Rulɛt kasino advantej
Di pat fɔ ɛni bɛt mɔni we di kasino de kip pan avrej.
Yuropian rulɛt: 2.70% pan ɛni nɔmal bɛt, bikɔs dɛn de kalkul di pe lɛk se na 36 pɔkit de, bɔt na 37 de.
Usay i de kɔmɔt
Fɛr pe fɔ bɛt pan wan nɔmbabɛtBɛt pan wan nɔmbaWan nɔmba nɔmɔ, i de pe 35:1.Rid ɔl → fɔ bi 36 to 1, bikɔs na 36 we fɔ lɔs de fɔ ɛni wan we fɔ win. Di kasino de pe 35 to 1. Di yunitmɔniYunitDi bes bɛt mɔni we sistɛm ɔ pleya de wok wit. Dɛn de ɛksplen prɔgrɛshɔn wit yunit so dat i go wok na ɛni tebul.Rid ɔl → we nɔ de, we yu sheb am pan 37 rizɔlt we gɛt di sem chans, na 1/37 = 2.70% fɔ di bɛt mɔni pan ɛni spin. Di sem shɔt de na ɛni pemɔniPeWetin bɛt we win de gi yu, dɛn de tɔk am as “X to 1” ɔn tɔp di bɛt mɔni we kam bak.Rid ɔl →, bikɔs ɛni pe de yuz di rul 36/n − 1: splitbɛtSplitTu nɔmba we de nia wan ɔda, i de pe 17:1.Rid ɔl → de pe 17 insay 17.5, dɔzinbɛtDɔzin1–12, 13–24 ɔ 25–36, i de pe 2:1.Rid ɔl → de pe 2 insay 2.083, rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl → de pe 1 insay 1.056. Di gap na ɔltɛm 1/n yunit pan ɛni win, ɛn n/37 win pan ɛni spin, so na ɔltɛm 1/37 pan ɛni spin.
Advantej ɛn hold
Advantej na di lɔs we fɔ ɛkspɛktmatematiksLɔs we fɔ ɛkspɛktValyu we fɔ ɛkspɛkt tɛm ɔl di mɔni we yu bɛt; di avrej mɔni we yu de lɔs insay wan sɛshɔn ɔ wan tɛm.Rid ɔl → pan ɛni yunit we yu bɛt: 2.70% pan ɛni spin. HoldmɔniHoldHold (di pat we di kasino kip): di pat pan di mɔni we pleya dɛn kɛr kam na di tebul we di kasino rili kip. I big pas di kasino advantej bikɔs pleya dɛn de bɛt dɛn win mɔni bak.Rid ɔl → (di pat we di kasino kip) na wetin di kasino rili kip frɔm di mɔni we yu bin kam wit na di tebul. I ay pas dat bad bad wan, bikɔs yu de bɛt yu win mɔni bak. If yu bay chiptebulBay chipFɔ chenj kash fɔ chip na di tebul. Yu de du am bitwin tu spin, ɛn yu put di kash pan di bɛt tebul, yu nɔ de gi am na di dila in an.Rid ɔl → fɔ $100 ɛn yu bɛt $10 wan tɛm fɔ 200 spin, yu dɔn bɛt $2,000 ɔlsay ɛn yu dɔn pe lɛk $54 fɔ advantej; di hold pan da bay chip de na 54%. Kasino de ripɔt hold; pleya fɔ tink bɔt advantej.
Wetin mek ɛni bɛt gɛt di sem advantej
Na so dɛn mek am; i nɔto bay lɔk. Dɛn bin fiks di rul 36/n − 1 na di 18 sɛntiri, ɛn leta dɛn bin pul di dɔbul zirokayn rulɛtDɔbul ziroDi 00 pɔkit na di Amɛrikan wil. Bikɔs i de, di kasino advantej de go ɔp frɔm 2.70% to 5.26%.Rid ɔl → bɔt dɛn nɔ bin tɔch di pe. If di pe bin fɛr fɔ 37 pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl →, bɛt pan wan nɔmba fɔ pe 36 to 1 ɛn di kasino nɔ go gɛt natin. Di sem advantej pan ɔl de mek tin izi: nɔ rulɛt bɛt nɔ na “ful-ful bɛt” pas ɔda wan, pas wan nɔmɔ: di Amɛrikan bɛt pan fayv nɔmba, we na 7.89%.
