Where 5.26% Comes From
The payout structure assumes 36 numbers. A straight-up bet pays 35:1. But there are 38 pockets, not 36.
Expected value per unit on a straight-up bet:
EV = (1/38 x 35) - (37/38 x 1) = 35/38 - 37/38 = -2/38 = -5.26%
On a European wheel with 37 pockets, that calculation yields -1/37 = -2.70%. The second zero pocket costs you an extra 2.56% on every single bet.
Over time, this difference is enormous. At $10 per spin over 1,000 spins, the expected loss on an American wheel is $526 versus $270 on a European wheel. That is $256 in extra losses for no added entertainment value.
Inside Bets: Full Odds Table
| Bet Type | Numbers Covered | Payout | Probability | House Edge |
|---|---|---|---|---|
| Straight Up | 1 | 35:1 | 2.63% | 5.26% |
| Split | 2 | 17:1 | 5.26% | 5.26% |
| Street | 3 | 11:1 | 7.89% | 5.26% |
| Corner (Square) | 4 | 8:1 | 10.53% | 5.26% |
| Six Line | 6 | 5:1 | 15.79% | 5.26% |
| Five-Number (0-00-1-2-3) | 5 | 6:1 | 13.16% | 7.89% |
Every bet has the same 5.26% edge except one. The five-number bet is worse.
The Five-Number Bet Trap: 7.89% House Edge
The five-number bet (also called the "top line" or "basket" bet) covers 0, 00, 1, 2, and 3. It pays 6:1.
The math:
EV = (5/38 x 6) - (33/38 x 1) = 30/38 - 33/38 = -3/38 = -7.89%
This is the single worst bet on any standard roulette table in any casino. The payout of 6:1 is mathematically wrong for 5 numbers out of 38. A "fair" payout relative to the rest of the table would be 6.6:1, but since fractional chip payouts are not practical, the casino rounds down and pockets the difference.
There is no strategic reason to make this bet. It exists because it covers the top of the layout and looks convenient. Convenience costs you an extra 2.63% over every other bet on the table.
Outside Bets: Full Odds Table
| Bet Type | Numbers Covered | Payout | Probability | House Edge |
|---|---|---|---|---|
| Red / Black | 18 | 1:1 | 47.37% | 5.26% |
| Odd / Even | 18 | 1:1 | 47.37% | 5.26% |
| High (19-36) / Low (1-18) | 18 | 1:1 | 47.37% | 5.26% |
| Dozen (1-12, 13-24, 25-36) | 12 | 2:1 | 31.58% | 5.26% |
| Column | 12 | 2:1 | 31.58% | 5.26% |
On a European wheel, even-money bets hit 48.65% of the time. On an American wheel, 47.37%. That 1.28 percentage point difference in hit rate translates to nearly double the house edge because of how the losses compound against the 1:1 payout.
American vs. European: Side-by-Side Comparison
| Metric | American (00) | European (Single 0) | European (La Partage) |
|---|---|---|---|
| Pockets | 38 | 37 | 37 |
| House Edge (all bets) | 5.26% | 2.70% | 2.70% |
| House Edge (even-money) | 5.26% | 2.70% | 1.35% |
| Worst bet on table | 7.89% | 2.70% | 1.35% |
| Expected loss per $1,000 wagered | $52.60 | $27.00 | $13.50 |
| Red/Black hit rate | 47.37% | 48.65% | 48.65% |
The La Partage column is the comparison that matters. European roulette with the La Partage rule on even-money bets gives the house just 1.35%, less than a quarter of the American roulette edge. For a full breakdown of single-zero math including call bets and en prison rules, see our European roulette odds analysis.
The Dollar Impact Over Real Sessions
Abstract percentages obscure real costs. Here is what the edge difference looks like over typical sessions:
| Session Length | Bet Size | American Expected Loss | European Expected Loss | Extra Cost of American |
|---|---|---|---|---|
| 50 spins | $5 | $13.15 | $6.76 | $6.39 |
| 100 spins | $10 | $52.63 | $27.03 | $25.60 |
| 200 spins | $10 | $105.26 | $54.05 | $51.21 |
| 500 spins | $25 | $657.89 | $337.84 | $320.05 |
| 1,000 spins | $25 | $1,315.79 | $675.68 | $640.11 |
At 500 spins and $25/spin, you are paying an extra $320 for the privilege of playing with a double zero. That money buys nothing. The game experience is identical.
American Wheels Persist Because They Earn More
American roulette is strictly worse for the player, and casinos keep it because it earns more.
Revenue. A double-zero wheel generates almost twice the revenue per hour as a single-zero wheel at the same bet volume. Most American casino patrons do not know the difference, so the demand-side impact is minimal.
Floor economics. Casinos pay the same dealer wages, same table maintenance, same floor space whether the wheel has one zero or two. The double zero nearly doubles the hourly yield without increasing costs.
Inertia. American roulette has been the standard layout in US casinos for over a century. Switching to single-zero would reduce revenue on existing tables. Casinos that offer European wheels typically set higher minimums to compensate.
Finding European Wheels in American Casinos
European (single-zero) wheels exist in US casinos. They are usually in high-limit rooms with $25, $50, or $100 minimums. Some properties to check:
- Most Las Vegas Strip casinos have at least one single-zero wheel in their high-limit area
- Borgata, MGM National Harbor, and Wynn properties frequently offer single-zero tables
- Online casinos almost always offer both variants; check before you click
If you are going to play roulette, the single-zero table with a higher minimum and fewer spins per hour is mathematically superior to the double-zero table with a lower minimum and more spins. Playing $25/spin on a European wheel costs you $0.68/spin in expected losses. Playing $10/spin on an American wheel costs $0.53/spin, but you will play 2-3x more spins per hour at the lower-limit table, so your hourly loss is higher.
Bankroll Guidelines
For an American roulette session on even-money bets:
- Expected loss per spin: 5.26% of bet size
- Standard deviation per spin: Approximately 1.0x bet size
- Session SD for N spins: Bet size x sqrt(N)
Example: 100 spins at $10 on red/black
- Expected loss: $52.63
- Session SD: $10 x sqrt(100) = $100
- 95% range: -$52.63 +/- $196 = +$143 to -$249
You will still finish ahead about 30% of the time over 100 spins. That number drops to about 15% over 500 spins and becomes negligible over thousands. The house edge is a slow grind, not a cliff, which is why it is easy to underestimate.
Roulette variance follows the same statistical patterns as poker variance. Our poker variance calculator uses identical underlying math if you want to model different session lengths.
Responsible Gambling
Roulette has a fixed negative expectation. No betting system changes the house edge. Martingale, reverse Martingale, D'Alembert, Fibonacci: all of them rearrange the distribution of your wins and losses without touching the expected value.
The most effective strategy in roulette is game selection: play European over American, seek La Partage rules, and set a hard stop-loss before your first bet.
If you are having difficulty controlling your gambling, the National Council on Problem Gambling (1-800-522-4700) and GamCare (0808-8020-133, UK) offer free, confidential support.
