This roulette house edge calculator turns a stake, a number of spins and a house edge into the average amount that play costs. With the default inputs, 100 spins at 10 units on a single-zero wheel have an expected loss of 27.00 units. Below the tool you will find the edge for every wheel and bet, the working, and how far a real session can stray from that average.
If you are new to the game, the roulette guide explains the layout and the bets, and our post on roulette odds and payouts lists what each bet pays. This page covers what those pages leave out: what the edge adds up to over a session.
How does the roulette house edge calculator work?
The calculator multiplies your stake by the number of spins to get the total staked, then multiplies that by the house edge. The result is the average you lose if you play the same bets many times. It is a long-run average, not a forecast for your next session.
In symbols: expected loss = stake x spins x house edge / 100. Researchers call this the theoretical loss, and Auer, Schneeberger and Griffiths (2012) define it as total bet size multiplied by the house advantage.
The tool does not know which wheel you are playing, so you type the edge yourself. The right edge depends on the number of zeros and the table rules, and the sections below give each one.
How do you use the roulette house edge calculator?
Enter your stake per spin, the number of spins and the house edge for your wheel, then read the expected loss and the total staked. The steps below cover each field.
- Stake per spin. Add up every chip on the layout for one spin. If you cover three bets of 5 units each, the stake per spin is 15.
- Number of spins. Use the total you plan to play, or spins per hour times hours. No regulator sets a pace, and published figures differ: Manitoba’s GameSense cost-of-play guide uses 26 spins an hour, and the Wizard of Odds assumes 35 an hour on a single-zero wheel and 38 on a double-zero wheel. Online games can run faster, but we have no source for how much, so treat the pace as your own estimate.
- House edge. Type the percentage from the table below: 2.70 for a single-zero wheel, 5.26 for double-zero, 7.69 for triple-zero, 1.35 for even-money bets with la partage.
- Read the result. The large number is the expected loss in units. The line under it shows the total staked, and the Formula line shows the multiplication with your numbers.
Example: a player stakes 10 units a spin for 100 spins on a single-zero wheel. Total staked is 10 x 100 = 1,000.00 units, and the expected loss is 1,000.00 x 2.70 / 100 = 27.00 units. Move to a double-zero wheel and the same play costs 1,000.00 x 5.26 / 100 = 52.60 units. At a pace of 30 spins an hour (an illustrative figure between the published 26 and 35), 10 units a spin stakes 300 units an hour, so the expected cost is about 8.10 units an hour on the first wheel and 15.78 on the second.
What is the house edge on each roulette wheel and bet?
Every standard bet on a single-zero wheel has a house edge of 2.70% (1/37). On a double-zero wheel it is 5.26% (2/38), and on a triple-zero wheel 7.69% (3/39). The American five-number bet is worse at 7.89%. Even-money bets under la partage cost 1.35%.
| Wheel and rule | Pockets | Bets it applies to | Edge as a fraction | House edge |
|---|---|---|---|---|
| Single zero (European) | 37 | Every standard bet | 1/37 | 2.70% |
| Single zero with la partage | 37 | Even-money bets only | 1/74 | 1.35% |
| Single zero with en prison | 37 | Even-money bets only | 18/1369 to 19/1369 (1/74 if a repeat zero keeps the bet held) | 1.31% to 1.39% |
| Double zero (American) | 38 | Every standard bet | 2/38 = 1/19 | 5.26% |
| Double zero, five-number bet | 38 | 0, 00, 1, 2, 3 at 6 to 1 | 3/38 | 7.89% |
| Triple zero | 39 | Every standard bet | 3/39 = 1/13 | 7.69% |
The payouts behind these numbers are public. The New Jersey Division of Gaming Enforcement roulette rule for a double-zero wheel lists straight-up at 35 to 1 and the first-five bet at 6 to 1, and Lake Tahoe Community College lecture notes on roulette give an expected value of -5.26 for a 100-unit bet on most layouts and -7.89 for the first five. The triple-zero edge is our own calculation from 39 pockets and a 35 to 1 straight-up payout (3/39 = 7.69%); we did not find a regulator page that states it. Triple-zero tables do exist: the Las Vegas Review-Journal reported a Strip casino removing them.
What do la partage and en prison change?
With la partage, an even-money bet that meets the zero loses only half its stake. The edge falls to 1/74, or 1.35%, and Peter Pflaumer of TU Dortmund reports the same expected value of about -0.0135 per unit. With en prison, the bet is held for the next spin and returned, without profit, if it then wins. How a second zero is treated changes the edge slightly, which is why the table shows a range: 1.31% if the stake comes back, 1.35% if the bet stays held, and 1.39% if it is lost. Check the table rules before you type the edge.
Why does every roulette bet have the same house edge?
A bet covering k numbers pays 36/k – 1 to 1, which would be fair on a wheel with 36 pockets. A single-zero wheel has 37, so each unit staked returns 36/37 on average and loses 1/37, whatever the bet. The extra pocket is the entire edge.
