Rulɛt matematiks · Fɔ yuz am · 7 minit

Di valyu we fɔ ɛkspɛkt fɔ kɔl bɛt dɛn

Voisins, tiers, orphelinsFR · sɛktaOrphelins“Di ɔfan dɛn”: di et nɔmba we voisins ɛn tiers lɛf: 17, 34, 6 ɛn 1, 20, 14, 31, 9.Rid ɔl →, nɛba dɛn ɛn jeu zéro, wi kalkul ɛni wan te i rich −1/37 fɔ ɛni chip.

Shɔt ansa

Kɔl bɛt dɛn na standad bɛt dɛn we dɛn jɔyn wit chip we nɔ ivin, so dɛn pe de chenj frɔm pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl → to pɔkit. Ɛni wan stil na −2.70% pan ɔl di bɛt mɔni, bikɔs valyu we fɔ ɛkspɛkt de ad. Dis pej de sho di kalkuleshɔn fɔ ɔl fayv.

kɔl bɛt
5 standad wan
chip
4 to 9
EV fɔ ɛni chip
−1/37
pe de chenj frɔm pɔkit to pɔkit
yɛs

Wetin mek dɛn luk difrɛn

Bɛt pan wan nɔmbabɛtBɛt pan wan nɔmbaWan nɔmba nɔmɔ, i de pe 35:1.Rid ɔl → gɛt wan rizɔlt nɔmɔ we de pe. Voisins du zéroFR · sɛktaVoisins du zéro“Di nɛba dɛn fɔ ziro”: di sɛvintin nɔmba frɔm 22 to 25 na di wil, yu bɛt dɛn wit nayn chip.Rid ɔl → gɛt tri difrɛn 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 →, akɔdin to if di bɔlikwipmɛntBɔlDi smɔl bɔl we dɛn trowe na di rod agens di rotɔ. Di nyu bɔl dɛn na ivorine ɔ Teflon, 18–21 mm.Rid ɔl → fɔdɔm na di stritbɛtStritTri nɔmba na wan rɔw fɔ di bɛt tebul, i de pe 11:1. Na Frɛnch: transversale.Rid ɔl → we gɛt tu chip, di kɔnabɛtKɔnaFɔ nɔmba we de sheb wan kɔna na di bɛt tebul, i de pe 8:1.Rid ɔl → we gɛt tu chip, ɔ wan splitbɛtSplitTu nɔmba we de nia wan ɔda, i de pe 17:1.Rid ɔl → we gɛt wan chip. Di difrɛn pe dɛn de ayd wan tin we nɔ de chenj: ɛni chipmɔniChipTokɛn we min wan sɛt mɔni; yu put am na di bɛt tebul fɔ mek bɛt. Dɛn kin kɔl am bak: check.Rid ɔl → insay di bɛt na nɔmal bɛt wit EV −1/37 pan insɛf, ɛn di ol bɛt na dɛn ɔl ad togɛda.

Voisins du zéro (9 chip, 17 nɔmba)

2 pan 0-2-3 (strit, i de pe 11), 2 pan 25-26-28-29 (kɔna, i de pe 8), 1 ɛni wan pan di split dɛn 4-7, 12-15, 18-21, 19-22, 32-35 (dɛn de pe 17). If i nak di strit: +22 − 7 = +15. If i nak di kɔna: +16 − 7 = +9. If i nak wan split: +17 − 8 = +9. If i mis: −9. EV = (3 × 15 + 4 × 9 + 10 × 9 − 20 × 9)/37 = (45 + 36 + 90 − 180)/37 = −9/37. Nayn chip, −9/37: −1/37 fɔ ɛni chip.

kɔl bɛtchipnɔmba we i kɔbarizɔlt dɛn (nɛt yunit, pɔkit)EV (yunit)
Voisins du zéro917+15 × 3 · +9 × 14 · −9 × 20−9/37
Tiers du cylindre612+12 × 12 · −6 × 25−6/37
Orphelins (en cheval)58+31 × 2 · +13 × 6 · −5 × 29−5/37
Nɛba dɛn (5)55+31 × 5 · −5 × 32−5/37
Jeu zéro47+32 × 1 · +14 × 6 · −4 × 30−4/37
Ɔl tri sɛkta dɛn togɛda2037+15/+9/+12/+31/+13 akɔdin to di pɔkit; i nɔ de ɛva mis−20/37
Divayd di EV bay di chip dɛn ɛn ɛni lain na −1/37.

