Roulette probabilities — the complete table (European & American)
Every roulette bet in one table: probability, payout, expected value. European and American side by side — so you can see exactly what a double zero costs.
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Roulette is mathematically one of the simplest casino games — every bet has an exact probability, exact payout and exact expected value. Once you understand the table, you see through the entire game.
Two base setups: European roulette has 37 pockets (0–36, one zero). American has 38 pockets (0–36 plus 00). With identical payouts, the extra pocket translates directly into the house edge.
Even-money bets (red/black, odd/even, 1–18/19–36): European 18/37 = 48.65%. American 18/38 = 47.37%. Payout 1:1. Expected value per $1: −$0.027 (EU) vs. −$0.0526 (US).
Dozen and column (12 numbers): European 12/37 = 32.43%. American 12/38 = 31.58%. Payout 2:1. Same house edge as even-money bets: 2.7% vs. 5.26%.
Six line (6 numbers): European 6/37 = 16.22%, payout 5:1.
Corner (4 numbers): European 4/37 = 10.81%, payout 8:1.
Street (3 numbers): European 3/37 = 8.11%, payout 11:1.
Split (2 numbers): European 2/37 = 5.41%, payout 17:1.
Straight up (1 number): European 1/37 = 2.70%, payout 35:1. EV: (1/37 × 35) − (36/37 × 1) = −$0.027. Identical house edge as every other European bet — a crucial insight: there is no 'better' European bet, only different volatility.
The one exception: American roulette five-number bet (0, 00, 1, 2, 3) — house edge 7.89%. The worst bet at the table. Always skip.
French roulette with La Partage halves the house edge on even-money bets to 1.35% — mathematically the best roulette variant whenever you bet red/black, odd/even or 1–18/19–36.
Practical: the house edge calculator lets you run any setup, the bankroll simulator shows the distribution across 500 spins — the visual gap between straight-up volatility and red/black volatility is dramatic, even though their expected value is identical.
Bottom line: roulette is transparent — every bet is solved. Play European, you pay 2.7% on every bet. Play American, you pay 5.26%. Play French with La Partage, you pay 1.35% on even-money. That's the whole math.