Roulette RTP and House Edge
Roulette RTP (Return to Player) is the theoretical percentage of total wagered money returned over the long run; house edge is the complementary expected loss. Use this roulette RTP calculator to compare European, American and French rules, including surrender, la partage, three exact en prison models and the American first five exception.
Roulette RTP calculator: house edge and expected loss
Select a wheel/rule model, bet group, currency, stake and spin count. The tool applies special rules only where they are mathematically valid.
Current calculation
A $10.00 stake over 100 European spins creates $1,000.00 in total action. At 97.30% RTP, the expected amount returned is $972.97 and the expected net result is −$27.03.
Build the expected value from each outcome
Multiply the probability of each outcome by its net result, then add the contributions. This explains the average for one new wager before scaling it to the count above.
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| Outcome | Probability | Net result | EV contribution |
|---|
Expected value is an average, not a promised session result. Rounded table entries may not sum exactly as displayed; the total uses unrounded fractions. “≈” marks rounded contributions, and nonzero amounts below 0.01 remain visible.
Estimate the cost of playing for a set time
Use the current stake and rules with your own pace estimate. The starting values are an illustration, not a measured casino speed. This preview has its own wager count.
Count only NEW stakes, excluding spins that merely resolve held stakes. Use a rate that already accounts for that resolution time. Expected returns include eventual settlement of each initial wager, even if it finishes after the planned time; this is not a cash balance at the stopping time.
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Planned count = minutes × new wagers per hour ÷ 60, rounded down. Expected loss = stake × planned count × house edge. Breaks, skipped rounds, a changing pace or an early stop change actual action. This does not estimate whether your bankroll lasts for the planned time.
Compare RTP and expected loss
A stays fixed. B follows the fields above. Differences are B minus A, rounded to two decimal places. pp means percentage points.
| Measure | A · Saved | B · Current | Difference |
|---|
RTP is a long-run return ratio, not a forecast of your ending balance. Different display units are not converted, so monetary differences are shown only when the units match.
Under en prison, the count means initial wagers. Extra spins used to resolve imprisoned stakes are included in the rule's expected value, not counted as new initial wagers. Equal initial-wager counts need not take equal playing time.
A is saved for this page visit only. Share result shares the current calculation (B), without the saved comparison.
Which roulette has the best RTP?
Among standard wheels, European and French single-zero roulette return 97.30% on regular fixed-payout bets, compared with 94.74% for standard American double-zero roulette. Special even-money rules can improve the theoretical return further: American surrender reaches 97.37%, while French la partage reaches 98.65%.
En prison can range from 98.61% to 98.69% in the models used here because repeated-zero treatment varies by table rule. Those reduced-edge figures apply only where the special rule is actually offered and only to qualifying even-money bets; they should not be transferred to inside bets or to a different roulette variant.
What RTP measures
Roulette RTP is the expected gross amount returned divided by total amount wagered. It includes returned stakes and winnings across all resolved wagers.
House edge is the expected loss divided by the same total action. The two figures are complements: 97.30% RTP corresponds to 2.70% house edge.
Theoretical return is not the ending bankroll. A player must first supply the wagers, so the expected net result is the returned amount minus total action.
Why a $100 deposit is not $100 wagered
Suppose a player starts with $100 and plans 100 standard European wagers of $10. If all those wagers are placed, the calculation uses $1,000 of action, including any money staked again after a return.
This fixed-action model does not calculate whether the starting $100 lasts for all 100 wagers. Stopping early changes the amount actually wagered.
RTP = expected gross return / total wagered House edge = 1 − RTP Expected net result = −(total wagered × house edge)RTP is not hit rate or a short-session result
Roulette RTP is not the same as hit rate: a straight number and an even-money bet can share the same theoretical return while having completely different probabilities of winning one spin. Use the roulette odds calculator for hit chance and repeated-spin probability, and the roulette payout calculator for stake-specific net profit and gross return.
Observed session return is a sample result. It can be 0%, 300% or more over a short sequence without changing the theoretical game model. The roulette session simulator shows how finite random sessions can finish above or below the theoretical return.
