Roulette maths · Inna practice · 7 minute

Expected value a di call bet dem

Voisins, tiers, orphelinsFrench · sectorOrphelins“Orphan dem”: di eight numba weh voisins an tiers lef ova: 17, 34, 6 an 1, 20, 14, 31, 9.Read di whole ting →, neighbour dem an jeu zéro, each one work out to it −1/37 fi evry chip.

Short ansa

Call bet a mix a standard bet wid weight weh nuh even, suh di payout dem change fram pocketgearPocketOne a di 37 compartment wid numba pon di rotor. Nex name: slot, cup.Read di whole ting → to pocket. Each one still a −2.70% a di total stake, cause expected value add up. Dis page show di arithmetic fi all five.

call bet
5 standard
chip
4 to 9
EV fi evry chip
−1/37
payout change by pocket
yes

Wah mek dem look different

A straight upbet demStraight upOne single numba, pay 35:1.Read di whole ting → have one result weh pay. Voisins du zéroFrench · sectorVoisins du zéro“Di neighbour dem a zero”: di seventeen numba fram 22 to 25 pon di wheel, bet wid nine chip.Read di whole ting → have tree different payoutmoney mattaPayoutWah a bet weh win gi yuh back, weh dem quote as “X to 1” on top a di stake weh come back.Read di whole ting →, dependin pon if di ballgearBallDi likkle ball weh di dealer fling roun di track di opposite way to di rotor. Modern ball mek outta ivorine or Teflon, 18–21 mm.Read di whole ting → land inna di streetbet demStreetTree numba inna a row pon di betting layout, pay 11:1. Inna French: transversale.Read di whole ting → weh have double weight, di cornerbet demCornerFour numba weh share a corner pon di betting layout, pay 8:1.Read di whole ting → weh have double weight, or one single splitbet demSplitTwo numba weh deh side by side, pay 17:1.Read di whole ting →. Di variety hide sumting weh nuh change: evry chipmoney mattaChipA token weh stand fi a fix amount, weh yuh put pon di betting layout fi mek a bet. Nex name: check.Read di whole ting → inna di bet a one ordinary bet wid EV −1/37 a itself, an di whole ting a di sum.

Voisins du zéro (9 chip, 17 numba)

2 pon 0-2-3 (street, pay 11), 2 pon 25-26-28-29 (corner, pay 8), 1 each pon di split dem 4-7, 12-15, 18-21, 19-22, 32-35 (pay 17). Hit inna di street: +22 − 7 = +15. Hit inna di corner: +16 − 7 = +9. Hit pon a split: +17 − 8 = +9. Miss: −9. EV = (3 × 15 + 4 × 9 + 10 × 9 − 20 × 9)/37 = (45 + 36 + 90 − 180)/37 = −9/37. Nine chip, −9/37: −1/37 fi evry chip.

call betchipcoverresult dem (net unit, pocket)EV (unit)
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
Neighbour dem (5)55+31 × 5 · −5 × 32−5/37
Jeu zéro47+32 × 1 · +14 × 6 · −4 × 30−4/37
All tree sector togedda2037+15/+9/+12/+31/+13 by pocket; it neva miss−20/37
Divide di EV by di chip dem an evry row come out −1/37.

Tiers du cylindre (6 chip, 12 numba)

Six split, each one pay 17. Any hit: +17 − 5 = +12. Miss: −6. EV = (12 × 12 − 25 × 6)/37 = (144 − 150)/37 = −6/37. Di flattes call betpon di tableCall betA bet yuh tell di dealer, yuh nuh put it dung wid yuh han, usually a bet pon a sector a di wheel like voisins or tiers. Nex name: “announce bet”.Read di whole ting →: one payout, one loss.

Orphelins (5 chip, 8 numba)

1 straight up pon 1 (pay 35), split 6-9, 14-17, 17-20, 31-34 (pay 17). Hit pon 1: +35 − 4 = +31. Hit pon 17 (two split): +34 − 3 = +31. Hit pon 6, 9, 14, 20, 31, 34: +17 − 4 = +13. Miss: −5. EV = (31 + 31 + 6 × 13 − 29 × 5)/37 = (62 + 78 − 145)/37 = −5/37.

Neighbour dem an jeu zéro

Neighbour dembet demNeighboursA numba an di two pocket pon evry side a it pon di wheel, five straight-up chip.Read di whole ting →: five straight up; any hit +35 − 4 = +31; EV = (5 × 31 − 32 × 5)/37 = (155 − 160)/37 = −5/37. Jeu zéroFrench · sectorJeu zéro“Zero game”: di seven numba closes to zero (12, 35, 3, 26, 0, 32, 15), bet wid four chip.Read di whole ting →: split 0-3, 12-15, 32-35 an a straight up pon 26; hit pon 26: +35 − 3 = +32; split hit: +17 − 3 = +14; EV = (32 + 6 × 14 − 30 × 4)/37 = (32 + 84 − 120)/37 = −4/37.

