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.
The number worth comparing
For Roulette Probability and Wheel Math, wheel type and special rules such as la partage or en prison determine the price; chip placement does not change the probability.
For Roulette Probability and Wheel Math, keep the rules and denominator fixed. A percentage per initial wager is not interchangeable with one per average total action.
Read Roulette Probability and Wheel Math as a model with named inputs. Change a rule or denominator and the quoted result no longer answers the same question.
What to record for Roulette
- Stated denominator
- strategy assumption
- exact rules used
If the inputs for Roulette Probability and Wheel Math cannot be matched, report the missing assumption instead of borrowing a cleaner number.
Roulette Probability and Wheel Math is reviewed against the Roulette rules described above. A different pay table or procedure is a different model. Editorial review updated September 24, 2026.