Rulɛt prɔbabiliti

Ɛni prɔbabiliti na rulɛt na ɔmɔs pɔkit yu kɔba, we yu sheb wit 37.

Shɔt ansa

p = nɔmba dɛn we yu kɔba / 37. Wan nɔmba: 2.70%. Eytin nɔmba: 48.65%. Fɔ wan patikula sikwens, yu de mɔltipay di prɔbabiliti fɔ ɛni wan spin.

bɛt pan wan nɔmba

1/37 · 2.70%

dɔzin

12/37 · 32.43%

ivin-mɔni

18/37 · 48.65%

tu rɛd

23.67%

Wan spin

Ɔl di 37 pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl → gɛt di sem chans, so fɔ no di chans fɔ win na rulɛt pan wan spin, yu jɔs fɔ kɔnt. Bɛt pan fɔ nɔmba de win 4/37 di tɛm, lɛk 10.8%. Natin nɔ de pas dat na di prɔbabilitimatematiksPrɔbabilitiDi chans fɔ wan rizɔlt, frɔm 0 to 1 ɔ frɔm 0% to 100%. Wan nɔmba: 1/37 = 2.70%.Rid ɔl → fɔ wan spin. Na dat mek yu kin analayz di ɔl gem pan smɔl pepa.

Prɔbabiliti fɔ win, fɔ ɛni bɛt% fɔ di spin dɛn

Bɛt pan wan nɔmba (1)

2.70%

Split (2)

5.41%

Strit (3)

8.11%

Kɔna (4)

10.81%

Siks lain (6)

16.22%

Dɔzin / kɔlɔm (12)

32.43%

Ivin-mɔni (18)

48.65%

% fɔ di spin dɛn

024.3248.65%

Ɛni bɛt na di nɔmba dɛn we i kɔba, sheb wit 37. Di pe de go dɔŋ we di kɔba de go ɔp, so di valyu we fɔ ɛkspɛkt na di sem −2.70% pan ɛni lain.

Bɔku spin

Di spin dɛn nɔ de dipen pan wan ɔda, so yu de mɔltipay di prɔbabiliti dɛn fɔ wan sikwens. Tu rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl → wan afta di ɔda: (18/37)² = 23.7%. Rɛd ɛn afta dat 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 →: (18/37)(1/37) = 1.3%. Sɛvintin tu tɛm wan afta di ɔda: (1/37)² = 0.073%, lɛk wan tɛm na 1,369. Di ɔda impɔtant fɔ wan patikula sikwens, bɔt i nɔ impɔtant fɔ kɔnt: “rɛd ɛn afta dat blakbɛtBlakIvin-mɔni bɛt pan di 18 blak nɔmba. Na Frɛnch: noir.Rid ɔl →” na 25.0%, bɔt “wan rɛd ɛn wan blak na tu spin, ɛni ɔda” na 50.0%.

Rulɛt spin we nɔ dipen pan ɔda wan

Wan tɛm ɔ mɔ

Yuz di ɔda say. Di chans se bɛt pan wan nɔmbabɛtBɛt pan wan nɔmbaWan nɔmba nɔmɔ, i de pe 35:1.Rid ɔl → nɔ go kam na 37 spin na (36/37)³⁷ = 36.3%. So di chans se i go kam wan tɛm ɔ mɔ na 63.7%. I nɔ na di “shɔ shɔ” we bɔku pleya de ɛkspɛkt frɔm 37 chans we na 1 na 37. Di sem kalkul se wan nɔmba gɛt lɛk 1 na 3 chans fɔ nɔ kam atɔl na 37 spin. Na dat mek di rizɔlt bɔd ɔltɛm de sho sɔm “kol” nɔmba.

spinp(i nɔ kam, wan nɔmba)p(i kam wan tɛm ɔ mɔ)

1076.0%24.0%

3736.3%63.7%

7413.2%86.8%

1006.5%93.5%

1501.7%98.3%

2000.4%99.6%

(36/37)ⁿ ɛn 1 − (36/37)ⁿ. Ivin afta 100 spin, wan nɔmba na fiftin nɔ dɔn kam yet.

Rulɛt rizɔlt dɛn: aw fɔ rid di bɔd

Aw lɔng yu fɔ ɛkspɛkt fɔ wet

Pan avrej, wan nɔmba de kam wan tɛm na ɛni 37 spin. Bɔt di wet de chenj bad bad wan: di midul valyu na lɛk 25 spin (af di tɛm i de kam bifo dat), ɛn wan wet na twɛnti de pas 110 spin. Di tɛm fɔ wet na jiomɛtrik prɔsɛs gɛt lɔng tel. Pleya we “no” se wan nɔmba fɔ kam afta 60 spin de tɔk bɔt sɔntin we de apin wan tɛm na fayv.