Wetin di rulɛt advantej nɔto
I nɔto di prɔbabilitimatematiksPrɔbabilitiDi chans fɔ wan rizɔlt, frɔm 0 to 1 ɔ frɔm 0% to 100%. Wan nɔmba: 1/37 = 2.70%.Rid ɔl → fɔ lɔs wan sɛshɔn. Na variansmatematiksVariansWan mɛzhɔ fɔ aw di rizɔlt dɛn sprɛd rawnd di valyu we fɔ ɛkspɛkt. I ay fɔ bɛt pan wan nɔmba, i lɔ fɔ ivin-mɔni bɛt.Rid ɔl → de disayd bɔku shɔt sɛshɔn, ɛn lɛk 42% fɔ ivin-mɔni sɛshɔn we gɛt 100 spin de dɔn wit prɔfit. I nɔto fi we yu de pe fɔ ɛni sɛshɔn; i de gro wit ɔl di mɔni we yu bɛtmɔniƆl di bɛt mɔniƆl di mɔni we yu bɛt na wan sɛshɔn ɔ wan tɛm, wit di win mɔni we yu bɛt bak. Dɛn kin kɔl am bak: handle, action.Rid ɔl →, so prɔgrɛshɔnstratɛjiPrɔgrɛshɔnƐni rul we de chenj di bɛt mɔni bay di rizɔlt dɛn we dɔn pas. Nɛgativ prɔgrɛshɔn de es am afta lɔs, pɔzitiv wan afta win.Rid ɔl → we de bɛt mɔ de pe mɔ. Nɔ we fɔ bɛt nɔ kin mek am smɔl, bikɔs di advantej fɔ bɛt dɛn we yu put di sem tɛm de ad, akɔdin to di bɛt mɔni.
Na mɔni
Pan ɛni $1,000 we yu bɛt, di lɔs we fɔ ɛkspɛkt na $27.03 na Yuropian rulɛtkayn rulɛtYuropian rulɛtWil wit wan ziro, 37 pɔkit, kasino advantej 2.70%. Na di main wil we dis sayt de yuz.Rid ɔl →, $52.63 na Amɛrikan, ɛn $13.51 pan ivin-mɔni bɛtbɛtIvin-mɔni bɛtRɛd/blak, ɔd/ivin, ay/lɔ. 18 nɔmba, i de pe 1:1.Rid ɔl → wit La PartagerulLa partageFrɛnch rul: if ziro kam, af fɔ di ivin-mɔni bɛt mɔni de kam bak. I de kɔt di kasino advantej pan dɛn bɛt ya to af, 1.35%.Rid ɔl →. Pɔsin we kin ple ɔltɛm, we de bɛt $500 ɛni ivintɛm, tu tɛm ɛni wik, fɔ wan ia, dɔn bɛt $52,000 ɔlsay ɛn dɔn pe lɛk $1,400 fɔ advantej pan Yuropian wil. Di nɔmba smɔl pan ɛni spin, bɔt i nɔ de lɛf yu ɛni ia.
