Matematik Ruleet · Kuutoragol · hojomaaji 8

Bonusuuji, Promosiyoŋ e Ruttinanɗe e Ruleet

Bonusuuji ruleet hono kupoŋji matchplay, jetoŋji ɗi waylataa kaalis e ruttinanɗe majjere ina ndimmina kaalis seeɗa iwde e kasino haa fijoowo. So coggu mum hiisaama no moƴƴi, woɗɗi e majji ina ɓuri ko taarorde ndee ina ƴetta.

Jaabawol rabbiɗngol

Kupoŋ ɓeydoowo njoɓdi pari njoɓdi fotndi laabi ɗiɗi ina foti hono 46% pari oo e taarorde Orop. Jetoŋ promosiyoŋ huutoreteeɗo laabi gooto ina foti (36 − n)/37 njaru mum e pari hupoowo limooje n: 95% e limoore wootere, 49% e boɗeere. Ruttinannde feccere majjere maa laaɓnde ina waɗa jonnde boɗeere ɓooyaani nde nafata fijaade. Hay gooto e ɗum waylataa taarorde ndee; ina waylita tan on yoɓoowo.

kupoŋ matchplay e boɗeere
+45,9% pari oo
jetoŋ $100 huutoreteeɗo laabi gooto, limoore wootere
ina foti $94,59
jetoŋ gooto oo e boɗeere
ina foti $48,65
ruttinannde majjere 50% e boɗeere
ɓurnde moƴƴude e taarle 25

Ko waɗi promosiyoŋ ina waawi ɓurde ɓural ngal

Ɓural kasinomatematikƁural kasinoGeɗal kala pari ngal kasino jogiiyata e hakkundeere: 2,70% e ruleet Orop.Tar fof → ko coggu e initekaalisInitePari fuɗɗoode mo sistem walla fijoowo gollirta. Jokkondirɗe pari ina cifee e initeeji ngam ɗi kuutoroo e kala taabal.Tar fof → kala pariyaande: 2,70% e taarorde Orop. Bonus ruleet ina ɓeyda kaalis e sara gooto pari, so ina ɓeyda ko ɓuri 2,70% pari oo, pari ndii ina ɓuri seero haa promosiyoŋ oo gasa. Kasinooji ina ndokka ɗum tawon sabu ɗum ina haaɗi: kupoŋ gooto e jillu kala, jetoŋjikaalisJetoŋMaande hollirde kaalis tabitiiɗo, waɗetee e tapi ngam waɗde pari. Ina wiyee kadi: check.Tar fof → ɗi waɗetee pari kono waylataa kaalis, ruttinanɗe ngam fijooɓe majjinooɓe kaalis keewɗo tan. Hiisa ngal ko gooto e ka nokku kala e lowre ndee: porobabilite fiilsaa e njoɓdikaalisNjoɓdiKo pari dañndi ruttata, wiyaa “X e 1” ɓeydaa e pari ruttaaɗo.Tar fof →, kawtaa e njeñtuɗi ɗii fof.

Kupoŋji matchplay

Kupoŋ matchplay ina waɗee takko pari kaalis, ina ɓeyda ko pari ndii yoɓata laabi ɗiɗi so dañii; dañii walla majjii, kasino oo ina jogitoo kupoŋ oo. Bollman (2024) hiisii coggu kupoŋ Las Vegas iwɗo 2022 ɓeydayno haa $50 e pari njoɓdi fotndipariPari njoɓdi fotndiBoɗeere/ɓaleere, peccotaake/peccotoonde, mawɗe/tokooseeje. Limooje 18, ina yoɓa 1:1.Tar fof →. E taarorde Orop, $50 e boɗeerepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof → e kupoŋ oo ina daña $100 e porobabilite 18/37 ina majjina $50 e porobabilite 19/37: fodaande +$22,97, walla 45,9% pari oo. E taarorde Amerik ko +$21,05, 42,1%. E limoore wooterepariLimoore wootereLimoore wootere tan, ina yoɓa 35:1.Tar fof → kupoŋ gooto oo ina foti laabi ɗiɗi, ɗum ko waɗi kupoŋji ina haaɗi e pariiji njoɓdi fotndi.

pariina yoɓa so dañiitaarorde Oroptaarorde Amerik
$50 e boɗeere, alaa kupoŋ$50−$1,35 (−2,70%)−$2,63 (−5,26%)
$50 e boɗeere e kupoŋ oo$100+$22,97 (+45,9%)+$21,05 (+42,1%)
$50 limoore wootere e kupoŋ oo, so jaɓaama$3 500+$45,95 (+91,9%)+$43,42 (+86,8%)

