The payout is where the edge hides
Every roulette bet pays less than the true odds of winning it. That gap is the entire house advantage, and you can see it on any layout without knowing a single formula. A straight-up bet on one number pays 35 to 1. If the wheel had 36 pockets and one of them was yours, a fair payout would be 35 to 1. But a European wheel has 37 pockets, and an American wheel has 38. The payout stayed at 35 to 1 while the number of losing pockets grew. The house keeps the difference between what a bet pays and what it would pay if the wheel had no extra pocket.
The calculation that matters is therefore not complicated. You compare two things for the same bet: the share of pockets that win, and the share of the stake the payout returns. When those two shares differ, the difference is the house edge on that bet.
Expected value is the calculation underneath
Expected value measures what a bet returns on average per unit wagered, before you place it. It does not predict your next spin. It describes what would happen if the same bet were repeated an enormous number of times under the same rules. The formula is simple: multiply each outcome by its probability, then add the results.
Suppose you wager 1 unit on a single number on a European wheel. There are 37 equally likely pockets. One pocket wins and pays 35 units plus your stake back, so your net gain is 35 units. Thirty-six pockets lose, so your net result is minus 1 unit. The expected value is (1/37 × 35) plus (36/37 × −1). Work that through and you get 35/37 minus 36/37, which is −1/37. That is the house edge expressed as a fraction of your stake: the bet loses, on average, one thirty-seventh of a unit for every unit wagered.
Now run the same bet on an American wheel. There are 38 pockets, still one winner paying 35 to 1, and 37 losers. The expected value becomes (1/38 × 35) plus (37/38 × −1), which is −2/38, or −1/19. The extra double-zero pocket changed the average loss per unit from one thirty-seventh to one nineteenth. The payout never changed; only the number of losing pockets did.
RTP and house edge are two names for one gap
Return to Player, or RTP, is the same relationship viewed from the opposite side. House edge and RTP sum to 100% for the same bet under the same rule set. If a bet's expected loss is one thirty-seventh of each unit wagered, then the theoretical return is the remaining thirty-six thirty-sevenths. Expressed as a percentage, that is the RTP. The house edge is the complement: the share of each unit the bet is expected to lose over the very long run.
This holds only when you compare the same bet on the same wheel type. A European straight-up bet and an American straight-up bet have different edges. A straight-up bet and an even-money bet on the same wheel can also differ once special rules come into play, which is why you cannot take one published RTP figure and apply it across a whole roulette table. The game information panel on a specific title, or the rules sheet for a physical table, is where the figure for that title or table is stated.
| Comparison point | European wheel (single zero) | American wheel (double zero) |
|---|---|---|
| Pockets on the wheel | 37 | 38 |
| Straight-up payout | 35 to 1 | 35 to 1 |
| Winning pockets for straight-up | 1 of 37 | 1 of 38 |
| Expected value per unit wagered | −1/37 of a unit | −1/19 of a unit |
| Relationship between edge and RTP | Edge plus RTP equals 100% for the same bet | Edge plus RTP equals 100% for the same bet |
Why the edge is built into every payout, not just some
Roulette does not hide its advantage in one sucker bet. The same structure applies to every wager on the layout, because every payout is calibrated to a wheel with an extra pocket. An even-money bet on red pays 1 to 1. On a European wheel, red covers 18 of 37 pockets, not 18 of 36. The payout would be fair if the wheel had 36 pockets. With 37, the bet wins 18 times and loses 19 times out of 37 in the long run. The expected value is (18/37 × 1) plus (19/37 × −1), which is again −1/37.
A split bet covering two numbers pays 17 to 1. Two winning pockets out of 37 would be fair at 17.5 to 1, but the payout is rounded down to 17 to 1. The same rounding happens on every multi-number bet. The house advantage is not an extra fee added at the end; it is the payout being slightly short of what the wheel's true odds require, on every bet, every spin.
Short sessions look nothing like the long-run average
The house edge is a long-run statistical average. It does not mean you will lose exactly one thirty-seventh of your stake in an evening. A single spin has only two outcomes for a straight-up bet: you win 35 units or you lose 1 unit. Neither outcome is the expected value. The average only emerges across a very large number of spins, and even then it is an average, not a schedule.
This is what volatility describes. Roulette is a high-variance game relative to its edge. A player can finish a session ahead because a few winning spins landed early, even though the bet they made carried a negative expected value. The reverse is equally true. What the edge tells you is the direction of the long-run average, not the shape of the next hour.
Decisions per hour multiply your exposure
The house edge applies to each unit wagered, not to each visit. A roulette table can produce a large number of spins per hour, and every spin is a fresh wager with the same negative expected value. Total expected loss is the product of three things: the edge per unit, the amount wagered per spin, and the number of spins. If you wager 1 unit per spin and the edge is one thirty-seventh of a unit, then a hundred spins produce an expected loss of one hundred thirty-sevenths of a unit. That arithmetic is an example built from a hypothetical stake; the edge itself comes from the wheel type.
This is why the pace of play matters more than many players assume. A slower table, a fuller table, or simply taking breaks between spins reduces the number of decisions per hour. The edge on each spin does not change. The total amount exposed to that edge does.
Progression systems redistribute outcomes, not edge
A common question is whether doubling a bet after a loss can overcome the house advantage. The answer is that no progression changes the expected value of the underlying bets. A Martingale-style progression increases the stake after losses and resets it after a win. Each individual wager still carries the same negative expected value as before. The progression changes the distribution of outcomes: many small wins and occasional very large losses, instead of a steadier pattern. It does not remove the one thirty-seventh or one nineteenth average loss per unit.
What a progression does change is the amount wagered and the speed at which a losing streak consumes a bankroll. Because the stake grows after each loss, the total amount exposed to the house edge grows faster than it would under flat betting. The edge remains the same fraction of each unit; there are simply more units in play. Table limits also cap how far a progression can run, which is a structural rule printed on the table or in the game's rules.
Where to find the figure that applies to your game
The calculation above gives you the method. The specific percentage for a given title or table is stated in the game's own documentation. For an online roulette title, the information or help panel usually lists the theoretical return. For a physical table, the posted rules or the venue's game guide carries the wheel type and any special rules, such as a la partage or en prison rule on even-money bets, which changes the edge on those specific bets only. Read the figure as applying to that rule set, not to roulette in general.
When you see an RTP figure, check which wheel it describes. A single-zero wheel and a double-zero wheel are different games for the purpose of the calculation. The same title can also offer both, so the figure on the panel is the one that matches the wheel you are playing.
FAQ
Does every roulette bet have the same house edge?
On a standard single-zero or double-zero wheel without special rules, most bets carry the same expected loss per unit because the payout is short by the same fraction on each. Special rules on even-money bets, such as la partage or en prison, reduce the edge on those specific bets only. Check the table rules to see whether such a rule applies.
Can I calculate the house edge from the payout alone?
You need both the payout and the number of pockets on the wheel. The payout tells you what a win returns; the wheel tells you how often a win occurs. The gap between the fair payout for the wheel's true odds and the actual payout is the edge. Without the wheel type, a payout figure tells you nothing about the house advantage.
Why does the house edge not show up in a short session?
The edge is an average over a very large number of spins. In a short session, variance dominates. A player can win more than expected or lose more than expected because each spin has only a few possible outcomes, none of which equals the long-run average. The edge describes the direction of the average, not the result of any particular sitting.
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