Pan ɛni spin ɔ pan ɛni bɛt we dɔn
Wan spin de pe ɔlmɔs ɛni rulɛt bɛt, so di advantej pan ɛni spin ɛn di advantej pan ɛni bɛt na di sem nɔmba. Bɛt we kin nɔ win nɔ lɔs ɛn tinap pan di bɛt tebulikwipmɛntBɛt tebulDi bɛt grid we dɛn print pan di tebul. Dɛn kin kɔl am bak: tebul, felt, klɔt.Rid ɔl → gɛt tu. Riverboat Roulette in teal bɛt de kɔba 3 nɔmba pan Amɛrikan wil. I de win 2 to 1 if wan pan dɛn kam bifo wan pan 8 White nɔmba, ɛn i nɔ win nɔ lɔs pan ɛni ɔda tin. Pan ɛni bɛt we dɔn, i de lɔs 2/11 fɔ di bɛt mɔni, 18.18%. Pan ɛni spin i de lɔs 2/38, 5.26%, bikɔs pan avrej di bɛt de tinap fɔ 38/11 spin, lɛk 3.5. Di tu nɔmba dɛn kɔrɛkt. Di nɔmba pan ɛni spin de kɔmpia di bɛt wit di res fɔ di tebul ɛn de sho ɔmɔs wan awa de kɔst; di nɔmba pan ɛni bɛt we dɔn de sho ɔmɔs fɔ ɛni bɛt mɔni de kam bak we di bɛt dɔn.
We kasino mek mistek wit di prays
Ɛni advantej pan dis pej kɔmɔt frɔm kalkul we kasino kin ɔltɛm du kɔrɛkt. Sɔntɛm dɛn nɔ kin du am kɔrɛkt. Na Ɔktoba 1994, di Grand Casino na Biloxi, Mississippi, bin de pe 80 to 1 if tri dayz ad to 4, ɛn di sem pan 17. Tri dayz kin fɔdɔm na 216 we, ɛn na 3 nɔmɔ pan dɛn de ad to 4, so di bɛt bin de gi bak 81 × 3/216 = 1.125 fɔ ɛni yunit: 12.5% advantej fɔ di pleya. Di pleya dɛn bin notis. Di kasino bin lɔs lɛk $180,000 insay wan de, i bin stɔp di bɛt, ɛn i bin opin am bak wit 60 to 1. Dat de tɔn di sem 3 chans na 216 to 15.3% advantej fɔ di kasino. Hunacek (2025) de tɛl di stori, ɛn i de kot Bollman. Di nɔmal rulɛt pe dɛn tu simpul fɔ mek dis kayn mistek; na di sayd bɛtbɛtSayd bɛtƐkstra bɛt we yu nɔ fɔs fɔ put, we dɛn jɔyn to di men gem, pas ɔl pan strik, bonus ɔ jakpɔt. I de kɔst mɔ pas di nɔmal bɛt dɛn, lɛk ɔltɛm.Rid ɔl → dɛn we nɔ kɔmɔn, yu fɔ chɛk di kalkul.
Sayd bɛt na di ɔda tebul gem dɛn
Bollman (2021) de put di men bɛt dɛn fɔ blackjack, baccarat, craps ɛn rulɛt nia di sayd bɛt dɛn we yu kin si pan di sem tebul. Na di fɔs tri gem, di sayd bɛt de kɔst pas di men bɛt, bɔku tɛm bɔku bɔku pas am. Di wan we difrɛn na di las gem na di tebul: di advantej fɔ Amɛrikan rulɛtkayn rulɛtAmɛrikan rulɛtWil wit 0 ɛn 00, 38 pɔkit, kasino advantej 5.26%. Nɔto di wil we dis sayt de yuz pas ɔl.Rid ɔl → na 5.26% pan di men bɛt dɛn. I ay so te sayd bɛt lɛk Colors ɔ WINGO kin chip pas am.
Fɔmula
Kwɛstyɔn dɛn
Nɔ. Na 2.70% fɔ wetin yu bɛt. If yu bɛt di sem mɔni bak, yu dɔn bɛt am wan tɛm bak.
Nɔ. Na pat fɔ di ol. Di lɔs we fɔ ɛkspɛkt na dɔla de gro wit di bɛt mɔni.
