By Rebecca Stone | Last updated: April 2, 2026
Rebecca Stone is a casino game analyst with 9 years of experience covering live dealer game variants, house edge analysis, and player strategy.
Affiliate disclosure: We earn commissions from casinos we recommend. This does not affect our editorial independence.
Roulette Odds Explained: House Edge, Payouts, and Win Probabilities
Roulette’s mathematics are elegant and unforgiving. Every bet type, every variant, every spin operates on the same underlying probability structure — and understanding that structure is the difference between playing with knowledge and playing on instinct.
This guide breaks down the complete probability framework for roulette: how the house edge works, why all European bets are equal, how payouts are set, what variance means in practice, and how the numbers differ across European, French, and American variants.
The Foundation: How Roulette Odds Work
European roulette has 37 equally likely outcomes (numbers 0-36). For any bet, the house edge emerges from the gap between the true odds and the payout odds.
True odds for a straight-up bet: 36:1 against (36 losing outcomes for every 1 winning outcome).
Payout: 35:1.
The casino pays 35:1 on a 36:1 probability. That one-unit gap — receiving 35 instead of 36 — is where the house edge comes from.
House edge calculation:
- Probability of winning: 1/37
- Probability of losing: 36/37
- EV = (35 × 1/37) + (-1 × 36/37) = (35 - 36)/37 = -1/37 = -2.70%
This applies to every single bet in European roulette, regardless of how many numbers are covered. The payouts are calibrated specifically to produce the same -2.70% expected value across all bet types.
Complete Odds Table: European Roulette
| Bet | Numbers | True Odds (Against) | Payout | House Edge |
|---|---|---|---|---|
| Straight Up | 1 | 36:1 | 35:1 | 2.70% |
| Split | 2 | 35:2 | 17:1 | 2.70% |
| Street | 3 | 34:3 | 11:1 | 2.70% |
| Corner | 4 | 33:4 | 8:1 | 2.70% |
| Six Line | 6 | 31:6 | 5:1 | 2.70% |
| Dozens | 12 | 25:12 | 2:1 | 2.70% |
| Columns | 12 | 25:12 | 2:1 | 2.70% |
| Red/Black | 18 | 19:18 | 1:1 | 2.70% |
| Odd/Even | 18 | 19:18 | 1:1 | 2.70% |
| High/Low | 18 | 19:18 | 1:1 | 2.70% |
The house edge is identical for every bet. The payout is the only variable — set precisely to produce 2.70% regardless of coverage.
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American Roulette Odds
Adding the double zero creates 38 equally likely outcomes. The same payout structure now produces a different house edge:
Straight-up house edge: EV = (35 × 1/38) + (-1 × 37/38) = (35 - 37)/38 = -2/38 = -5.26%
The casino now collects 2 extra units of edge per 38 spins instead of 1 per 37 — nearly double the house advantage.
| Bet | Numbers | Payout | House Edge (American) |
|---|---|---|---|
| All standard bets | Various | Same as European | 5.26% |
| Basket (0,00,1,2,3) | 5 | 6:1 | 7.89% |
American roulette pays the same as European roulette but on a 38-pocket wheel instead of 37. The player receives the same payouts for worse odds.
French Roulette: La Partage and En Prison
La Partage Effect on Even-Money Bets
When zero lands, La Partage returns 50% of even-money bets. The revised house edge calculation:
For a $1 Red/Black bet on French roulette:
- 18/37 spins: win $1
- 18/37 spins: lose $1
- 1/37 spins: zero — receive $0.50 back (lose $0.50)
EV = (1 × 18/37) + (-1 × 18/37) + (-0.50 × 1/37) = (18/37) - (18/37) - (0.50/37) = -0.50/37 = -1.35%
La Partage exactly halves the house edge on even-money bets. This is the best available expected value in any standard roulette variant.
French roulette inside bets: The La Partage rule applies only to even-money bets. Inside bets on French roulette retain the standard 2.70% edge.
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Variance: What the Numbers Mean in Practice
Expected value tells you the average outcome over many spins. Variance describes how far from that average any individual session will land.
Standard Deviation Per Spin
For even-money bets (bet = $1):
- σ per spin ≈ $1.00 (approximately)
For straight-up bets (bet = $1):
- σ per spin ≈ $5.77
The straight-up bet has nearly 6x the standard deviation per spin — meaning individual results are far more scattered around the expected value.
Session Variance (100 Spins, $25/spin)
Even-money bets:
- Expected loss: 100 × $25 × 2.70% = $67.50
- Standard deviation over 100 spins: $25 × √100 ≈ $250
- 68% of sessions end within $250 of the expected loss: roughly -$317 to +$182
Straight-up bets ($25 per number, 100 spins):
- Expected loss: same $67.50
- Standard deviation over 100 spins: much wider (~$1,440)
- Results spread across a far wider range
Practical implication: Straight-up betting provides the same expected outcome as even-money betting, but with dramatically higher variance. You’re more likely to either win big or lose big — the expected average is the same.
Win Rate vs. Expected Value
A common confusion: win rate (how often you win a spin) vs. expected value (how much you win or lose per dollar).
