Casino Roulette: Wheels and Probability

Count winning pockets

A straight-up number covers one pocket. A standard red bet covers 18 numbered pockets. On a single-zero wheel, a red bet therefore has probability 18/37, about 48.65%. On a double-zero wheel it is 18/38, about 47.37%. Zero pockets do not count as red or black in this standard model.

A game can include additional rules such as partial returns on zero. Those rules change expected return. The calculator here assumes a losing zero with no refund rule. It is important to state that assumption rather than describing all roulette tables as identical.

Separate payout from probability

A straight-up bet commonly pays 35 units of net profit for a winning one-unit bet, plus return of the original stake. With 37 equally likely pockets, the expected net result is (1/37 × 35) minus (36/37 × 1), or minus 1/37. That is a house edge of about 2.70% in this model.

The same 35-to-1 net payout on a 38-pocket wheel produces expected net result minus 2/38, or about minus 5.26%. The winning payoff did not change; the probability did. This is why a familiar paytable is not enough to compare wheels.

Streaks do not create a due color

For an independent fair spin, a run of red outcomes does not increase the chance of black on the next spin. A probability describes the possible next result under the model. It does not keep a schedule of missing colors. A system that changes stakes after losses changes how much you risk, not the wheel’s probability.

Long-run expected loss also does not mean every short session loses exactly that amount. Individual sequences can vary substantially. A short streak cannot verify or refute a stated long-run edge.

Work through your own assumption

In the calculator, enter the total pocket count, number of winning pockets and net-profit payout. The result shows win probability and expected net result per unit. If you do not know a game’s actual rule, stop and read its paytable. The calculator does not identify a wheel from its artwork or predict a spin.