If yu mɛzh am wit di advantej, ɔl di nɔmal Yuropian bɛt dɛn na di sem; na ɔmɔs tɛm dɛn de win ɛn ɔmɔs dɛn de pe nɔmɔ difrɛn. Wit La Partage, ivin-mɔni bɛt na af fɔ di ɔda wan dɛn.
Ple wit Mat
Tray dɛn yusɛf fɔs. Ɛni ansa de ayd; opin am we yu rɛdi.
Pan Yuropian wil, bɛt pan wan nɔmbabɛtBɛt pan wan nɔmbaWan nɔmba nɔmɔ, i de pe 35:1.Rid ɔl → ɛn bɛt pan rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl → dɛn tu de kɔst 2.70%, pan ɔl we wan kɔba jɔs wan nɔmba ɛn di ɔda wan kɔba etin. Wetin mek ɛni bɛt gɛt di sem kasino advantejmatematiksKasino advantejDi pat pan ɛni bɛt mɔni we di kasino de kip pan avrej: 2.70% na Yuropian rulɛt.Rid ɔl →?
Sho di ansa
Ansa Dɛn sɛt ɛni pemɔniPeWetin bɛt we win de gi yu, dɛn de tɔk am as “X to 1” ɔn tɔp di bɛt mɔni we kam bak.Rid ɔl → lɛk se di zirowilZiroDi wan grin pɔkit we nɔ ivin-mɔni, dɔzin ɔ kɔlɔm bɛt nɔ kɔba; na usay di kasino advantej kɔmɔt. Dɛn kin kɔl am bak: wan ziro, 0.Rid ɔl → nɔ de, so ɛni bɛt de lɔs wan yunitmɔniYunitDi bes bɛt mɔni we sistɛm ɔ pleya de wok wit. Dɛn de ɛksplen prɔgrɛshɔn wit yunit so dat i go wok na ɛni tebul.Rid ɔl → pan 37 spin, ilɛk wetin i kɔba.
Tek wan bɛt pan n nɔmba. I de pe (36 − n)/n to 1. Pan 37 spin, pan avrej, i de win n tɛm ɛn lɔs 37 − n tɛm.
Di win dɛn de bring n × (36 − n)/n = 36 − n yunit. Di lɔs dɛn de kɔst 37 − n yunit. Di difrɛns na −1 yunit fɔ ɛni 37 spin, ɛn n dɔn kansɛl: di rizɔlt na di sem fɔ bɛt pan wan nɔmba, kɔnabɛtKɔnaFɔ nɔmba we de sheb wan kɔna na di bɛt tebul, i de pe 8:1.Rid ɔl → ɔ dɔzinbɛtDɔzin1–12, 13–24 ɔ 25–36, i de pe 2:1.Rid ɔl →. Wan yunit we yu lɔs pan 37 na 2.70%.
Pan wil we gɛt N pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl →, di sem kalkul de gi (36 − N)/N, so −2/38 = 5.26% pan Amɛrikan wil. Di wan bɛt we nɔ fala dis rul na di Amɛrikan bɛt pan fayv nɔmba: di rul se i fɔ pe 6.2 to 1, i de pe 6, ɛn i de kɔst 7.89%.
Keno, di gem we tan lɛk lɔtri, de kip 25% ɔ mɔ pan wetin pipul bɛt. If wan kasino ad ziro dɛn pan rulɛt wil ɛn lɛf di pe dɛn lɛk aw dɛn de, ɔmɔs ziro i go nid fɔ mek rulɛt kɔst lɛk keno?
Sho di ansa
Ansa Twɛlv ziro: wil we gɛt 48 pɔkit.
If di wil gɛt z ziro, i gɛt 36 + z pɔkit, bɔt di pe dɛn stil de tink se na 36. Bay di rul na di pazul we de ɔp, ɛni bɛt de lɔs z yunit pan 36 + z spin, so di kasino advantej na z/(36 + z).