Tiers du cylindre (6 chip, 12 nɔmba)

Siks split, ɛni wan de pe 17. Ɛni nak: +17 − 5 = +12. If i mis: −6. EV = (12 × 12 − 25 × 6)/37 = (144 − 150)/37 = −6/37. Na di kɔl bɛttebulKɔl bɛtBɛt we yu tɔk to di dila insay fɔ put am wit yu an, pas ɔl bɛt pan wan sɛkta na di wil lɛk voisins ɔ tiers. Dɛn kin kɔl am bak “bɛt we yu tɔk”.Rid ɔl → we flat pas ɔl: wan pe, wan lɔs.

Orphelins (5 chip, 8 nɔmba)

1 bɛt pan wan nɔmba pan 1 (i de pe 35), split dɛn 6-9, 14-17, 17-20, 31-34 (dɛn de pe 17). If i nak 1: +35 − 4 = +31. If i nak 17 (tu split): +34 − 3 = +31. If i nak 6, 9, 14, 20, 31, 34: +17 − 4 = +13. If i mis: −5. EV = (31 + 31 + 6 × 13 − 29 × 5)/37 = (62 + 78 − 145)/37 = −5/37.

Nɛba dɛn ɛn jeu zéro

Nɛba dɛnbɛtNɛba dɛnWan nɔmba ɛn di tu pɔkit dɛn na ɛni sayd fɔ am na di wil, fayv chip pan wan nɔmba ɛni wan.Rid ɔl →: fayv bɛt pan wan nɔmba; ɛni nak +35 − 4 = +31; EV = (5 × 31 − 32 × 5)/37 = (155 − 160)/37 = −5/37. Jeu zéroFR · sɛktaJeu zéro“Ziro gem”: di sɛvin nɔmba we nia ziro pas ɔl (12, 35, 3, 26, 0, 32, 15), yu bɛt dɛn wit fɔ chip.Rid ɔl →: split dɛn 0-3, 12-15, 32-35 ɛn bɛt pan wan nɔmba pan 26; if i nak 26: +35 − 3 = +32; if i nak split: +17 − 3 = +14; EV = (32 + 6 × 14 − 30 × 4)/37 = (32 + 84 − 120)/37 = −4/37.

Prɔbabiliti fɔ ɛni nak, kɔl bɛt dɛn% pan di spin dɛn
Jeu zéro (7)
18.9%
Nɛba dɛn (5)
13.5%
Orphelins (8)
21.6%
Tiers (12)
32.4%
Voisins (17)
45.9%
Ɔl tri (37)
100%
% pan di spin dɛn
050100%
If yu kɔba ɔltin wit 20 chip, yu shɔ fɔ gɛt rizɔlt bitwin −2 ɛn +16 yunit, ɛn EV −20/37. Dat shɔ de kɔst 2.70% lɛk ɔltin.

Jeu Zéro rulɛt bɛt

Pan ilɛktrɔnik wil

IGT in Roulette Evolution, as Bollman (2021) de tɔk bɔt am, de gi dɛn kɔl bɛt ya pan ilɛktrɔnik wil wit wan 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 →. Di kalkuleshɔn nɔ de chenj: ɛni wan stil na −1/37 fɔ ɛni chip. Wetin chenj na di wan agyumɛnt we pleya dɛn de mek fɔ sɛktawilSɛktaPɔkit dɛn we de fala wan ɔda na wan pat fɔ di wil, nɔto grup na di bɛt tebul.Rid ɔl → bɛt. Na rial tebul, sɔm pipul biliv se dɛn kin rid di dila in abit ɛn aw di spin fast fayn te dɛn gɛs usay di bɔl go fɔdɔm, ɛn dɛn kɔl dat tɛm di wil; kɔl bɛt na di izi we fɔ bɛt pan wan eria. Ilɛktrɔnik wil nɔ gɛt dila fɔ rid, so dat agyumɛnt, we wik ivin na rial tebul, dɔn go.

Pan ilɛktrɔnik wil, dila nɔ de fɔ rid, ɛn di rizin fɔ bɛt pan wan eria pan di wil dɔn go wit am.

Ilɛktrɔnik rulɛt mashin dɛn

Wetin wi lan

Kɔl bɛt dɛn na fɔ mek tin izi, nɔto matematiks. Dɛn na di fastis we fɔ bɛt pan wan sɛkta pan di wil ɛn di wan we nɔmɔ fɔ du am wit wan tɔk. Dɛn valyu we fɔ ɛkspɛktmatematiksValyu we fɔ ɛkspɛktDi avrej rizɔlt fɔ ɛni bɛt if yu ple lɔng tɛm. −1/37 fɔ di bɛt mɔni fɔ ɛni nɔmal Yuropian bɛt.Rid ɔl → na di sem fɔ ɛni chip lɛk di bɛt pan wan nɔmba we simpul pas ɔl, ɛn di difrɛn pe dɛn na jɔs buk-kip, nɔto advantej.