Longer play tends to make the observed ratio more stable, but it also increases total money exposed to the house edge. Convergence does not turn a negative expectation into a positive one, and a staking progression does not change the edge per unit wagered; the roulette strategy guide covers that bankroll and system-risk boundary separately.
Exact roulette RTP comparison
Each roulette RTP figure below separates standard wheel math from bet-specific exceptions and special zero treatment. Reduced rules apply only to even-money wagers.
| Model | Applicable bets | Exact edge | House edge | RTP | Rule note |
|---|---|---|---|---|---|
| European standard | Standard fixed-payout bets | 1 / 37 | 2.70% | 97.30% | One zero; full standard treatment. |
| American standard | Standard bets except first five | 2 / 38 | 5.26% | 94.74% | 0 and 00 are losing pockets for outside bets. |
| American surrender | Even-money only | 1 / 38 | 2.63% | 97.37% | Half the stake is returned on 0 or 00. |
| American first five | 0, 00, 1, 2 and 3 | 3 / 38 | 7.89% | 92.11% | Five pockets, 6:1 profit payout. |
| French standard | Standard fixed-payout bets | 1 / 37 | 2.70% | 97.30% | Same base wheel math as European roulette. |
| French la partage | Even-money only | 1 / 74 | 1.35% | 98.65% | Half the stake is returned immediately on zero. |
| En prison · repeat releases | Even-money only | 18 / 1369 | 1.31% | 98.69% | Repeated zero releases the imprisoned stake without profit. |
| En prison · remains held | Even-money only | 1 / 74 | 1.35% | 98.65% | Repeated zero returns the stake to prison. |
| En prison · repeat loses | Even-money only | 19 / 1369 | 1.39% | 98.61% | Repeated zero loses the imprisoned stake. |
American surrender and first five
American roulette RTP with surrender reaches 97.37% on red/black, odd/even and high/low. When 0 or 00 lands, half the even-money stake is returned and half is lost.
The expected gross return per unit is therefore (18 × 2 + 2 × 0.5) / 38 = 37/38, giving 97.37% RTP and a 2.63% edge. Inside bets, dozens and columns keep the standard 5.26% edge.
First five is a different exception. Five winning pockets return seven units gross on a 6:1 payout, so RTP is 35/38 = 92.11% and edge is 3/38 = 7.89%.
French la partage and en prison
Under la partage, French roulette RTP rises to 98.65% because half an even-money stake is returned immediately when zero lands. Its exact expected gross return is 73/74.
En prison holds the full stake for another resolution. A favorable result returns the stake without profit; an unfavorable result loses it. The treatment of a repeated zero determines the final edge.
If repeated zero releases the stake, RTP is 98.69%. If it remains imprisoned, RTP is 98.65%. If it loses, RTP is 98.61%. The calculator keeps these models separate rather than hiding them behind one approximate value.
La partage and the en prison “remains held” model produce the same exact 1/74 house edge because the unresolved stake is worth one half of its original amount in both calculations, even though the table mechanics are different.
Why en prison has more than one RTP
After the initial zero, the imprisoned stake still has residual value. That value depends on what the table does when zero appears again.
If a repeated zero releases the stake without profit, the expected returned fraction from prison is 19/37. If the stake stays imprisoned, the recursive value is exactly one half. If repeated zero loses, the returned fraction is 18/37.
Edge = (1 / 37) × (1 − value of imprisoned stake) Repeat releases: (1 / 37) × (1 − 19/37) = 18/1369 Remains in prison: (1 / 37) × (1 − 1/2) = 1/74 Repeat loses: (1 / 37) × (1 − 18/37) = 19/1369Expected loss examples
Expected loss scales with total amount wagered. The table uses exact fractions before rounding to two decimal places.
