The math of roulette

About our calculations

Clear formulas, explicit assumptions and worked examples. Learn how Roulette Odds separates payout arithmetic from prediction.

What Roulette Odds offers

Roulette Odds explains the mathematics of roulette: the chance of winning each standard bet, the payout it carries, the house edge and what happens over repeated spins. It includes a roulette odds calculator, a payout chart, a Martingale progression tool and guides to each wheel type and bet.

The site is educational. It does not accept bets or deposits, list or rank casinos, or contain affiliate links.

Who it is for

  • Players who want to understand a bet before deciding whether to place it.
  • Beginners learning the rules of roulette and the table layout.
  • Students, writers and teachers who need a clear worked example of probability and expected value.

How calculations are produced

Every tool states its inputs, formula and supported rules. We use independent arithmetic checks and known boundary cases to test outputs. Rounding happens for display after the underlying calculation.

How the calculations are tested

These reference cases are run against the calculator code before every publication:

  • A $10 red bet on 37 pockets: 48.65% win chance, −$0.2703 expected net, 2.70% house edge.
  • $10 on red plus $10 on black: no profitable pocket, 97.30% break-even, 2.70% loss.
  • $1 on 0 plus $1 on 00 on 38 pockets: 5.26% profit chance, −$0.1053 expected net.
  • Ten reds in a row on 37 pockets: (18/37)^10 = 0.07425%.
  • Martingale from $1 after six losses: $63 lost, $64 next stake, 1.83% fixed-block chance.

Money is settled in whole cents and probabilities use exact pocket counts, so a break-even outcome is never shown as a win. Guide tables use standard payout and pocket-count formulas; the reference tests check calculator outputs independently.

Editorial principles

  • State the model. Every figure names the wheel, the payout and the zero rule it assumes.
  • Separate probability from payout. A payout says what a win pays; a probability says how often it happens.
  • No predictions. Nothing on the site forecasts a spin or claims a betting system can overcome the house edge.
  • Label variation. When a rule differs between tables or games, the variation is described rather than averaged away.
  • Keep gambling decisions separate from the math. See responsible play.

Review and corrections

Game definitions are checked against the published rule sources listed below. Mathematical examples are recalculated for the exact assumptions shown whenever a page changes. Each page's last meaningful update is reflected in the sitemap.

If you find an error, email contact@rouletteodds.co with the page address, the figure and the inputs you used. Confirmed errors are corrected on the page.

Education, not real-money play

Roulette Odds does not accept bets or deposits, choose an operator or predict an outcome. An example stake is a number used to explain a calculation.

Independence

The site does not promote gambling operators, and its pages contain no affiliate links. Any proposed contribution should meet the same factual standards and disclose commercial interests. Read the disclaimer for the limits of what the site provides.

Contact

Questions, corrections and editorial enquiries: contact@rouletteodds.co. More detail is on the contact page.

Read the primary sources