Fɔmula

EV(kɔl bɛt) = Σ EV(chip dɛn) = −(chip dɛn)/37
nɛt if i nak = pe pan di chip(dɛn) we win − di chip dɛn we lɔs

Kwɛstyɔn dɛn

Ɛni kɔl bɛt gɛt bɛtɛ valyu?

Nɔ. Ɛni wan na −1/37 fɔ ɛni chip. Na ɔmɔs pɔkit dɛn kɔba ɛn di shep fɔ dɛn pe nɔmɔ mek dɛn difrɛn.

Wetin mek orphelins de pe +31 pan 17?

Tu split gɛt 17 insay, so if i nak, i de pe 17 tu tɛm ɛn na jɔs tri chip lɔs.

Wetin if a bɛt voisins wit 2 chip pan ɛni ples?

18 chip, ɛni pe dɔbul, EV −18/37. If yu mek am big, natin nɔ chenj.

Ple wit Mat

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

  1. Wan ilɛktrɔnik wil de gi di Frɛnch kɔl bɛttebulKɔl bɛtBɛt we yu tɔk to di dila insay fɔ put am wit yu an, pas ɔl bɛt pan wan sɛkta na di wil lɛk voisins ɔ tiers. Dɛn kin kɔl am bak “bɛt we yu tɔk”.Rid ɔl → dɛn: tiers (6 chipmɔniChipTokɛn we min wan sɛt mɔni; yu put am na di bɛt tebul fɔ mek bɛt. Dɛn kin kɔl am bak: check.Rid ɔl →), jeu zéroFR · sɛktaJeu zéro“Ziro gem”: di sɛvin nɔmba we nia ziro pas ɔl (12, 35, 3, 26, 0, 32, 15), yu bɛt dɛn wit fɔ chip.Rid ɔl → (4), orphelinsFR · sɛktaOrphelins“Di ɔfan dɛn”: di et nɔmba we voisins ɛn tiers lɛf: 17, 34, 6 ɛn 1, 20, 14, 31, 9.Rid ɔl → (5), voisins (9) ɛn nɛba dɛnbɛtNɛba dɛnWan nɔmba ɛn di tu pɔkit dɛn na ɛni sayd fɔ am na di wil, fayv chip pan wan nɔmba ɛni wan.Rid ɔl → (5). Fɔ ɛni wan, ɔmɔs tɛm i de win sɔntin, ɛn ɔmɔs i de kɔst?

    Sho di ansa

    Ansa Ɛni wan de kɔst 2.70%. Dɛn de win sɔntin pan 12, 7, 8, 17 ɛn 5 spin pan 37.

    Di kɔst de kɔmɔt frɔm di rul pan dis pej: ɛni chip na nɔmal bɛt we de lɔs 1/37 pan insɛf, ɛn valyu we fɔ ɛkspɛktmatematiksValyu we fɔ ɛkspɛktDi avrej rizɔlt fɔ ɛni bɛt if yu ple lɔng tɛm. −1/37 fɔ di bɛt mɔni fɔ ɛni nɔmal Yuropian bɛt.Rid ɔl → de ad.

    Di chans fɔ win sɔntin na ɔmɔs pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl → di bɛt kɔba, pan 37. Tiers de kɔba 12, jeu zéro 7, orphelins 8 ɛn voisins 17. Nɛba dɛn de kɔba wan nɔmba ɛn tu pɔkit na ɛni sayd pan di wil: 5.

    Bollman (2021) tɔk se jeu zéro gɛt fɔ chip pan 26, nɔto wan. Dat de mek bɛt wit 7 chip ɛn i de chenj in 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 → dɛn, nɔto in kɔst: i stil na 2.70%.

    bɛtchippɔkit we i kɔbai de win sɔntinkasino advantej
    tiers61232.4%2.70%
    jeu zéro4718.9%2.70%
    orphelins5821.6%2.70%
    voisins91745.9%2.70%
    nɛba dɛn5513.5%2.70%

Smɔl jok fɔ ɛz di maynd

Nayn chip, nayn pat pan tati-sɛvin. Di kalkuleshɔn na di chip dɛn.

Nayn chip, nayn pat pan tati-sɛvin. Di kalkuleshɔn na di chip dɛn.

Usay wi gɛt am frɔm

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Chapta 13, rulɛt.
  2. Wykes, A. The Complete Illustrated Guide to Gambling. Doubleday, 1964.
  3. Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette. CRC Press, 2021. Chapta 2, rulɛt.
wi chɛk am 2026-09-28mɔdɛl: Yuropian, wan ziromɛtɔdɔlɔji ↗usay wi gɛt am frɔm ↗