Probability a any hit, call bet% a di spin dem
Jeu zéro (7)
18.9%
Neighbour dem (5)
13.5%
Orphelins (8)
21.6%
Tiers (12)
32.4%
Voisins (17)
45.9%
All tree (37)
100%
% a di spin dem
050100%
If yuh cover evryting wid 20 chip, yuh sure fi get a result between −2 an +16 unit an a EV a −20/37. Dat guarantee cost 2.70% like evryting else.

Di Jeu Zéro bet inna roulette

Pon a electronic wheel

IGT Roulette Evolution, as Bollman (2021) describe it, offa dese call bet pon a electronic single-zeropon di wheelZeroDi one green pocket weh no even-money, dozen or column bet nuh cover; a weh di house edge come fram. Nex name: single zero, 0.Read di whole ting → wheel. Di arithmetic nuh change: each one still a −1/37 fi evry chip. Wah change a di one argument weh playa mek fi sectorpon di wheelSectorA piece a di wheel weh di pocket dem follow one anodda roun di arc, nuh a group pon di betting layout.Read di whole ting → bet. At a real table some people believe seh dem can read di dealer habit dem an di speed a di spin good enough fi guess di part a di wheel weh di ball wi drop, weh dem call clockin di wheel, an a call bet a di natural way fi bet pon a part a di wheel. A electronic wheel nuh have no dealer fi read, an dat argument, weh did weak a ready at a real table, done.

Pon a electronic wheel nuh dealer nuh deh fi read, an di reason fi bet pon a part a di wheel gone wid it.

Electronic roulette terminal dem

Di lesson

Call bet a fi convenience, nuh fi mathematics. Dem a di fastes way fi bet a wheel sector an di only way fi do it inna one announcement. Dem expected valuemathsExpected valueDi average result pon evry bet inna di long run. −1/37 a di stake fi evry standard European bet.Read di whole ting → a di same fi evry chip as di plaines straight up, an di variety a payout a jus bookkeepin, nuh edge.

Formula

EV(call bet) = Σ EV(chip) = −(chip)/37
net pon a hit = payout pon di chip weh win − di chip weh lose

Question dem

Any call bet give betta value?

No. Each one a −1/37 fi evry chip. Dem only different inna coverage an payout shape.

Wah mek orphelins pay +31 pon 17?

Two split have 17 inna dem, suh a hit pay 17 two time an only lose tree chip.

Wah if mi bet voisins wid 2 chip pon evry spot?

18 chip, evry payout double, EV −18/37. Fi scale it up nuh change nutten.

Fun wid maths

Try dem yuhself fus. Evry ansa fold up; open it wen yuh ready.

  1. A electronic wheel offa di French call betpon di tableCall betA bet yuh tell di dealer, yuh nuh put it dung wid yuh han, usually a bet pon a sector a di wheel like voisins or tiers. Nex name: “announce bet”.Read di whole ting → dem: tiers (6 chipmoney mattaChipA token weh stand fi a fix amount, weh yuh put pon di betting layout fi mek a bet. Nex name: check.Read di whole ting →), jeu zéroFrench · sectorJeu zéro“Zero game”: di seven numba closes to zero (12, 35, 3, 26, 0, 32, 15), bet wid four chip.Read di whole ting → (4), orphelinsFrench · sectorOrphelins“Orphan dem”: di eight numba weh voisins an tiers lef ova: 17, 34, 6 an 1, 20, 14, 31, 9.Read di whole ting → (5), voisins (9) an neighbour dembet demNeighboursA numba an di two pocket pon evry side a it pon di wheel, five straight-up chip.Read di whole ting → (5). Fi each one, ow often it win sumting, an wah it cost?

    Show di ansa

    Ansa Each one cost 2.70%. Dem win sumting pon 12, 7, 8, 17 an 5 spin outta 37.

    Di cost follow fram di rule pon dis page: each chip a a regular bet weh lose 1/37 a itself, an expected valuemathsExpected valueDi average result pon evry bet inna di long run. −1/37 a di stake fi evry standard European bet.Read di whole ting → add up.

    Di chance fi win sumting a di numba a pocketgearPocketOne a di 37 compartment wid numba pon di rotor. Nex name: slot, cup.Read di whole ting → di bet cover, outta 37. Tiers cover 12, jeu zéro 7, orphelins 8 an voisins 17. Neighbours cover a numba an two pocket each side a it pon di wheel: 5.

    Bollman (2021) describe jeu zéro wid four chip pon 26 instead a one. Dat mek a 7-chip bet an change di payoutmoney mattaPayoutWah a bet weh win gi yuh back, weh dem quote as “X to 1” on top a di stake weh come back.Read di whole ting → dem, nuh di cost: still 2.70%.

    betchippocket it coverwin sumtinghouse edge
    tiers61232.4%2.70%
    jeu zéro4718.9%2.70%
    orphelins5821.6%2.70%
    voisins91745.9%2.70%
    neighbour dem5513.5%2.70%

Sumting fi laugh

Nine chip, nine thirty-sevent. Di arithmetic a di chip dem.

Nine chip, nine thirty-sevent. Di arithmetic a di chip dem.

Source dem

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Chapta 13, roulette.
  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, roulette.
wi check it 2026-09-28model: European wheel, single zeroow wi work it out ↗source dem ↗