The working shows it. On a single-zero wheel, a straight-up bet wins 1/37 of the time and returns 36 units: 36/37. A red bet wins 18/37 of the time and returns 2: 36/37. A dozen wins 12/37 of the time and returns 3: 36/37. On a double-zero wheel the same bets return 36/38, a loss of 2/38 or 5.26%. Ethier and Hoppe show that the permitted roulette bets on a double-zero wheel share one expected value of -1/19.
The five-number bet is the exception. It covers five of 38 pockets and returns 7 units on a win, so it returns 35/38 and loses 3/38. That is why it is the one bet worth skipping on a double-zero wheel. The choice between a straight-up bet and a red bet changes how bumpy the ride is, not what it costs.
How much does roulette cost over 100, 500 and 1,000 spins?
At 10 units a spin, 100 spins cost about 27.00 units on average on a single-zero wheel, 52.60 on a double-zero wheel and 76.90 on a triple-zero wheel. Expected loss grows in proportion to the total staked, so 1,000 spins cost ten times as much as 100 spins.
The table below applies the formula at four stakes. Every cell is stake x spins x edge / 100, using the edges as you would type them into the calculator.
| Stake per spin (units) | Spins | Total staked | Single zero 2.70% | Double zero 5.26% | Triple zero 7.69% | Single zero, la partage, even money 1.35% |
|---|---|---|---|---|---|---|
| 1 | 100 | 100 | 2.70 | 5.26 | 7.69 | 1.35 |
| 1 | 500 | 500 | 13.50 | 26.30 | 38.45 | 6.75 |
| 1 | 1,000 | 1,000 | 27.00 | 52.60 | 76.90 | 13.50 |
| 10 | 100 | 1,000 | 27.00 | 52.60 | 76.90 | 13.50 |
| 10 | 500 | 5,000 | 135.00 | 263.00 | 384.50 | 67.50 |
| 10 | 1,000 | 10,000 | 270.00 | 526.00 | 769.00 | 135.00 |
| 25 | 100 | 2,500 | 67.50 | 131.50 | 192.25 | 33.75 |
| 25 | 500 | 12,500 | 337.50 | 657.50 | 961.25 | 168.75 |
| 25 | 1,000 | 25,000 | 675.00 | 1,315.00 | 1,922.50 | 337.50 |
| 100 | 100 | 10,000 | 270.00 | 526.00 | 769.00 | 135.00 |
| 100 | 500 | 50,000 | 1,350.00 | 2,630.00 | 3,845.00 | 675.00 |
| 100 | 1,000 | 100,000 | 2,700.00 | 5,260.00 | 7,690.00 | 1,350.00 |
Expected loss follows the total staked, not the money you bring. A player who keeps winnings on the layout can stake many times a starting 100 units, and the edge applies to every unit staked. Doubling the pace doubles the hourly cost.
How far can a real session stray from the expected loss?
A long way. The expected loss is an average, and single sessions scatter around it. The scatter is measured by the standard deviation: about 1.00 stakes per spin on an even-money bet and 5.84 on a straight-up bet. Over N spins it grows with the square root of N.
The formula for one spin is the square root of E[X squared] minus the mean squared. For an even-money bet on a single-zero wheel, X is +1 with chance 18/37 and -1 with chance 19/37, so the variance is 1 – (1/37)^2 = 0.99927, matching the figure Pflaumer reports, and the standard deviation is 0.9996. For a straight-up bet, X is +35 with chance 1/37 and -1 with chance 36/37, so E[X squared] = (1,225 + 36)/37 = 34.081, the variance is 34.0804 and the standard deviation is 5.838. Over N spins, multiply by the square root of N and by your stake.
Example: 100 even-money spins of 10 units on a single-zero wheel. The expected loss is 27.03 units (about 27.00 as typed). The standard deviation is 0.9996 x 10 x 10 = 99.96 units, so a typical session lands anywhere from about 73 units ahead to about 127 units behind. The same 100 straight-up spins have a standard deviation of 5.838 x 10 x 10 = 583.8 units, because one hit pays 360 units back on 10 staked.
The next table gives the exact chance of finishing a session strictly ahead, and the standard deviation in multiples of your stake. We computed the chances by summing the exact outcome probabilities for every possible number of wins, and checked the method against the 48% figure Pflaumer gives for a straight-up bettor on a single-zero wheel after 205 spins: we get 47.9%.
