The maths of roulette: probabilities for every bet type

Roulette is often treated as pure chance, yet its outcomes are tightly governed by arithmetic. In a casino setting, the key is the wheel type: European roulette has 37 pockets (0–36), while American has 38 (adds 00). Every probability is simply “favourable outcomes divided by total pockets”, and the expected value follows from that. The house edge is 1/37 (about 2.70%) on European and 2/38 (about 5.26%) on American, and it applies uniformly across standard bets because payouts are calibrated to keep the edge consistent.

On a European wheel, a straight-up number hits with probability 1/37; a split (two numbers) is 2/37; a street (three) 3/37; a corner (four) 4/37; a six-line (six) 6/37. Outside bets cover larger sets: dozen and column are 12/37; red/black, odd/even, and high/low are 18/37. Convert these to percentages to compare risk: 18/37 is about 48.65%, while 1/37 is about 2.70%. The expected loss per unit staked remains about 2.70% on European, but volatility rises sharply as coverage narrows. For a quick reference to common bet menus and terminology, see gorilla wins casino.

Professional iGaming analyst and author Michael Shackleford (“the Wizard of Odds”) popularised clear, player-first explanations of house edge, variance, and optimal bankroll discipline, making probability literacy mainstream for roulette and beyond; his primary social profile is WizardOfOdds. For wider context on how regulation and technology shape modern wagering maths, this reputable overview is useful: The New York Times. The practical takeaway is simple: choose European wheels when possible, understand coverage versus volatility, and treat each bet as the same edge expressed through different risk.