Taarorde e Sariyaaji Ruleet Amerik

Jetoŋji ɗi waylataa kaalis

Jetoŋji promosiyoŋ, wiyeteeɗi kadi jetoŋji ɗi njeeyetaake, ina mbaɗee pari kono ina mbaylitaake kaalis. Sariya ɓurngo heewde ko huutoraade laabi gooto: pari dañiindi ina yoɓee e jetoŋji ndenndaaɗi, jetoŋ promosiyoŋ oo ina ƴettee; pari majjiindi kadi ina ƴettee. Jetoŋ $100 e pari hupoowo limooje n ina daña (36 − n)/n × $100 e porobabilite n/37, ɗum noon ina foti (36 − n)/37 njaru mum. Njaru jetoŋ oo e hoore mum ruttotaako abadaa, ko dañaa tan, pari dañoowo seeɗa kono yoɓoowo keewɗo ko ɓuri famɗude majjude e ndeen laawol: $94,59 e limoore wootere, $48,65 e boɗeere. Ɗo jetoŋ oo waawi heddaade e tapikuutorɗeTapiKaare pariiji winndaande e taabal. Ina noddee kadi: taabal, feetere, sanyo.Tar fof → oo haa majja, pari njoɓdi fotndi ina foti 18/19 njaru mum e taarorde Orop e 9/10 e taarorde Amerik (Bollman, 2024).

parilimoojenjaru jetoŋ $100 huutoreteeɗo laabi gooto
Limoore wootere1$94,59
Limooje ɗiɗi2$91,89
Limooje tati3$89,19
Limooje nay4$86,49
Limooje jeegom6$81,08
Sappo e ɗiɗi12$64,86
Boɗeere18$48,65

Waylude jetoŋji ɗii kaalis

Njaru ko hakkundeere; fijoowo yiɗɗo kaalis oo e hoolaare ina waawi soodde ɗum e reenugol. Misal Bollman iwii e kasino Vegas World kiɓɗo oo: $1 000 jetoŋji huutoreteeɗi laabi gooto e taarorde Amerik, $500 e boɗeere e $500 e ɓaleerepariƁaleerePari njoɓdi fotndi e limooje 18 ɓaleeje. E Farayse: noir.Tar fof →, e $20 kaalis e 0 e 00 kala. Boɗeere walla ɓaleere ina daña $500 ina majjina $40 kaalis oo: +$460. 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 → ina majjina jetoŋji ɗiɗi ɗii ina yoɓa $700 e kaalis oo: +$680. Fijoowo oo ina heɓa ko famɗi fof $460, hakkundeere ndee, $471,58, ko 99,6% ko jetoŋji ɗii poti e boɗeere tan. Ɗo sariyaaji ina njaɓa jetoŋji e limooje gooto-gooto, taarorde Orop ina rokka reenugol ɓurngol moƴƴude: jetoŋji $25 e limooje 36 ɗee fof ($900) e $25 kaalis e seero. Kala limoore yaltii ina yoɓa $875, kaalis oo e seero ina majja so wonaa seero e hoore mum yaltii, ɗum noon fijoowo oo ina hettina ko famɗi fof $850, 94% njaru jetoŋji ɗii, tawa alaa faayre fey.

Jetoŋji huutoreteeɗi laabi gooto ina kupi boɗeere e ɓaleere, tawa pariiji kaalis tokooseeji ina kupi seeroɗi ɗiɗi ɗii.

Saŋkitugol Pariiji e Reenugol Hoore e Ruleet

Ruttinanɗe majjere

Fijooɓe pariiji mawɗi ina keewi rokkeede ruttinannde: feccere majjere mum laaɓnde ina ruttanee ɓe e gasgol jonnde jaɓondiraande. Ruttinannde ina yoɓa tan so a majjii, ɗum noon ina ɓuri foti so njeñtuɗi ina yeccitoo no feewi, jonnde ndee kadi ina rabbi haa ɓural ngal fooldaani tawon. Epstein (2013) hiisii ɗum ngam taarorde Amerik; limooje amen ngam taarorde Orop ina njokki. So feccere majjere laaɓnde ina ruttee, pari fotɗi njoɓdi fotndi ina nafa fijaade haa taarle 103, ina ɓuri moƴƴude e 25, foti +0,51 pariiji e hakkundeere. E limoore wootere yeccitte ɗee ina mawni no feewi haa jonnde ndee ina heddoo ɓurde seero haa hono taarle 3 600, ina ɓuri moƴƴude e 882, foti +17,25 pariiji. E ruttinannde 10% ɓurnde heewde, njoɓdi fotndi ina ɓuri seero e taarol gootol tan, tawa limoore wootere ina ɓuri moƴƴude e taarle 20, foti +0,62 pariiji.

ruttinanndepariina ɓuri seero haajonnde ɓurnde moƴƴudefoti e ko ɓuri moƴƴude
50%njoɓdi fotnditaarle 103taarle 25+0,51 pariiji
50%limoore wooterehono taarle 3 600taarle 882+17,25 pariiji
10%njoɓdi fotnditaarol 1taarol 1+0,02 pariiji
10%limoore wooteretaarle 85taarle 20+0,62 pariiji
Taarorde Orop, pari gooto e taarol kala e pari gooto ndii, ruttinannde ndee ina yoɓee e majjere laaɓnde caggal limoore taarle tabitnde. Kawtal binomial goonga.

