Start with the bet, not the wheel
The calculation that answers your question is not about the wheel as a whole. It is about one specific bet placed on that wheel. A straight-up bet on a single number, a split on two numbers, a red/black bet, and a dozen bet each carry their own payout, and the gap between that payout and the true odds of the bet is where the edge sits. You can calculate that gap for any bet on any roulette layout using the same two-step method.
Roulette is a clean place to learn this because the wheel is a fixed, countable set of pockets. A European wheel has 37 pockets with a single zero. An American wheel has 38 with a single and a double zero. Those are the only two counts you need, and they are the reason the same bet can have a different edge on a different table.
The two numbers every calculation needs
House edge is the difference between two probabilities expressed in money terms: the chance a bet wins, and the payout the table offers when it does. If a bet paid at exactly its true odds, the edge would be zero. A roulette table never pays at true odds, because the zero pockets sit on the wheel without belonging to any of the outside or inside betting categories.
To calculate the edge on any roulette bet, you need the number of pockets that win the bet and the payout the table gives. The payout is printed on the layout or in the game information panel. The number of winning pockets you can count directly from the wheel and the bet's definition. Everything else follows from those two inputs.
Worked example: a straight-up bet on a European wheel
Suppose you place one unit on a single number on a European wheel. There is 1 winning pocket out of 37 total pockets. The true odds against winning are therefore 36 to 1. The table, however, pays 35 to 1. That one-unit shortfall, repeated across every possible outcome, is the house edge.
To see the shortfall as a percentage, imagine a complete cycle of 37 spins in which each pocket comes up exactly once, and suppose you bet one unit on the same number each time. You would lose 36 units on the losing spins and win 35 units on the winning spin. After 37 units wagered, you are down 1 unit. One unit lost per 37 units wagered is the edge expressed as a fraction. Multiply by 100 to convert it to a percentage. The arithmetic is the same for any bet: total the losses and the win, compare the result to the total amount staked, and express the difference as a percentage of that stake.
Why the same bet changes on an American wheel
Place the same one-unit straight-up bet on an American wheel, and the count changes. There is still 1 winning pocket, but now there are 38 pockets in total. The true odds against winning are 37 to 1, yet the table still pays 35 to 1. The payout has not changed, but the chance of winning has fallen because an extra pocket has been added that does not belong to the bet.
Run the same full-cycle example: 38 spins, one unit staked each time, one win paying 35 units and 37 losses. You are down 2 units after 38 wagered. The fraction lost per unit staked is larger than on the European wheel, and the percentage edge is correspondingly higher. The extra zero pocket is the entire reason for the difference.
| Element | European wheel | American wheel |
|---|---|---|
| Total pockets | 37 | 38 |
| Winning pockets on a straight-up bet | 1 | 1 |
| True odds against winning | 36 to 1 | 37 to 1 |
| Table payout | 35 to 1 | 35 to 1 |
| Units lost per full cycle of one-unit bets | 1 per 37 wagered | 2 per 38 wagered |
Applying the method to other roulette bets
The same two-step method works for any bet on the layout. Count the winning pockets, compare the true odds to the posted payout, and run the full-cycle arithmetic. A red/black bet on a European wheel has 18 winning pockets out of 37, so the true odds against are 19 to 18, while the table pays even money, or 1 to 1. A dozen bet has 12 winning pockets out of 37, true odds of 25 to 12, and a posted payout of 2 to 1. In each case the shortfall per unit staked is identical on a European wheel, because the zero pocket is excluded from every category in the same way.
On an American wheel, the count of winning pockets is the same for each of these bets, but the total rises to 38. The shortfall per unit staked grows for every bet, not just straight-up bets. The method does not care which bet you choose; it only cares about the two inputs.
Where RTP fits into the same arithmetic
Return to Player, or RTP, is the complement of the house edge for the same bet under the same rule set. If a bet returns a certain percentage of all money wagered over a very large number of spins, the house edge is what remains. The two figures always sum to 100% for the same bet. A European straight-up bet returning a given percentage to players leaves the remainder as the edge; an American straight-up bet returns a smaller percentage and leaves a larger remainder.
RTP is a long-run statistical average, not a per-session guarantee. It describes what happens across an enormous number of spins, not what happens in the next hour. The edge is built into every single spin, but the result of any one spin is a random draw from the wheel's pockets.
Why short sessions look nothing like the calculation
The house edge is a statement about the average over many independent bets. A short session is a small sample of that average, and small samples are noisy. You may win more than the edge predicts, or lose more than it predicts, because variance dominates when the number of spins is small. The edge does not disappear during a winning session, and it does not become larger during a losing one. It is simply being obscured by the randomness of a few dozen outcomes.
What changes with session length is not the edge but the total amount you expose to it. Each spin carries the same percentage cost on average. More spins mean more total wagered, which means the expected loss in absolute terms grows even though the rate stays the same. The number of decisions per hour matters for the same reason: a faster table or a faster player places more bets in the same time, and each bet carries the same built-in percentage.
What progression systems do and do not change
A progression system is a rule for changing your bet size after wins or losses. Doubling after a loss, halving after a win, or any other pattern changes the distribution of outcomes, but it does not change the edge on any individual bet. The edge is a property of the bet and the wheel, not of the sequence of stakes placed on it.
What a progression does is redistribute the same underlying expected loss across different outcomes. It creates many small wins and a few large losses, or the reverse, depending on the pattern. The total expected loss over a large number of bets remains the product of the edge and the total amount wagered. A progression can change how a session feels, but it cannot change what the wheel is built to return over time.
FAQ
Can I calculate the house edge without knowing the payout?
No. The edge is the gap between the true odds of a bet and the payout the table offers. You need both numbers. The payout is always printed on the table layout or shown in the game's information panel, so it is available before you place the bet.
Does the house edge apply to every spin equally?
Yes. The edge is built into the bet's payout relative to its true odds, and that relationship is the same on every spin. What varies from spin to spin is the random outcome, not the percentage cost of the wager.
Why do some roulette games show a different RTP for the same bet?
Because the wheel or the rule set differs. A European wheel and an American wheel have different pocket counts, and some tables add rules that change how losing outside bets are treated when a zero appears. The RTP and the edge are always tied to the specific wheel and rule set in play, which is why the game information panel should be checked for the table you are sitting at.
Gambling can be addictive. Play responsibly, set limits, and seek help if gambling stops being fun. If you or someone you know is struggling with gambling, contact local support services or visit BeGambleAware.org for help and advice.
Play responsibly
Gambling should be treated as paid entertainment, never as a way to earn income or recover losses. 1-800-MY-RESET (1-800-697-3738)
18+ or 21+ depending on where you are; follow the minimum age that applies to you.
This article is general information about how these mechanics work. It is not legal advice and not a recommendation to gamble or to use any particular operator. Availability and legality differ by jurisdiction — check the rules that apply where you are.