƴaaka e heddaade e tapikuutorɗeTapiKaare pariiji winndaande e taabal. Ina noddee kadi: taabal, feetere, sanyo.Tar fof → ina jogii ɗiɗi. Pari bulaa-haako Riverboat Roulette ina kuuɓa limooje 3 e taarorde Amerik, ina daña e 2 e 1 si gooto e majji ummiima ado gooto e limooje daneeje 8, ina heddoo e goɗɗe fof. E kala pari taƴaaɗo ina majjina 2/11 pari, 18,18%. E kala taarol ina majjina 2/38, 5,26%, sabu e hakkundeere pari ina heddoo taarle 38/11, hedde 3,5. Limooje ɗiɗi ɗee fof ko goonga. Limoore kala taarol ina fota pari ngal e taabal ngal fof kadi ina holla ko waktu gootu coggotoo; limoore kala pari taƴaaɗo ina wiya ko feccere kala pari ruttotoo nde pari ngal taƴii sakket.

Pari Riverboatlimoojenjoɓdiɓural e kala pari taƴaaɗoɓural e kala taarol
bulaa-haako, oolo32 e 118,18%5,26%
roos, wiyole48 e 513,33%4,21%
oraas, bulaa57 e 57,69%2,63%
Ɓural e kala taarol × taarle hakkundeere e tapi = ɓural e kala pari taƴaaɗo: 5,26% × 38/11 = 18,18%.

Taarorde e Sariyaaji Ruleet Amerik

Nde kasino juumi e coggu

Kala ɓural e ngoo hello ina iwi e limto ngo kasinooji ina ngoowi feewnude. Sahaaji goɗɗi ɓe peewnataa ɗum. E Oktoobar 1994 Grand Casino to Biloxi, Mississippi, rokkii 80 e 1 e deeji tati ɗi kawrital mum ko 4, e ko wootere e 17. Deeji tati ina njana e laabi 216 tawa ko 3 tan e majji kawrital mum ko 4, ɗuum waɗi pari ngal ruttinii 81 × 3/216 = 1,125 e kala inite pariyaande: ɓural 12,5% ngam fijoowo. Fijooɓe tiiɗnii ɗum. Kasino majjinii hedde $180 000 e ñalnde wootere, uddi pari ngal, udditi ɗum kadi e 60 e 1, ɗum waylata sahaaji 3 e nder 216 ɗin ɓural 15,3% ngam kasino. Hunacek (2025), ina woowa Bollman, ina hokka ndee daarol. Njoɓdi aadanteendi ruleet ina welii no feewi ngam juumde e ndee laawol; ko pariiji serapariPari seraPari ɓeydaando suɓotoondo ƴowaando e fijo mawngo, ko ɓuri heewde e jokkondire, hewtere bonis walla jakpot. Ko ɓuri heewde ina ɓuri coggude pariiji laawol.Tar fof → mum ɗi woowaaka woni ɗo limto ngo haanaa ƴeewteede.

Deeji tati kawrital mum ko 4 e 80 e 1 rokkii fijooɓe ɓural ngal.

Pariiji sera e fijooji taabal goɗɗi

Bollman (2021) ina wattita pariiji mawɗi blackjack, baccarat, craps e ruleet sera pariiji sera aadanteeji e taabalji ɗiin. E fijooji tati arani ɗii, pari sera ina ɓura coggude pari mawngal, heewi ko laabi keewɗi. Ko fijo sakkitiingo e tabalo ngoo woni ceerngo: ɓural ruleet AmerikfannuRuleet AmerikTaarorde jogiinde 0 e 00, cuuɗi 38, ɓural kasino 5,26%. Wonaa modeel ngal lowre nde huutortoo.Tar fof → ko 5,26% e pariiji mawɗi, ina toowi no pari sera hono Colors walla WINGO waawi ɓurde hoyde.

fijopari mawngalɓural kasinopari seraɓural kasino
blackjackjuuɗe fijoowo, e sariyaaji e no fijotee0,5–5%Lucky Ladies24,94%
WINSURE10,20% walla ko ɓuri
baccaratFijoowo1,36%Baccarat World2,32% walla ko ɓuri
Bankoowo1,17%WINSUIT2,89%
crapsPass1,41%Field5,56%
Don’t Pass1,36%All Tall, All Small7,76%
ruleet Amerikkala pari si wonaa limooje joy5,26%Colors4,34%
pari limooje joy7,89%WINGO3,78%
Baccarat e kala juuɗe taƴaaɗe, fotaare ittaa. Ɓuraaji pariiji sera ina ndaari tabalo njoɓdi rokkaaɗo; ɗee ko mbaadi ɗi Bollman (2021).

