Roulette Odds and Probability Table
Every standard bet with its probability, payout, expected valuemathsExpected valueThe average result per bet over the long run. −1/37 of the stake for every standard European bet.Read full → and standard deviation.
All bets share the same expected value, −2,70% of stake. They differ only in probability and spread.
How to read this roulette odds chart
ProbabilitymathsProbabilityChance 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; the payoutmoneyPayoutWhat a winning bet returns, quoted as “X to 1” on top of the returned stake.Read full →, quoted as roulette odds, 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 variancesmathsVarianceA 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.
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.
Over several spins
Probabilities of at least one hit over k spins, for a few common questions.
Session spreads
Standard deviationmathsStandard 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.
Questions
Because every payout is 36/n − 1 against a fair 37/n − 1. See the house edgemathsHouse edgeThe share of each stake the casino keeps on average: 2,70% in European roulette.Read full → page.
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.
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.
Sources
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.