Roulette: Complete Odds & Strategy Guide
Everything you need to understand roulette mathematically: wheel variants, bet types, payouts, probabilities, house edge, and why no betting system can overcome the math.
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What is Roulette?
Roulette is a casino table game in which a ball is spun on a rotating wheel divided into numbered pockets. Players place bets on where the ball will land — on specific numbers, groups of numbers, colors, or odd/even — and the outcome is entirely determined by chance. There are no player decisions after the bet is placed that affect the result.
Roulette is one of the oldest and most recognizable casino games. Its mathematics are transparent: every bet has a known probability, a fixed payout, and a calculable house edge. This makes it an excellent game for understanding casino probability, even though the house edge ensures that all bets have negative expected value over time.
How Roulette Works
A roulette spin follows a simple sequence: players place their bets on the layout, the dealer (croupier) spins the wheel and releases the ball, the ball settles into a pocket, and bets are resolved. Winning bets are paid according to fixed payout ratios, and losing bets are collected by the house.
Each spin is an independent event — previous results have no influence on future outcomes. The wheel has no memory. The probability of any number appearing is the same on every spin, regardless of what happened on prior spins. This independence is fundamental to understanding why pattern-based strategies cannot work.
Roulette Wheel Layout
The roulette wheel alternates red and black pockets with numbers arranged in a specific sequence (not in numerical order). The green zero pocket(s) are positioned to visually separate sections of the wheel.
The European wheel has 37 pockets: numbers 1-36 alternating red and black, plus a single green 0. The American wheel has 38 pockets: the same numbers plus an additional green 00. The number sequence on the wheel is designed to distribute odd/even, high/low, and red/black as evenly as possible around the circumference.
European vs American vs French Roulette
The three main roulette variants differ primarily in the number of zero pockets and special rules, which directly affects the house edge.
European Roulette
37 pockets (1-36 + single 0). House edge: 2.70%. This is the standard variant found in most casinos outside of North America. All bets have the same house edge of 1/37.
American Roulette
38 pockets (1-36 + 0 + 00). House edge: 5.26%. The additional double-zero pocket nearly doubles the house edge compared to European roulette. Common in North American casinos. Payouts remain the same as European roulette despite the extra pocket.
French Roulette
37 pockets (same wheel as European) with special rules: La Partage returns half of even-money bets when the ball lands on zero, and En Prison holds even-money bets for the next spin when zero hits. These rules reduce the effective house edge on even-money bets to approximately 1.35%.
Compare variants in detail: European vs American Roulette guide
Inside Bets
Inside bets are placed on specific numbers or small groups of numbers within the numbered grid of the layout. They have higher payouts but lower probabilities of winning.
Straight (Single Number)
Bet on one specific number. Highest payout, lowest probability.
Split (Two Numbers)
Bet placed on the line between two adjacent numbers.
Street (Three Numbers)
Bet on a row of three numbers (e.g., 1-2-3).
Corner (Four Numbers)
Bet placed at the intersection of four numbers.
Six Line (Six Numbers)
Bet spanning two adjacent rows of three numbers.
Probabilities shown for European roulette (37 pockets). American roulette probabilities differ slightly due to the additional 00 pocket.
Outside Bets
Outside bets cover larger groups of numbers and are placed outside the main number grid. They have lower payouts but higher probabilities of winning, resulting in lower variance per spin.
Red / Black
Bet on all 18 red or all 18 black numbers.
Odd / Even
Bet on all 18 odd or all 18 even numbers.
High / Low
Bet on numbers 1-18 (low) or 19-36 (high).
Dozens
Bet on 1st dozen (1-12), 2nd dozen (13-24), or 3rd dozen (25-36).
Columns
Bet on one of three vertical columns of 12 numbers.
Roulette Payouts
Roulette payouts are fixed and do not change between variants. The payout ratio is the same whether you play European or American roulette — but the probability of winning changes because American roulette has one more pocket.
Payouts are the same across all roulette variants. The difference in house edge comes from the number of pockets on the wheel, not the payouts.
See all payouts and probabilities: roulette payouts reference
Roulette Probabilities
Every roulette probability can be calculated from a simple formula: the number of winning pockets divided by the total number of pockets. Use our Roulette Calculator for exact figures on any bet and variant.