Coggu Waktu Gooto, KawrondiraaɗoPariiji Sera Ruleet

Formil

ɓural = 1 − (n/37)(36/n) = 1 − 36/37 = 1/37
majjere fodaande = ɓural × kaalis pariyaaɗo fof

Naamne

Mbele 2,70% ko majjinde 2,70% kaalis pari am?

Alaa. Ko 2,70% ko waɗ-ɗaa pari. Waɗde pari kadi e kaalis gootun ina waɗa ɗum pari laawol goɗngol.

Mbele ɓural kasino ruleet ina waylitoo e pari?

Alaa. Ko feccere. Majjere fodaande e dolaaruuji ina ɓeydoo e pari.

Pari honngal ɓuri kot moƴƴi e ruleet?

So ɓural ngal ƴeewaama, pariiji aadanteeji Orop fof ina potti; ɗi ceertaa si wonaa e no ɗi ndañata sahaaji keewɗi e no ɗi njoɓata. E la partage, pariiji njoɓdi fotndi ko feccere goɗɗi ɗii.

Weltaare e Matematik

Etu ɗum hoore maa adii. Kala jaabawol ina suuɗii; uddit ɗum so a heblii.

  1. E taarorde Orop, pari limoore wooterepariLimoore wootereLimoore wootere tan, ina yoɓa 35:1.Tar fof → e pari e boɗeerepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof → fof ina coggi 2,70%, hay so gooto ina hawta limoore wootere, goɗngo oo limooje sappo e jeetati. Ko waɗi pariiji fof ina jogii ɓural kasinomatematikƁural kasinoGeɗal kala pari ngal kasino jogiiyata e hakkundeere: 2,70% e ruleet Orop.Tar fof → gootal?

    Hollu jaabawol ngol

    Jaabawol NjoɓdikaalisNjoɓdiKo pari dañndi ruttata, wiyaa “X e 1” ɓeydaa e pari ruttaaɗo.Tar fof → kala ina taƴee wano 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 → ngoo alaa, ndeen pari kala ina majja initekaalisInitePari fuɗɗoode mo sistem walla fijoowo gollirta. Jokkondirɗe pari ina cifee e initeeji ngam ɗi kuutoroo e kala taabal.Tar fof → wootere e taarle 37, hay ko honɗum hawti.

    Ƴettu pari e limooje n. Ina njoɓa (36 − n)/n e 1. E taarle 37, ina daña, e hakkundeere, laabi n, ina majja laabi 37 − n.

    Dañe ɗee ina addana n × (36 − n)/n = 36 − n initeeji. Majjere ɗee ina coggi 37 − n initeeji. Ceerndugol ngol ko −1 inite e taarle 37 kala, n kadi momtii: njeñtudi ndii ko wootere e pari limoore wootere, limooje naypariLimooje nayLimooje nay sendiiɗe kooñal gootal e tapi, ina yoɓa 8:1.Tar fof → walla sappo e ɗiɗipariSappo e ɗiɗi1–12, 13–24 walla 25–36, ina yoɓa 2:1.Tar fof →. Inite wootere majjaande e 37 ko 2,70%.

    E taarorde jogiinde cuuɗikuutorɗeSuuduGootel e cuuɗi 37 limoraaɗi e rotoor. Ina noddee kadi: wenndu, kopp.Tar fof → N, hiisa oo kanko tigi ina rokka (36 − N)/N, ɗum ko −2/38 = 5,26% e taarorde Amerik. Pari gootal tan ina feewtaa e mbaadi ndii ko pari limooje joy Amerik: sariya oo ina wiya ina foti njoɓeede 6,2 e 1, ina njoɓa 6, ina coggi 7,89%.

  2. Keno, fijo nanndungo e loto, ina jogii 25% walla ko ɓuri ɗum e ko pariyaa. Si kasino ɓeydii seeroji e taarorde ruleet, accii njoɓdi no wonnoo, seeroji njelu ngoni ngam ruleet coggoo hono keno?

    Hollu jaabawol ngol

    Jaabawol Seeroji sappo e ɗiɗi: taarorde cuuɗi 48.