Lay-lay tɔk: nɔmba ‘fɔ kam’

Mistek we pipul kin mek

Fɔ ad prɔbabiliti fɔ tin dɛn we kin apin di sem tɛm (rɛd ɔ ɔd nɔto 36/37; na 26/37, bikɔs tɛn nɔmba na di tu). Fɔ mɔltipay fɔ tin dɛn pan di sem spin (rɛd ɛn ɔd pan wan spin na 10/37, nɔto 18/37 × 18/37). Fɔ tek di spin dɛn we dɔn pas lɛk se dɛn na pat fɔ di sikwens we yu de bɛt pan naw: afta tɛn rɛd, di chans fɔ di ilɛvin wan na 18/37, nɔto (18/37)¹¹.

Wetin na di ɔds na rulɛt, ɛn aw dɛn difrɛn frɔm prɔbabiliti?

Kasino de tɔk di 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 ɔds. Wan nɔmba de win wit prɔbabiliti 1/37, so di ɔds fɔ win pan wan nɔmba na rulɛt na 36 to 1 agens yu. Pe we na 35 to 1 nɔ rich 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 →. Dat na di kasino advantejmatematiksKasino advantejDi pat pan ɛni bɛt mɔni we di kasino de kip pan avrej: 2.70% na Yuropian rulɛt.Rid ɔl → na in fɔs fɔm. Fɔ chenj am: ɔds agens = (1 − p)/p; prɔbabiliti = 1/(ɔds + 1).

Fɔmula

p(bɛt) = n / 37

p(A ɛn afta dat B) = p(A) · p(B)

p(wan tɛm ɔ mɔ na k) = 1 − (1 − p)ᵏ

ɔds agens = (1 − p) / p

Kwɛstyɔn dɛn

Wetin na di prɔbabiliti fɔ ziro tu tɛm wan afta di ɔda?

(1/37)² = 1/1369 ≈ 0.073%.

Wetin na di chans fɔ rɛd ɔ blak?

36/37 = 97.3%. Ziro na di res.

Na 17 na di nɔmba we de kam pas ɔl?

Ɔl di 37 na 1/37. Na Sɛvintin pipul de bɛt pan pas ɔl, ɛn dat na tin bɔt pipul.

Ple wit Mat

Tray dɛn yusɛf fɔs. Ɛni ansa de ayd; opin am we yu rɛdi.

Yu de bɛt pan rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl →, spin afta spin. Wetin na di chans se yu fayv win go kam rayt rayt pan di et spin? Ɛn se yu go gɛt fayv win insay di fɔs et spin?
Sho di ansa
Ansa 12.9%, lɛk 1 insay 8, fɔ di fayv win pan spin et. 33.4% fɔ fayv win bay da tɛm.
Di fayv win pan spin et min tu tin: spin et win, ɛn di fɔs sɛvin spin gɛt fɔ win ɛn tri lɔs rayt rayt, ilɛk aw dɛn arenj. 35 we de fɔ put fɔ win insay sɛvin spin.
So di chans na 35 × (18/37)⁵ × (19/37)³ = 35 × 0.02725 × 0.1354 = 12.9%.
Fɔ fayv win bay spin et, ad di sem kayn pat fɔ di fayv win pan spin fayv, siks ɛn sɛvin: 2.7% + 7.0% + 10.8% + 12.9% = 33.4%. Statistiks pipul dɛn kɔl dis di “negative binomial” distribyushɔn: ɔmɔs tray i de tek fɔ gɛt sɛt nɔmba fɔ win. Taylor (2021) du di sem kwɛstyɔn pan Amɛrikan wil, 12.2%.

Smɔl jok fɔ ɛz di maynd

$Kɔnt di pɔkit dɛn. Sheb wit 37. Mɔltipay fɔ sikwens. I dɔn.$

Kɔnt di pɔkit dɛn. Sheb wit 37. Mɔltipay fɔ sikwens. I dɔn.

Usay wi gɛt am frɔm

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3rd ed., 1968. Gambler’s ruin, chapta XIV.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Chapta 13, rulɛt.
Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021.

wi chɛk am 2026-09-28mɔdɛl: Yuropian, wan ziromɛtɔdɔlɔji ↗usay wi gɛt am frɔm ↗