For an equal-action comparison, save $10 × 100 European wagers as A, then use $5 × 200 as B. Both total $1,000 and have the same $27.03 expected loss. The stake sizes, session length and short-term risk differ; this comparison does not estimate the chance of exhausting a bankroll.
| Total wagered | European standard | American standard | American surrender | First five | French special-rule range |
|---|---|---|---|---|---|
| $100 | $2.70 | $5.26 | $2.63 | $7.89 | $1.31–$1.39 |
| $500 | $13.51 | $26.32 | $13.16 | $39.47 | $6.57–$6.94 |
| $1,000 | $27.03 | $52.63 | $26.32 | $78.95 | $13.15–$13.88 |
| $5,000 | $135.14 | $263.16 | $131.58 | $394.74 | $65.74–$69.39 |
| $10,000 | $270.27 | $526.32 | $263.16 | $789.47 | $131.48–$138.79 |
Method and assumptions
The calculator assumes published fixed payouts and independent outcomes from the selected wheel model. It calculates expectation from initial wagers rather than simulating session paths.
Special zero rules are applied only to even-money bets. Selecting another bet group returns the control to the corresponding standard wheel model.
For en prison, spin count means initial wagers. Additional spins used to resolve imprisoned stakes are part of the rule's expected value and are not added to total initial action.
What can change the displayed RTP
A different payout table, triple-zero wheel, multiplier mechanic or proprietary side bet requires a separate model. The Lightning Roulette calculator handles boosted straight-number payouts separately; the standard values on this page should not be transferred to those games.
Table signage also matters for surrender, la partage and en prison. A single-zero wheel does not automatically guarantee either French rule, and a double-zero wheel does not automatically offer surrender.
When reviewing casino roulette options by wheel and zero rule, match the exact game and qualifying bet to its published payout table. A casino name alone does not determine the RTP of every table in its lobby.
Changing bet size does not change the percentage edge. Fixed packages and staking progressions can change stake distribution, variance and total action, but each unit remains exposed to the same underlying rule.
Rule sources for payouts and surrender
Pennsylvania § 617a.4 lists the standard payout odds used in these calculations, including 35:1 for a straight, 17:1 for a split, 11:1 for three numbers, 8:1 for four numbers, 6:1 for first five, 5:1 for six numbers, 2:1 for dozens and columns, and 1:1 for even-money bets.
New Jersey’s surrender option is a separate rule: on a double-zero wheel, 0 or 00 may cause either a full loss or a half loss on red, black, odd, even, 1–18 and 19–36, with the remaining half returned. The table must display which option is in force.
58 Pa. Code § 617a.4 — standard roulette payout odds
Cornell LII reproduction of N.J.A.C. 13:69F-5.2 — double-zero half-loss option
Wheel-specific RTP calculators
Use these pages when a specific European, American or French wheel/rule model is the primary question.
Common questions about roulette RTP
What is the RTP of roulette?
Standard European and French single-zero roulette have 97.30% theoretical RTP on regular fixed-payout bets. Standard American double-zero roulette has 94.74%. Qualifying even-money bets can reach 97.37% with American surrender, 98.65% with French la partage, and about 98.61% to 98.69% under the en prison models used on this page.
Can observed roulette RTP be higher than 100%?
Yes, over a finite session. Observed RTP is actual gross return divided by actual wagers and can exceed 100% during a profitable sample. Theoretical RTP remains the long-run expectation of the selected rule.
Does a higher hit rate mean a higher RTP?
No. Even-money bets hit more often than straight bets, but their payouts are smaller. On a standard wheel, both can have the same RTP despite very different volatility.
Does surrender improve every American roulette bet?
No. It reduces the edge only on even-money bets when 0 or 00 lands. Other standard bets keep the normal 5.26% double-zero edge, while first five keeps its 7.89% edge.
Why are there three en prison RTP values?
Casinos can resolve a repeated zero differently. Releasing, retaining or losing the imprisoned stake changes its expected value and produces RTP of about 98.69%, 98.65% or 98.61%.
Does a betting system change RTP?
No. A progression can change stake distribution, variance and total action, but the expected return per unit wagered remains tied to the wheel and rule model.
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