Mathematics of Roulette · Reference · 5 min

Table of Odds and Probability for Roulette

Q: Where la partage dey?

Even-money bets for French table: p and payout no change, EV −1.35%, σ ≈ 0.99.

Every standard bet with im probability, payout, expected valuemathsExpected valueDi average result for each bet for di long run. −1/37 of di stake for every standard European bet.Read di whole tin → and standard deviation.

Short answer

All bets get di same expected value, −2.70% of di stake. Dem different only for probability and spread.

bets wey dey di list

EV, all bets

−2.70%

σ range

1.00 to 5.84

call bets

na 2.70% too

How to Read Dis Roulette Odds Chart

ProbabilitymathsProbabilityDi chance of one outcome, from 0 to 1 or from 0% to 100%. One number: 1/37 = 2.70%.Read di whole tin → dey tell you how often you go win; di payoutmoniPayoutWetin bet wey win dey return, wey dem dey quote as “X to 1” on top di stake wey dem return.Read di whole tin →, wey dem dey quote as roulette odds, dey tell you how much; σ dey tell you how rough di ride go be. Di EV column na di same for every row by design, so di table na really menu of variancesmathsVarianceOne measure of how wide di results dey spread around di expected value. E high for straight up, e low for even-money bets.Read di whole tin → for one fixed price.

bete coverp(win)e dey payσ for every $1

Straight up1/372.70%35:15.84

Split2/375.41%17:14.09

Street3/378.11%11:13.28

Corner4/3710.81%8:12.84

Six line6/3716.22%5:12.23

Dozen12/3732.43%2:11.39

Column12/3732.43%2:11.39

Even money18/3748.65%1:11.00

EV na −$0.027 for every $1 for every row.

Call Bets

SectorwheelSectorPockets wey follow each oda for one arc of di wheel, no be group for di layout.Read di whole tin → bets na combinations of standard bets and dem dey inherit dia edge. Each one get im own payout shape becos di chipsmoniChipToken wey stand for one fixed amount, wey you put on top di layout to make bet. Dem also dey call am: check.Read di whole tin → no dey spread equal.

call betchipse coverp(any hit)net when e hit (units)EV for every unit

Neighbours (5)55/3713.51%+31−2.70%

Jeu zéro47/3718.92%+14 or +32−2.70%

Orphelins58/3721.62%+13 or +31−2.70%

Tiers du cylindre612/3732.43%+12−2.70%

Voisins du zéro917/3745.95%+9 or +15−2.70%

Expected Value for Call Bets

Over Many Spins

Probabilities of at least one hit over k spins, for some questions wey pipo dey ask often.

betinside 10 spinsinside 37 spinsinside 100 spins

Straight up24.0%63.7%93.5%

Split42.6%87.1%99.6%

Corner68.1%98.6%> 99.9%

Dozen98.0%> 99.9%> 99.9%

Zero (only zero)24.0%63.7%93.5%

1 − (1 − p)ᵏ.

How Sessions Dey Spread

Standard deviationmathsStandard deviationSquare root of variance; di normal distance between one result and di expected value.Read di whole tin → of session of 100 spins with $10 flat, by bet, with di same expected result of −$27 for all.

σ of 100 spins with $10$

Straight up

$584

Split

$409

Street

$328

Corner

$284

Six line

$223

Dozen / column

$139

Even money

$100

0292$584

Questions wey pipo dey ask

Why EV na di same for every row?

Becos every payout na 36/n − 1 against di fair 37/n − 1. See di house edgemathsHouse edgeDi part of each stake wey di casino dey keep for average: 2.70% for European roulette.Read di whole tin → page.

Where la partage dey?

Even-money betsbetEven-money betRed/black, odd/even, high/low. 18 numbers, e dey pay 1:1.Read di whole tin → for French table: p and payout no change, EV −1.35%, σ ≈ 0.99.

Table dey for di American wheel?

Divide by 38 instead of 37 and di EV column go become −5.26% for every row, −7.89% for di five-number bet.

Small laugh

$Nine bets, one expected value, and dem no get memory.$

Nine bets, one expected value, and dem no get memory.

Sources

Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Chapter 13, roulette.

we check am 2026-09-28model: European wheel, single zerohow we work am ↗where we get am ↗