Understanding roulette probabilities
Roulette is purely a game of chance where every spin is independent. Understanding the math helps you make informed betting decisions.
Wheel types explained
European roulette has 37 pockets (0-36) with 2.7% house edge. American roulette adds a double zero (00), increasing numbers to 38 and house edge to 5.26%. French roulette uses European layout but offers La Partage/En Prison rules that reduce even-money bet house edge to 1.35%.
La Partage and En Prison rules
La Partage returns half your stake when zero hits on even-money bets. En Prison "imprisons" your bet for the next spin instead. Both rules cut the house edge in half for outside bets, making French roulette the best choice for players.
Inside vs outside bets
- Inside bets (straight, split, street, corner, six line) cover fewer numbers with higher payouts.
- Outside bets (dozens, columns, red/black, odd/even, high/low) cover more numbers with lower payouts.
- The house edge is the same regardless of bet type on the same wheel.
Common Mistakes
- Believing in the Gambler's Fallacy — 10 reds in a row does NOT make black more likely on the next spin. Each spin is completely independent with the same fixed probabilities. The ball has no memory of previous results, and roulette tables displaying past numbers are designed to encourage this fallacy.
- Thinking betting systems (Martingale, Fibonacci, D'Alembert) can overcome the house edge — no staking system changes the expected value of each bet. Martingale doubles your bet after losses, but one extended losing streak wipes out all previous gains and hits the table limit. The house edge applies to every spin equally.
- Playing American roulette when European is available — the extra zero (00) on an American wheel nearly doubles the house edge from 2.70% to 5.26%. Always choose European single-zero wheels when given the option. The difference costs you approximately $25 extra per $1,000 wagered.
Worked Examples
Single Number Bet Comparison
You want to bet $5 on number 17 straight up. On a European wheel (37 pockets), the probability is 1/37 = 2.70%, with a house edge of 2.70%. On an American wheel (38 pockets), the probability drops to 1/38 = 2.63%, with a house edge of 5.26%. Enter these into the calculator to compare: over 100 bets ($500 total wagered), you'd expect to lose $13.50 on European but $26.30 on American — nearly double. The payout is the same 35:1 on both wheels, but the extra zero costs you significantly.
Red/Black Over a Session
You plan to bet €10 on red for 100 consecutive spins on a European wheel. The probability of red on each spin is 18/37 = 48.65%. The calculator shows your expected loss after 100 spins is €27 (2.7% of €1,000 total wagered). There's approximately a 37% chance you'll be ahead after 100 spins, a 4% chance of breaking exactly even, and a 59% chance of being down. Even on the 'safest' bet, the house edge grinds away at your bankroll over time.
Session Bankroll Planning
You have a $200 bankroll and want to play $5 outside bets (e.g., odd/even) on a European wheel. The calculator estimates approximately 800-1,000 spins before your bankroll is depleted, giving you roughly 2-3 hours of play at 5 spins per minute. After 200 spins ($1,000 wagered), your expected loss is $27, leaving an expected bankroll of $173. There's about a 34% chance you'll be ahead at that point — so set a realistic session goal and walk away if you reach it.
