Title: Probability and Payouts in Double Zero Roulette Explained
Double-zero roulette (commonly called American roulette) is one of the most popular casino table games worldwide. It looks simple — place chips on numbers or groups of numbers and wait for the ball — but beneath that simplicity lies a fixed mathematical advantage for the house. This article explains how the wheel is constructed, the probabilities of common bets, how payouts compare to true odds, the resulting house edge, and what that means for your bankroll and betting choices.
The wheel and the numbers
An American roulette wheel has 38 pockets: the numbers 1–36, plus 0 and 00. The presence of both 0 and 00 is the key difference between American (double-zero) and European (single-zero) roulette; it increases the casino’s edge. Each spin is independent and — assuming a fair wheel — every pocket has equal probability 1/38 ≈ 0.026316 (2.6316%).
Types of bets and payouts
Roulette bets are usually divided into “inside” bets (specific numbers or small groups) and “outside” bets (larger groups, typically even-money or 2:1). Common bets and their standard payouts on American roulette:
- Straight-up (single number): pays 35:1 (covers 1 number)
- Split (two adjacent numbers): pays 17:1 (covers 2 numbers)
- Street (three numbers in a row): pays 11:1 (covers 3 numbers)
- Corner (four numbers): pays 8:1 (covers 4 numbers)
- Line / Six-line (two adjacent rows, six numbers): pays 5:1 (covers 6 numbers)
- Column or Dozen: pays 2:1 (covers 12 numbers)
- Even-money bets (Red/Black, Odd/Even, 1–18/19–36): pays 1:1 (covers 18 numbers)
- Five-number (specific to American wheels: 0, 00, 1, 2, 3): pays 6:1 (covers 5 numbers; not always listed as a separate bet on all tables, but it is common where allowed)
True odds vs casino payouts
The critical point is that casino payouts do not reflect the true odds of winning. True (fair) odds for a bet are based on the ratio of losing outcomes to winning outcomes. The casino’s payout is slightly less generous than the fair odds, and that difference creates the house edge.
Example calculations
To show how this works, calculate the expected value (EV) of a $1 bet. EV = (probability of winning) × (net win when you win) + (probability of losing) × (net loss when you lose).
1) Straight-up bet (one number)
- Probability of winning: 1/38
- Payout: 35:1 (you win $35 net and keep your $1 stake)
- EV = (1/38) × 35 + (37/38) × (−1) = (35 − 37) / 38 = −2/38 = −1/19 ≈ −0.0526316
- Percentage house edge: 5.26316% (you lose about $5.26 per $100 bet on average)
2) Any even-money bet (e.g., Red)
- Probability of winning: 18/38
- Payout: 1:1
- EV = (18/38) × 1 + (20/38) × (−1) = (18 − 20) / 38 = −2/38 ≈ −0.05263
- House edge: 5.263%
3) Column / Dozen (12 numbers)
- Probability of winning: 12/38
- Payout: 2:1
- EV = (12/38) × 2 + (26/38) × (−1) = (24 − 26) / 38 = −2/38 ≈ −5.263%
4) Five-number bet (0, 00, 1, 2, 3)
- Probability of winning: 5/38
- Payout: 6:1
- EV = (5/38) × 6 + (33/38) × (−1) = (30 − 33) / 38 = −3/38 ≈ −0.078947
- House edge: 7.8947% (this is the worst single bet on the American wheel)
Notice a pattern: almost every standard bet (except the five-number special) has the same house edge of about 5.263%. The five-number bet is particularly poor from a player’s perspective because its payout is less favorable relative to the true odds.
Why the house edge is constant
For most bets the casino uses paytables that give payouts slightly below fair odds so that the difference is always the same proportion. For a wheel with 38 pockets, the relationship between payout and true odds results in the ubiquitous 2/38 = 1/19 ≈ 5.263% disadvantage for the player on standard bets. The five-number bet deviates from this because the payout is set differently, hence the larger edge.
Expected loss per stake and long-term play
The house edge tells you your average loss per unit bet over the long run. If you consistently bet $100 on an even-money bet, you can expect to lose about $5.26 per spin on average. That’s an expectation — over a small number of spins you might win or lose much more due to variance, but over many spins the Law of Large Numbers makes the average loss approach the house edge.
Variance and volatility
Different bets have different variance (volatility). Inside bets (straight-up, splits, streets) have high variance: low chance to win but large payouts when you do. Outside bets (reds, dozens) have lower variance: higher chance to win but smaller payouts. Variance affects the bankroll swings you’ll experience. For example, a straight-up $1 bet has a large standard deviation: the big 35:1 payout makes outcomes spread far from the mean. Over time, high variance strategies can lead to both large quick wins and large quick losses; the house edge, however, still determines the long-term expectation.
Common misconceptions and betting systems
Many betting systems (Martingale, Fibonacci, etc.) claim to overcome the house edge by adjusting bet size after wins or losses. These systems do not change the expected value; they only change the distribution of wins and losses and typically increase the risk of catastrophic loss. Martingale, for example, requires doubling after each loss to recover prior losses and gain one unit. It can work for a few rounds with small stakes but will fail against table limits and finite bankrolls: a long losing streak can bankrupt you, and the expected loss (based on the house edge) remains the same.
Practical advice
- Know the odds and the house edge: on American wheels, expect about a 5.263% loss on most bets. Avoid the five-number bet if your goal is reducing expected losses.
- Choose bets based on your risk tolerance: inside bets for excitement and big but rare wins; outside bets for steadier, smaller returns.
- Manage your bankroll: set loss limits and session time-limits to avoid chasing losses.
- Understand variance: short sessions are dominated by luck; the house edge only becomes certain in the long run.
- Consider table rules and limits: minimums and maximums limit how some strategies can be applied, and special rules (like “en prison” or “la partage”) that reduce house edge are usually not applied on American wheels.
Conclusion
Double-zero roulette is a mathematically simple game: each bet’s payout is set so that the casino retains an edge — usually 5.263% on standard bets and even higher on the five-number bet. Knowing the probabilities, payouts, and expected values will not change how the ball falls, but it lets you make informed choices about which bets to place and how much risk you want to accept. If you play, do so for entertainment, be aware of the built-in disadvantage, and treat any wins as a fortunate outcome rather than an investment.