Sariyaaji promosiyoŋ ruleet: ko kasino oo hoolii

Promosiyoŋ kala ina jogii keerol, keerol ngol kadi ina reena kasino oo: kupoŋ gooto e jillu, jetoŋji rokkaaɗi e limoore tabitnde, ruttinanɗe jaɓondiraaɗe tan e fijooɓe ɓe majjere fodaande mum e nder jillu ina ɓuri ruttinannde ndee no feewi. Fijoowo huutoriiɗo kupoŋ oo, heddii kiikiiɗe pariiji $50 e boɗeere ina rutta $22,97 ɗee e nder taarle 17, e $1,35 e taarol. Njaru nden ko goonga ngam fijoowo ƴettoowo ɗum yaha, walla fijoowo fijayno ko foti ɗum hay so alaa ɗum.

Formil

jetoŋ huutoreteeɗo laabi gooto e limooje n: njaru = (36 − n)/37 njaru mum
kupoŋ ɓeydoowo dañal njoɓdi fotndi laabi ɗiɗi: EV = (2 × 18 − 19)/37 pari oo
ruttinannde r majjere laaɓnde: EV = E[njeñtudi] + r × E[majjere laaɓnde]

Naamne

Mbele kupoŋ ina waawi waɗde ruleet fijo dañoowo?

Ngam pari gootiri ndi ɗum jokkondiri, eey. Pari woɗndi kala ina coggoo tawon 2,70% pari oo.

Ko waɗi kasinooji ina njaɓa reenugol ngol?

Fijooɓe seeɗa miijotoo ɗum, jetoŋji ɗii ina haaɗi, kasino oo kadi hiisii coggu promosiyoŋ oo hono piɓlisite.

Mbele ruttinanɗe ina rokkee fijooɓe ɓe ngonaa mawɓe kaalis?

Seeɗa. Ɗum ko sariya fijooɓe mawɗe kaalis, ko heewi jaɓondiraa e jaɓɓoowo kasino oo, yoɓee e majjere laaɓnde e nder jillu.

Weltaare e Matematik

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

  1. A rokkaama jetoŋkaalisJetoŋMaande hollirde kaalis tabitiiɗo, waɗetee e tapi ngam waɗde pari. Ina wiyee kadi: check.Tar fof → promosiyoŋ $25 mo ɓettetee caggal pari gootal, daña walla majja. Hoto ngoni ɗum waɗetee: e boɗeerepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof →, e sappo e ɗiɗipariSappo e ɗiɗi1–12, 13–24 walla 25–36, ina yoɓa 2:1.Tar fof → walla e limoore wootere?

    Hollu jaabawol ngol

    Jaabawol E limoore wootere. Toon ina foti $23,65 e hakkundeere; e sappo e ɗiɗi $16,22, e boɗeere $12,16.

    Jetoŋ oo e hoore mum ruttotaake fey, ko ɗum dañi tan. E boɗeere ina daña $25 e porobabilite 18/37: $12,16. E sappo e ɗiɗi ina daña $50 e porobabilite 12/37: $16,22. E limoore wootere ina daña $875 e porobabilite 1/37: $23,65.

    E kuuɓal, pari e limooje n ina foti (36 − n)/37 jetoŋ oo, ɗum waɗi ko limooje ɗee ɓuri famɗude fof, ko ɓuri moƴƴude. E jetoŋ aadanteeɗo ɗum waylataa hay huunde, sabu pari ngal ina ruttoo e kala dañal, kala pari ina foti 36/37 mum. Ɓettude pari ngal ina lorna pariiji dañooji sahaa heewɗo, ina meemaa seeɗa tan pari ngal dañata laabi gooto e nder 37.

  2. Kasino ina rutta feccere majjere maa laaɓnde caggal taarol gootol tigi. Hol $100 e boɗeere ina foti fijeede? E $100 e limoore wootere?

    Hollu jaabawol ngol

    Jaabawol Ɗiɗi ɗii fof: hono +$22,97 e boɗeere e +$45,95 e limoore ndee.