Probability Comparison
| Bet | European | American |
|---|---|---|
| Single number | 1/37 = 2.70% | 1/38 = 2.63% |
| Red or Black | 18/37 = 48.65% | 18/38 = 47.37% |
| Dozen / Column | 12/37 = 32.43% | 12/38 = 31.58% |
| Any even-money bet | 18/37 = 48.65% | 18/38 = 47.37% |
Detailed probability analysis: roulette probability guide | red or black odds
House Edge Explained
The house edge is the mathematical advantage the casino has over the player, expressed as a percentage of each wager. In roulette, the house edge comes from the gap between the true probability of winning and the payout offered.
How It Works (European Example)
- •A straight-up bet pays 35:1, but there are 37 possible outcomes
- •Fair payout would be 36:1 (36 losing outcomes for 1 winning)
- •The difference (36:1 fair vs 35:1 actual) is the house edge
- •Mathematically: 1/37 = 2.70% — this applies to every bet type
For every $100 wagered on European roulette, the expected loss is $2.70 regardless of bet type. On American roulette, the expected loss is $5.26 per $100 wagered. These are long-term averages — individual sessions will vary due to variance.
Deep dive: roulette house edge guide | house edge academy | house edge comparator tool
Why the Zero Matters
The zero pocket is the single most important feature of a roulette wheel. Without it, every bet would be mathematically fair — the payouts would exactly match the probabilities. The zero creates an extra losing outcome while payouts remain as though it doesn't exist.
Without Zero (Hypothetical)
With Zero (Reality)
American roulette has two green pockets (0 and 00), which is why its house edge is nearly double that of European roulette. The payouts are identical across both variants — only the number of pockets changes.
Learn more: how zero creates the house edge
Simplified European roulette betting layout
Common Roulette Betting Systems
Many players use betting systems that change the size of bets based on previous outcomes. While these systems can alter the variance profile of a session, none of them change the expected value.
Martingale
Double your bet after every loss, return to the base bet after a win. In theory, this recovers all losses with a single win. In practice, losing streaks hit table limits or deplete bankrolls before recovery occurs. A 10-spin losing streak on even-money bets requires a 1,024x bet to recover — common enough to make this system unsustainable.
Fibonacci
Follow the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13...) for bet sizing after losses. Move two steps back after a win. Bets grow more slowly than Martingale, but losses still accumulate during extended losing streaks. The system does not change the expected value of any individual spin.
D'Alembert
Increase your bet by one unit after a loss, decrease by one unit after a win. More conservative than Martingale with slower bet growth. However, the system still relies on the false assumption that wins and losses will eventually balance out in a way that overcomes the house edge.
Labouchere
Write a sequence of numbers. Bet the sum of the first and last numbers. Cross both off after a win; add the loss amount to the end after a loss. The system is complete when all numbers are crossed off. More complex to execute but shares the same fundamental flaw: it cannot change the negative expected value built into each spin.
Why Betting Systems Do Not Remove the House Edge
Every roulette spin is an independent event with the same probabilities. Betting systems change when and how much you bet, but they cannot change the probability of winning or the payout ratio. The expected value of each spin remains negative regardless of bet size or pattern.
The Mathematical Reality
- •Expected value per spin = (win probability × payout) - (loss probability × stake)
- •This formula produces a negative number for every roulette bet
- •Changing the stake does not change the percentage — it only scales the expected loss
- •A negative EV repeated any number of times produces a negative total
Systems can create different variance profiles — Martingale produces many small wins and occasional large losses, while flat betting produces more moderate fluctuations. But variance is not the same as expected value. Lower variance makes the outcome more predictable; it does not make it positive.
More on this topic: roulette strategy myths | expected value explained
Beginner Strategy
No strategy can give you a positive expected value in roulette. However, you can make choices that reduce the cost of play and manage your bankroll more effectively:
- •Choose European or French roulette over American. The house edge is roughly half.
- •Set a budget before playing and stop when it's gone. Don't chase losses.
- •Understand that no bet is better than another in terms of expected value. Even-money bets have lower variance, not lower house edge.
- •Avoid progressive betting systems. They don't change the math and can lead to large losses during losing streaks.
