The Mathematics of the House Edge in American Roulette
The house edge is the single most important number in casino gambling. On the American double-zero roulette wheel, it is 5.26% — and it applies to almost every bet on the table. Understanding exactly where this number comes from, and what it means in practice, is essential before developing any betting strategy.
Where the 5.26% Comes From
The American wheel has 38 pockets: numbers 1 through 36 (18 red, 18 black) plus 0 and 00 (both green). A straight-up bet on a single number pays 35:1 — you win 35 units plus your original stake back. But the true odds of winning are 1-in-38, which would require a fair payout of 37:1. The casino pays 35:1 instead of 37:1, keeping 2 units of every 38 wagered on average.
The formula: House Edge = (True Odds − Payout Odds) / (True Odds + 1). For a straight-up bet: (37 − 35) / 38 = 2/38 = 5.26%.
| Bet Type | True Odds | Payout | House Edge |
|---|---|---|---|
| Straight Up | 37:1 | 35:1 | 5.26% |
| Split | 18:1 | 17:1 | 5.26% |
| Street | 11.67:1 | 11:1 | 5.26% |
| Corner | 8.5:1 | 8:1 | 5.26% |
| Top Line (0,00,1,2,3) | 6.6:1 | 6:1 | 7.89% |
| Double Street | 5.33:1 | 5:1 | 5.26% |
| Column / Dozen | 2.17:1 | 2:1 | 5.26% |
| Even Money (Red/Black, etc.) | 1.11:1 | 1:1 | 5.26% |
The Top Line Exception
The Top Line bet (0, 00, 1, 2, 3) is the only bet on the American wheel with a higher house edge than 5.26%. It covers 5 numbers but pays 6:1 — the same as a bet covering 6 numbers would pay. The correct payout for 5 numbers would be 6.6:1. This discrepancy gives the Top Line a house edge of 7.89%. Avoid this bet.
Expected Value Per Spin
Expected value (EV) is the average amount you win or lose per unit wagered over a large number of spins. With a 5.26% house edge, the EV of every $1 bet is −$0.0526. On a $10 bet, you lose an average of $0.526 per spin. On 100 spins at $10 each, your expected loss is $52.60.
This does not mean you will lose exactly $52.60 — individual sessions have high variance. But over thousands of spins, the actual results converge toward this expectation. No betting system changes the EV; it only changes the distribution of wins and losses around that expectation.
European vs American: The Cost of the Double Zero
The European single-zero wheel has 37 pockets. A straight-up bet pays 35:1 with true odds of 36:1, giving a house edge of 1/37 = 2.70%. The American double-zero adds one more pocket without increasing payouts, nearly doubling the house edge. Over 1,000 spins at $10 each, the difference is $256 in additional expected losses on the American wheel versus the European.
If you have access to a European wheel, use it. The statistical analysis and strategy principles in this simulator apply equally to both — the only difference is the house edge you are working against.
What Strategy Can and Cannot Do
No betting strategy eliminates the house edge. What statistical analysis can do is concentrate your bets on pockets with empirically higher hit rates, improving your short-term expected value relative to a random bet selection. Over a long enough time horizon, the house edge always wins. The goal of a data-driven strategy is to maximize the probability of a profitable session, not to guarantee long-term profit.
For a full list of every bet and its house edge, see American Roulette Bet Types Explained. For the specific case of the worst bet on the table, see The Five-Number (Top Line) Bet: The Worst Bet on the American Roulette Table.
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