Red/Black:
- Win rate: 48.65% (you win slightly less than half your spins)
- Expected value: -2.70% per dollar
Straight Up:
- Win rate: 2.70% (you win about 1 in 37 spins)
- Expected value: -2.70% per dollar
Same expected value, radically different win rates. High coverage bets win more often but pay less per win. Low coverage bets win rarely but pay a lot per win. Over many spins, the financial outcome converges to the same -2.70% expected loss.
The Mathematics of Multiple Bets
When you place multiple bets simultaneously, the combined expected value is the sum of each individual bet’s expected value.
Example: $25 on Red + $10 on number 17 (one spin of European roulette):
- Red bet EV: -$25 × 2.70% = -$0.675
- Number 17 EV: -$10 × 2.70% = -$0.27
- Combined EV: -$0.945 per spin
The house retains 2.70% of every dollar wagered, regardless of how bets are combined. Spreading bets across multiple types doesn’t create a mathematical advantage — it simply increases total dollars wagered per spin.
Odds in Betting Systems Context
Betting systems like Martingale, Fibonacci, and D’Alembert change bet sizes but not odds. From a probability standpoint:
- Each spin is independent: prior results don’t affect the next spin’s odds
- The house edge applies to every dollar wagered: doubling your bet after a loss doubles your expected loss on that spin
- Systems redistribute session variance: they don’t change long-run expected value
The Martingale at $10 base over 100 total dollars wagered has the same expected loss as flat betting $10 over 100 spins: approximately -$27. The distribution of when those losses occur changes — the expected total does not.
Probability of Specific Outcomes Over Multiple Spins
Straight-Up Number Hit Rate
The probability of hitting a specific number at least once in N spins:
- P(hit at least once) = 1 - (36/37)^N
| Spins | Probability of Hitting a Specific Number |
|---|---|
| 10 | 23.9% |
| 20 | 42.0% |
| 37 | 63.4% |
| 74 | 86.7% |
| 100 | 93.4% |
| 148 | 98.2% |
Common misconception: “My number hasn’t hit in 50 spins — it’s due.” The probability of hitting in any individual spin remains 1/37 regardless of recent history. The cumulative probability above tells you the probability before you start playing, not the probability after a number has failed to hit.
House Edge by Game Category (For Context)
| Game | House Edge |
|---|---|
| French Roulette (even-money, La Partage) | 1.35% |
| Blackjack (basic strategy, 6-deck S17) | 0.26-0.30% |
| European Roulette | 2.70% |
| Baccarat (Banker bet) | 1.06% |
| American Roulette | 5.26% |
| Slots (typical) | 3-8% |
| Keno | 20-35% |
Roulette sits in the middle range. It’s better than slots and keno, worse than optimal blackjack and baccarat banker. French roulette’s 1.35% on even-money bets is competitive with baccarat — the second-lowest live casino house edge commonly available.
Frequently Asked Questions: Roulette Odds
What is the house edge in European roulette? 2.70% on all bets. Every dollar wagered has an expected return of $0.973 — you keep 97.3 cents on average.
Why is the house edge the same for every bet in European roulette? The payouts are set specifically to produce the same -1/37 expected value across all bet types. The single zero pocket creates an asymmetry between true odds (36:1 for straight up) and payout odds (35:1) that applies uniformly.
What is the probability of red coming up 10 times in a row? (18/37)^10 ≈ 0.56% — approximately 1 in 180. This sounds rare, but in 1,000 sessions of 100 spins each, you’d expect to see it roughly 5-6 times.
Does covering more numbers improve my odds? It improves your win rate (how often you win per spin) but doesn’t change your expected value per dollar wagered. More coverage = lower payout per win = same expected value.
Why does American roulette have a higher house edge? The double zero creates 38 pockets while payouts remain calibrated for 37. The casino collects the extra -1/38 on every bet, approximately doubling the house edge.
Can roulette ever be positive expected value? In standard live online roulette: no. The wheel is certified random and the house edge is structural. In historical cases of biased physical wheels (worn bearings, uneven pocket sizes), some edge was achievable — not applicable to modern certified wheels.
What is variance in roulette? Variance measures how much actual results deviate from expected value in the short term. High-payout bets (straight up) have higher variance — wider swings from expectation. Even-money bets have lower variance. Long-run expected value is the same for both.
Is there a way to calculate roulette odds for any bet? Yes. House edge = (payout - true odds) / (true odds + 1) × 100. For European roulette, true odds for any bet = (37 - coverage) / coverage. Payout = (36 / coverage) - 1 (rounded). The gap between true odds and payout produces the 2.70% edge.
Summary: The Odds in One Table
European Roulette (best standard variant):
| Coverage Type | Expected Win Rate | Payout | EV per $25 Bet |
|---|---|---|---|
| 1 number | 2.70% | 35:1 | -$0.68 |
| 6 numbers | 16.2% | 5:1 | -$0.68 |
| 12 numbers | 32.4% | 2:1 | -$0.68 |
| 18 numbers | 48.6% | 1:1 | -$0.68 |
The expected loss is $0.68 per $25 bet regardless of coverage. The choice of bet type is a variance preference, not an odds preference.
For application of these odds to specific betting strategies, see our complete roulette strategy guide. For bet-type selection, see our betting types guide.
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