- •Use the calculator. Understand the exact probability, expected value, and house edge of every bet before placing it.
Advanced Concepts
Variance
Variance measures how much results spread out from the expected value. High-variance bets (like straight-up numbers) produce rare large wins and frequent small losses. Low-variance bets (like red/black) produce frequent small wins and losses close to even. Both have the same house edge — the difference is in how the wins and losses are distributed across spins.
Expected Loss
Your expected loss over a session equals: total amount wagered × house edge. If you bet $10 per spin for 100 spins on European roulette, your total wager is $1,000 and your expected loss is $27. This is an average over many sessions — any individual session may be higher or lower due to variance.
Bankroll Risk
The risk of going bust (losing your entire bankroll) depends on your bet size relative to your bankroll and the variance of your chosen bet. Betting 1% of your bankroll per spin gives you a long runway; betting 20% per spin makes ruin likely within a few spins. Use the Risk Lab to simulate bankroll trajectories.
Table Limits
Every roulette table has minimum and maximum bet limits. Minimum limits set the floor for participation; maximum limits cap the most you can wager on a single bet. Maximum limits are particularly relevant because they make progressive betting systems like Martingale unsustainable — a losing streak will eventually push the required bet above the table maximum.
Responsible Play
Roulette is a game of pure chance with a negative expected value on every bet. No strategy, system, or pattern can overcome the house edge. The casino has a mathematical advantage on every spin, and this advantage compounds over time.
Set strict loss limits and time limits before you play. Never chase losses — the math does not change based on previous results. Treat roulette as a form of entertainment with a known cost, not as a way to make money. If gambling becomes a problem, seek help from organizations like Gamblers Anonymous or your local responsible gaming resources.
Frequently Asked Questions
What is the house edge in roulette?
The house edge depends on the variant. European roulette has a house edge of approximately 2.70% (1/37), because the single zero pocket gives the casino its advantage. American roulette has a house edge of approximately 5.26% (2/38), because it adds a second zero pocket (00). French roulette with the La Partage rule can reduce the effective house edge on even-money bets to approximately 1.35%. The house edge applies to every bet on every spin — it cannot be removed by any betting pattern or strategy.
Is European roulette better than American roulette?
From a mathematical perspective, European roulette offers better odds for the player. The house edge is 2.70% compared to 5.26% in American roulette. This means that for every $100 wagered, the expected loss is $2.70 on European roulette versus $5.26 on American roulette. Both variants still have negative expected value — European roulette simply loses less per wager over time.
What is the probability of red or black?
In European roulette, there are 18 red pockets and 18 black pockets out of 37 total (including the green zero). The probability of red (or black) is 18/37, which is approximately 48.65% — not 50%. In American roulette, the probability drops to 18/38 (approximately 47.37%) because of the additional 00 pocket. The difference from 50% is what creates the house edge.
Do roulette systems work?
No betting system can overcome the house edge in roulette. Systems like Martingale (doubling after losses), Fibonacci, D'Alembert, and Labouchere change the size and pattern of bets, but they do not change the expected value of each spin. Over time, all systems produce results consistent with the house edge. Some systems increase short-term variance, which can create the illusion of effectiveness, but the mathematical expectation remains negative.
Why does zero matter in roulette?
The zero (and double-zero in American roulette) is what gives the casino its mathematical edge. Without zero pockets, roulette bets would have exactly fair payouts — for example, red/black would be a true 50/50 proposition paying 1:1. The zero creates an extra losing outcome for most bets while the payouts remain the same as if the zero didn't exist. This gap between the true probability and the payout ratio is the house edge.
What is the safest roulette bet?
No roulette bet is 'safe' in the sense of having positive expected value — all bets carry the same house edge for a given variant. Even-money bets (red/black, odd/even, high/low) have the lowest variance because they win close to half the time, which means your bankroll fluctuates less per spin. However, lower variance does not mean lower expected loss over time. Playing European or French roulette with even-money bets is mathematically the least costly option, but the house edge still ensures a long-term loss.
Roulette Tools & Resources
This is educational content only. Gambling laws vary by jurisdiction. Consult local regulations before participating in any gambling activity. All roulette bets have negative expected value — no strategy or system can overcome the house edge.