| Bet and wheel | Ahead after 100 spins | Ahead after 500 spins | Ahead after 1,000 spins | Std. dev. at 100 spins (stakes) | Std. dev. at 1,000 spins (stakes) |
|---|---|---|---|---|---|
| Even money, single zero | 35.53% | 25.80% | 18.76% | 10.0 | 31.6 |
| Even money, single zero, la partage | 43.73% | 37.57% | 33.00% | 9.9 | 31.3 |
| Even money, double zero | 26.50% | 11.07% | 4.48% | 10.0 | 31.6 |
| Even money, triple zero | 19.15% | 3.85% | 0.68% | 10.0 | 31.5 |
| Straight up, single zero | 50.94% | 48.40% | 45.11% | 58.4 | 184.6 |
| Straight up, double zero | 49.16% | 44.45% | 39.61% | 57.6 | 182.2 |
| Straight up, triple zero | 47.44% | 40.70% | 34.49% | 56.9 | 179.9 |
Notice what the table says. An even-money bettor on a single-zero wheel is ahead after 100 spins 35.5% of the time, and after 1,000 spins 18.8% of the time. On a double-zero wheel the 1,000-spin figure falls to 4.5%. The longer you play, the more the edge outweighs luck. Straight-up bets look better at 100 spins (50.9% on a single-zero wheel) because three hits are enough to finish ahead and the average is only 2.7 hits. That is a feature of the uneven payout, not a sign the bet is cheaper: its expected loss is the same 2.70%.
Do betting systems change the expected loss?
No. A betting system changes the size and timing of your stakes, not the chance of any spin, so the expected loss is always the total staked times the house edge. A system can change how that total builds up and how often you finish ahead, but not the edge.
Take the Martingale, which doubles the stake after each loss and stops after a win or after seven straight losses, with a 127-unit bankroll. On a single-zero wheel with an even-money bet, a seven-loss run has probability (19/37)^7 = 0.94%. The round then wins 1 unit with probability 99.06% and loses 127 units with probability 0.94%, an average of 1 – 128 x 0.0094 = -0.205 units per round.
Those rounds stake 7.594 units on average (1 + 2 x 19/37 + 4 x (19/37)^2 and so on). The loss of 0.205 divided by 7.594 is 2.70%, exactly the house edge. Peter Pflaumer of TU Dortmund reaches the same conclusion in a statistical analysis of the Martingale: in the long run a loss is inevitable because the expected value is negative. Systems trade many small wins for a rare large loss.
What mistakes do people make with a roulette house edge calculator?
- Typing the edge as a decimal. The field takes a percentage, so enter 2.70, not 0.027.
- Counting spins instead of bets. If you place three bets per spin, the stake per spin is the sum of all three, or the number of bets rises. Total staked is what matters.
- Using the wrong wheel. The same play costs about twice as much on a double-zero wheel as on a single-zero wheel. Check for the 00 before you choose the edge.
- Reading the result as a prediction. An expected loss of 27.00 units does not mean you will lose 27.00. The table above shows how wide the range is.
- Applying 1.35% to every bet. La partage and en prison apply to even-money bets only, and only when the table offers them.
- Believing a short win means the edge has gone. Finishing ahead is common over 100 spins and rare over 1,000. Past spins do not change the next one.
What should you do with your result?
Compare the expected loss with what you are happy to spend, and set a limit on stake and time before you play, not during. If the number is more than you planned, lower the stake, play fewer spins, or choose not to play. Our Safer play toolkit has simple ways to set and keep a limit.
To turn the cost into an hourly figure, try the session cost calculator for gambling, and for other games see the expected loss calculator. If gambling is costing more than you intended, the Get help page lists free, confidential support.
How to read the result
Expected loss is the average amount the spins cost you, in units, if you played the same bets many times. It is not what will happen in one session, which can finish well above or below it. The line under it shows the total staked, which is stake per spin multiplied by the number of spins. The bar shows the house edge on a scale of 0 to 30%. Typical roulette edges are 2.70% on a single-zero wheel, 5.26% on a double-zero wheel, 7.69% on a triple-zero wheel and 1.35% on even-money bets with la partage. Open the Formula line to see the multiplication with your numbers.
How it is calculated
Total staked = stake per spin x number of spins. Expected loss = total staked x house edge / 100. The house edge is entered as a percentage, so 2.70 means 2.70%. The result and the total staked are rounded to two decimal places for display. The calculator accepts a stake of 0.01 or more, at least 1 spin, and a house edge from 0 to 30. The unit label is taken from the stake field.
Worked example
Worked example
Stake per spin 10 units, 100 spins, house edge 2.70% (the default inputs, a single-zero wheel). Total staked: 10 x 100 = 1,000.00 units. Expected loss: 1,000.00 x 2.70 / 100 = 27.00 units. The result card shows 27.00 units, the line Total staked: 1,000.00 units., and the edge bar at 2.70% on a scale of 0 to 30%. Change the edge to 5.26 for a double-zero wheel and the expected loss becomes 52.60 units.
Limits
The calculator multiplies the total staked by the house edge you enter and nothing else. It gives an average over many spins, not a prediction for one session, and it does not show how far results can vary. It assumes the same stake and the same edge on every spin. It does not know which wheel you play, so you must enter the edge for your wheel and rules. It does not model a bankroll running out, and it does not include tips, fees or side bets with their own edge. Typing 2.70 instead of the exact 1/37 (2.7027%) changes the result by a few hundredths of a unit per 1,000 staked. The edge must be between 0 and 30, the stake at least 0.01 and the number of spins at least 1. Amounts are shown in units, not a currency. Results are estimates.