Roulette reference library

Roulette Probability and Wheel Math

Calculate coverage, fair odds, casino payouts, expected value, and the chance of repeated events.

Bottom line: Probability comes from pockets covered divided by total pockets. Expected value also requires the net payout when the bet wins.

Single-spin probability

A bet covering k distinct pockets on a wheel with N pockets wins with probability k/N. It loses with probability (N−k)/N.

Coverage must not double-count overlapping chips when evaluating a portfolio of wagers.

Expected value

For a one-unit bet with net win payout P, player EV is (k/N × P) − ((N−k)/N × 1). The negative of player EV is the expected casino win per unit.

A single-zero straight-up bet gives (1/37 × 35) − (36/37) = −1/37.

Repeated spins

If spins are independent, the chance an event misses n times is (1−p)^n. The chance it appears at least once is 1−(1−p)^n.

These formulas describe a planned sequence before it occurs. A long completed miss does not make the next spin more likely.

Multiple bets

Add the expected value of each chip to obtain portfolio expectation. Overlapping outcomes affect variance and settlement, but they do not cancel the edge.

The site calculator can model coverage and payout without implying that a likely win is a profitable bet.

Practical checklist

  • Use total wheel pockets
  • Count unique covered outcomes
  • Enter net payout
  • Separate probability from expected value
  • Do not apply sequence probability to a single next spin
Scope and review

Rules, probabilities, and payouts apply only to the model stated on this page. Posted casino rules control when they differ. Last reviewed September 20, 2026.