    E seeroji z, taarorde ndee ina jogii cuuɗi 36 + z, njoɓdi kadi ina miijoo 36 tan. E sariya caɗeele dow ɗoo, pari kala ina majja initeeji z e taarle 36 + z, ndeen ɓural kasino ko z/(36 + z).

    Foondu ɗum e nayaɓal: 4z = 36 + z, ndeen z = 12. Seeroji sappo e ɗiɗi e taarorde cuuɗi 48 ina coggoo 25%.

    Taarorde seero tati Las Vegas Strip, ruleet ɓurnde coggude nde ko ɓuri heewde e fijooɓe kawrittata, ina jogii nayaɓal keewal ngal.

    seerojicuuɗiɓural kasino
    1372,70%
    2385,26%
    3397,69%
    44010,00%
    124825,00%
  3. Loto Massachusetts udditii e hitaande 2023 taarorde jogiinde limooje 36 tee alaa seero. Limoore wootere ina njoɓa 25 ngam 1, boɗeere, ɓaleerepariƁaleerePari njoɓdi fotndi e limooje 18 ɓaleeje. E Farayse: noir.Tar fof →, peccotaake walla peccotoonde ina njoɓa 3 ngam 2. Nde tawnoo alaa seero, hol ina ɓuri ruleet famɗude coggu?

    Hollu jaabawol ngol

    Jaabawol Alaa, ina ɓuri coggude no feewi: 30,56% e limoore wootere e 25% e boɗeere walla ɓaleere, nde ruleet Orop woni 2,70%.

    “Ngam” ina hawti pari oo. Pari $1 e limoore ina rutta $25 laawol gootol e taarle 36 e hakkundeere: $25 ruttaaɗo ngam $36 pariyaaɗo, majjere $11 e 36, 30,56%.

    Pari $2 e boɗeere ina rutta $3 feccere sahaaji ɗii: $3 ruttaaɗo ngam $4 kala pariyaaɗo, majjere 25%.

    Seero ko laawol gootol tan e taƴde coggu. Ruleet ina njoɓa wano tawnoo cuuɗi 36 ngoni, ɓeyda suudu 37ɓiire; taarorde ndee ina jogii cuuɗi 36, ina ɓuri famɗude njoɓdi tan. Bollman (2024) ina rokka ɗum hono golle jaŋde.

  4. Kasino ina yiɗi pari keso e limooje aranndeejematematikLimoore aranndeereLimoore timmunde ɓurnde 1 nde 1 e hoore mayre tan peccata no feewi: 2, 3, 5, 7, 11, 13 e ko nanndi e ɗum.Tar fof → sappo e gooto hakkunde 1 e 36: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 e 31. Ko njelu foti njoɓeede ngam coggoo 2,70% wano pari kala e taarorde Orop? Ko ɗum coggata e 2 e 1?

    Hollu jaabawol ngol

    Jaabawol 25 e 11, hedde 2,27 e 1. E 2 e 1 ina coggoo 10,81%.

    Huutoro sariya caɗeele adanɗe ɗee: pari e limooje n ina njoɓa (36 − n)/n e 1. E n = 11 ɗum ko 25/11 e 1, njoɓdi caɗndi, ko jetoŋkaalisJetoŋMaande hollirde kaalis tabitiiɗo, waɗetee e tapi ngam waɗde pari. Ina wiyee kadi: check.Tar fof → $10 ina daña $22,73.

    E 2 e 1, pari $1 ina daña $2 e taarle 11 e 37, ina majja $1 e 26 goɗɗe ɗee: 22 − 26 = −4 initeeji e taarle 37 kala, 10,81%.

    Ɗum waɗi ruleet ina yeeya pariiji e limooje 1, 2, 3, 4, 6, 12 e 18: 36 ina feccoo e mum en fof, ndeen njoɓdi potndi ko limoore timmunde. Taylor (2021) ina rokka golle ngal e limooje aranndeeje sappo; ko sappo e gooto ɗe ngoni.

Ƴeewndo weltinoowo

1/37 kala pari, e kala pari, e kala taarol.

1/37 kala pari, e kala pari, e kala taarol.

Iwdi

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Pecce 13, ruleet.
  2. Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed. Academic Press, 2013.
  3. Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette. CRC Press, 2021. Pecce 2, ruleet.
  4. Hunacek, M. Quantitative Literacy Through Games and Gambling. Chapman & Hall/CRC, 2025.
ƴeewtaa 2026-09-28misal: ruleet Orop, seero gootolaawol golle ↗iwdi ↗