    E boɗeere a dañata $100 e porobabilite 18/37, caggal ruttagol ngol, a majjinta $50 e porobabilite 19/37: (1 800 − 950)/37 = +$22,97.

    E limoore wootere a dañata $3 500 e porobabilite 1/37, a majjinta $50 e porobabilite 36/37: (3 500 − 1 800)/37 = +$45,95.

    Ɗum ko limooje kupon matchplay ɗee kadi. Pari $100 majjinoowo $50 tan ina daña $100 walla ina majjina $50, tigi hono pari $50 joginngal kupon ɗiɗiɓinoowo dañal mum. E jonnde ɓurnde juutde, ruttagol ngol ina yoɓee tan e njeñtudi laaɓndi, dañal e majjere ina mumtondira hade mum yoɓeede, njaru ndu ina ustoo; ngam boɗeere e feccere ruttaande, taarle 25 ko juuteendi ɓurndi moƴƴude.

  3. Kasino ina rutta feccere majjere maa laaɓnde caggal limoore pariiji $100 e boɗeere suɓaande adii: taarle 1, 2 walla 3. Hol ko ɓuri foti?

    Hollu jaabawol ngol

    Jaabawol Taarle tati: hono +$31,45. Taarol gootol ina foti +$22,97, ɗiɗi kadi +$20,96 tan.

    Taarol gootol: daña $100 e porobabilite 18/37, walla majjin $100 a heɓa $50 e porobabilite 19/37: +$22,97, hono e golle dow ɗee.

    Taarle ɗiɗi: ɗiɗi ɗii fof ina daña (laabi 324 e nder 1 369), +$200. Gootol e gootol (laabi 684), $0, alaa ko ruttetee. Ɗiɗi ɗii fof ina majja (laabi 361), −$200, −$100 caggal ruttagol. Hakkundeere: (200 × 324 − 100 × 361)/1 369 = +$20,96. Ruttagol ngol ina yoɓa tan so majjere woodi, taarle ɗiɗi ina mbaylita majjeeje keewɗe taarol gootol fotde.

    Taarle tati mbaawataa fotde fey. Dañe tati (laabi 5 832 e nder 50 653): +$300. Dañe ɗiɗi (18 468): +$100. Dañal gootal (19 494): −$100, ruttaa haa −$50. Alaa (6 859): −$300, ruttaa haa −$150. Hakkundeere: +$31,45.

    Ruttagol ngol ina ɓuri foti so a fodii ko ɓuri juutde, tawa ɓural ngal ina coftina $2,70 tan e kala taarol, ɗum waɗi njaru ndu ina ƴenta haa hono +$51 e taarle 25 (ƴeew tabalo dow oo), limoore taarle peccotaake ina ɓura sahaa fof limoore peccotoonde rewnde e mayre.

  4. Kasino Las Vegas rokkiino kupon: waɗ pari $5 e 00, so dañii, a yoɓetee $250 nde wonaa $175 aadanteeɗo. Pari $5 ina foti no foti e kupon oo, so ina limtee e geɗal pari ngal, e taarorde mum 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?

    Hollu jaabawol ngol

    Jaabawol Hono +34%: pari ngal ina foti +$1,71 e hakkundeere. So $250 ɗum ina jogii $5 ruttaaɗo oo, ko +31,6%.

    00 ina daña laabi gooto e nder taarle 38. E kupon oo: +$250 laabi gooto, −$5 laabi 37 goɗɗi ɗii. Hakkundeere: (250 − 37 × 5)/38 = 65/38 = +$1,71, ɗum ko 34,2% $5. So kupon alaa: (175 − 185)/38 = −$0,26, −5,26% aadanteeɗo oo.

    So $250 ko ko ruttetee fof, dañal ngal ko $245, hakkundeere ndee ko (245 − 185)/38 = +$1,58, walla 31,6%.

    Bollman (2024) ina waɗa kupon oo, iwde e kasino Lady Luck (jooni Downtown Grand), golle ekkorgol; jaabawol fiyaangol e mum, 7,89%, hawrataa e hay faamuya gooto. Hono kupon matchplay, ina foti huunde laabi gooto: fij ɗum ndeen dar.

Ƴeewndo weltinoowo

Promosiyoŋ ina ɓuri nafde fijoowo ƴettoowo ɗum ruttoo galle.

Promosiyoŋ ina ɓuri nafde fijoowo ƴettoowo ɗum ruttoo galle.

Iwdi

  1. Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed. CRC Press, 2024.
  2. Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed. Academic Press, 2013.
ƴeewtaa 2026-09-28misal: ruleet Orop, seero gootolaawol golle ↗iwdi ↗