Mek dat ikwal wan kwata: 4z = 36 + z, so z = 12. Twɛlv ziro pan wil we gɛt 48 pɔkit go kɔst 25%.
Di wil wit tripul ziro na di Las Vegas Strip, di rulɛt we kɔst pas ɔl we bɔku pleya go mit, gɛt jɔs wan kwata pan da ɔmɔs ziro de.
ziropɔkitkasino advantej1372.70%2385.26%3397.69%44010.00%124825.00%Di Massachusetts Lottery bin bigin wan wil na 2023 we gɛt 36 nɔmba ɛn nɔ gɛt ziro. Wan nɔmba de pe 25 fɔ 1, ɛn rɛd, blakbɛtBlakIvin-mɔni bɛt pan di 18 blak nɔmba. Na Frɛnch: noir.Rid ɔl →, ɔd ɔ ivin de pe 3 fɔ 2. We i nɔ gɛt ziro, i kɔst smɔl pas rulɛt?
Sho di ansa
Ansa Nɔ, i kɔst pas fa: 30.56% pan wan nɔmba ɛn 25% pan rɛd ɔ blak, we Yuropian wil na jɔs 2.70%.
“Fɔ” de inklud di bɛt mɔni. Wan $1 bɛt pan nɔmba de gi $25 bak wan tɛm pan 36 drɔ pan avrej: $25 kam bak fɔ $36 we yu bɛt, lɔs fɔ $11 pan 36, 30.56%.
Wan $2 bɛt pan rɛd de gi $3 bak af di tɛm: $3 kam bak fɔ ɛni $4 we yu bɛt, lɔs fɔ 25%.
Ziro na jɔs wan we fɔ sɛt prays. Rulɛt de pe lɛk se na 36 pɔkit de, ɛn i ad wan ɛkstra pɔkit, nɔmba 37; dis wil gɛt 36 pɔkit ɛn i jɔs de pe smɔl. Bollman (2024) gi am as ɛksasayz.
Wan kasino want nyu bɛt pan di ilɛvin praym nɔmbamatematiksPraym nɔmbaFul nɔmba we pas 1 we na ɔnli 1 ɛn insɛf kin sheb am rayt: 2, 3, 5, 7, 11, 13 ɛn so.Rid ɔl → frɔm 1 to 36: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 ɛn 31. Ɔmɔs i fɔ pe fɔ mek i kɔst di sem 2.70% lɛk ɛni ɔda bɛt pan Yuropian wil? Ɔmɔs i go kɔst if i pe 2 to 1?
Sho di ansa
Ansa 25 to 11, lɛk 2.27 to 1. If i pe 2 to 1, i go kɔst 10.81%.
Yuz di rul frɔm di fɔs pazul: bɛt pan n nɔmba de pe (36 − n)/n to 1. If n = 11, dat na 25/11 to 1, pe we nɔ izi, bikɔs $10 chipmɔniChipTokɛn we min wan sɛt mɔni; yu put am na di bɛt tebul fɔ mek bɛt. Dɛn kin kɔl am bak: check.Rid ɔl → go win $22.73.
If i pe 2 to 1, $1 bɛt de win $2 pan 11 spin pan 37 ɛn lɔs $1 pan di ɔda 26: 22 − 26 = −4 yunit fɔ ɛni 37 spin, 10.81%.
Na dat mek rulɛt de sɛl bɛt pan 1, 2, 3, 4, 6, 12 ɛn 18 nɔmba: 36 de divayd bay ɛni wan pan dɛn, so di fɛr pe na ful nɔmba. Taylor (2021) gi di ɛksasayz wit tɛn praym nɔmba; bɔt na ilɛvin de.
Smɔl jok fɔ ɛz di maynd
1/37 fɔ ɛni bɛt mɔni, pan ɛni bɛt, ɛni spin.
Usay wi gɛt am frɔm
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Hunacek, M. Quantitative Literacy Through Games and Gambling.