Even-money bets on a French table: p and payout unchanged, EV −1.35%, σ ≈ 0.99.

Mathematics · Reference · 5 min

Roulette Probability Table

Every standard bet with its probability, payout, expected valuemathExpected valueThe average result per bet over the long run. −1/37 of the stake for every standard European bet.Read full → and standard deviation.

Short answer

All bets share the same expected value, −2.70% of stake. They differ only in probability and spread.

bets listed

EV, all bets

−2.70%

σ range

1.00 to 5.84

call bets

also 2.70%

How to use it

ProbabilitymathProbabilityChance of an outcome, from 0 to 1 or 0% to 100%. One number: 1/37 = 2.70%.Read full → tells you how often you win; payoutmoneyPayoutWhat a winning bet returns, quoted as “X to 1” on top of the returned stake.Read full → tells you how much; σ tells you how bumpy the ride is. The EV column is the same on every row by construction, so the table is really a menu of variancesmathVarianceA measure of how widely results spread around the expected value. High for straight up, low for even-money bets.Read full → at a fixed price.

betcoversp(win)paysσ per $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 is −$0.027 per $1 on every row.

Call bets

SectorwheelSectorA contiguous arc of pockets on the wheel, as distinct from a group on the layout.Read full → bets are combinations of standard bets and inherit their edge. Each has its own payout shape because the chipsmoneyChipA token representing a fixed amount, placed on the layout to make a bet. Also: check.Read full → are weighted unevenly.

call betchipscoversp(any hit)net on hit (units)EV per unit

Neighbors (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 of Call Bets

Over several spins

Probabilities of at least one hit over k spins, for a few common questions.

betin 10 spinsin 37 spinsin 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 (specific)24.0%63.7%93.5%

1 − (1 − p)ᵏ.

Session spreads

Standard deviationmathStandard deviationSquare root of variance; the typical distance of a result from the expected value.Read full → of a 100-spin session at $10 flat, by bet, with the shared expected result of −$27.

σ of 100 spins at $10$

Straight up

$584

Split

$409

Street

$328

Corner

$284

Six line

$223

Dozen / column

$139

Even money

$100

0292$584

Questions

Why is EV the same on every row?

Because every payout is 36/n − 1 against a fair 37/n − 1. See the house edgemathHouse edgeThe share of each stake the casino keeps on average: 2.70% in European roulette.Read full → page.

Where is la partage?

Even-money betsbetEven-money betRed/black, odd/even, high/low. 18 numbers, pays 1:1.Read full → on a French table: p and payout unchanged, EV −1.35%, σ ≈ 0.99.

Is there a table for the American wheel?

Divide by 38 instead of 37 and the EV column becomes −5.26% on every row, −7.89% for the five-number bet.

Comic relief

$Nine bets, one expected value, no memory.$

Nine bets, one expected value, no memory.

Sources

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

reviewed 2026-09-28model: European, single zeromethodology ↗sources ↗