The claim, and a caution
On a given roulette wheel, the standard bets all carry the same house edge. That says nothing good about any of them: roulette is a game of chance, no bet or system changes the odds in the player’s favor over time, most players lose money in the long run, and nobody should gamble money they cannot afford to lose.
An example that needs no probability
Imagine a single-zero wheel with 37 pockets and a player who places $1 on every one of the 37 numbers. That is $37 staked. Exactly one number wins, and it pays 35 to 1: the player receives $35 plus the $1 stake back, a total of $36. The net result is $36 − $37 = −$1, every single spin, with certainty.
That $1 loss on $37 staked is 1/37, about 2.70%. Each individual straight bet, taken alone, therefore must carry a 1/37 edge on average, since the 37 bets together always cost 1/37 of the total stake, and by symmetry no number is treated differently from another.
The algebra for any bet
Take any bet covering n numbers on the 37-pocket wheel. It wins with probability n/37 and pays (36 ÷ n) − 1 to 1. For a $1 stake:
- Win: probability n/37, profit (36/n) − 1.
- Lose: probability (37 − n)/37, loss 1.
Expected result = [n × ((36/n) − 1) − (37 − n)] / 37 = [36 − n − 37 + n] / 37 = −1/37.
The n cancels. That cancellation is the whole reason the edge is uniform: the payout ratio is set by dividing 36 by the number of pockets covered, so that more pockets always mean a proportionally smaller payout.
A few checks:
| Bet | Numbers | Win chance | Profit if win | Expected result per $1 |
|---|---|---|---|---|
| Straight | 1 | 1/37 | $35 | (35 − 36)/37 = −1/37 |
| Split | 2 | 2/37 | $17 | (34 − 35)/37 = −1/37 |
| Street | 3 | 3/37 | $11 | (33 − 34)/37 = −1/37 |
| Corner | 4 | 4/37 | $8 | (32 − 33)/37 = −1/37 |
| Even-money | 18 | 18/37 | $1 | (18 − 19)/37 = −1/37 |
On a double-zero wheel the same algebra gives −2/38 for each bet, about 5.26%. The principle is that the edge comes from the pockets nobody wins on, the zero or zeros, spread evenly across every bet.
Same cost, different risk
Equal expected cost does not mean equal experience. Compare a $1 straight bet and a $1 even-money bet on a single-zero wheel.
- The straight bet wins about once in 37 spins and pays well. Its standard deviation per spin is roughly $5.84.
- The even-money bet wins close to half the time and pays $1. Its standard deviation per spin is about $1.00.
(The first figure comes from the variance of the outcomes: (35² + 36)/37 − (1/37)² ≈ 34.08, whose square root is about 5.84. The second is about 1 − (1/37)² ≈ 0.999, whose square root is about 1.0.)
Both lose 1/37 of a dollar per spin on average. The straight bet has far larger swings, so the same average cost arrives through long dry stretches and occasional big wins. Standard deviation is the usual measure of that difference. A player who bets $1 on a straight number for 37 spins and one who bets $1 on red for 37 spins both expect to lose about $1 total, but the first outcome is far more spread out.
This is also why session results can depart sharply from the long-run figure. A lucky session does not show that a bet is cheaper; it shows how wide the short-term fluctuation is.
What this means for choosing bets
The point of the uniform edge is that the choice between bets is a choice of risk profile, not of cost per unit wagered. A player cannot find a cheaper bet by looking at the layout. The real levers are:
- Which wheel: 37 pockets versus 38 pockets roughly doubles the edge.
- How much is wagered in total, and how fast: expected loss equals the edge times the amount staked, so more spins or larger bets mean a larger expected loss. Speed of play and the expected cost per hour follow directly.
- The exceptions below.
Exceptions to the rule
The equal-edge rule applies to standard bets with standard payouts. Departures include:
- The American five-number bet (0, 00, 1, 2, 3), which pays 6 to 1 with 5 of 38 pockets and has an edge of 3/38, about 7.89%.
- French rules such as la partage, which lower the edge on even-money bets to about 1.35% on a single-zero wheel, while leaving other bets at 2.70%.
- Any table that changes payouts from the standard ones. A game with a different payout schedule has a different edge, and the sum of payout ratios against win probabilities shows by how much.
Why this matters beyond roulette
Games like craps or blackjack have bets with very different costs, and side bets often cost far more than the main game. Roulette is unusual because its standard bets are uniform. That makes it a clean case for learning how expected value, house edge and variance fit together, but it does not make it a good way to make money. The edge is a long-run cost, and outcomes in any session are uncertain.
If gambling stops feeling like entertainment, a local support service can help.