Roulette probability by variant: house edge maths

Published: April 16, 2026 | Updated: 2 October 2026 | Reading time: 7 min | By: azimutbet.net editorial team

Roulette is one of the few casino games where all of the maths is in plain sight: a fixed number of pockets and a fixed payout for every bet. That makes it possible to calculate exactly what each variant and each bet costs on average. This article sets out those numbers for European, French and American roulette and for Evolution's Lightning Roulette, works through an expected-loss example, explains why betting systems do not change the result, and notes what AzimutBet publishes about its roulette tables as of 2 October 2026. Nothing here is a way to win: every roulette bet has a negative expected value. Gambling is for adults (18+) only.

Roulette wheel illustration for an article on roulette probability and house edge by variant

Where the house edge comes from

A European wheel has 37 pockets: the numbers 1 to 36 plus a single zero. A straight-up bet on one number pays 35:1, so a win returns 36 units including the stake. A fair payout would be 36:1, returning 37 units. Over many spins the average return is therefore 36/37 = 97.30% of the amount staked, and the house edge is 1/37 = 2.70%.

Every standard bet on a single-zero wheel works out to the same 2.70%, because the payouts are scaled to the number of pockets covered as if the zero did not exist. The American wheel adds a second zero (00): 38 pockets with the same payouts, so the edge rises to 2/38 = 5.26%. In other words, the edge comes from the zero pockets, not from which bet is chosen. Definitions of house edge, RTP and variance are in the glossary.

Probability and house edge by bet type

Bet Numbers covered Payout Win chance (single zero) Win chance (0 and 00) House edge (single zero / 0 and 00)
Straight up135:12.70%2.63%2.70% / 5.26%
Split217:15.41%5.26%2.70% / 5.26%
Street311:18.11%7.89%2.70% / 5.26%
Corner48:110.81%10.53%2.70% / 5.26%
Five-number (0, 00, 1, 2, 3)56:1not offered13.16%– / 7.89%
Six line65:116.22%15.79%2.70% / 5.26%
Dozen or column122:132.43%31.58%2.70% / 5.26%
Even money (red/black, odd/even, 1–18/19–36)181:148.65%47.37%2.70% / 5.26%

The chance of winning rises with the number of pockets covered, but the average cost stays the same. Choosing between a straight-up bet and red/black changes how bumpy the results are (volatility), not how much is lost on average. The one bet that is worse than the rest is the American five-number bet.

The main variants compared

Variant Zero pockets House edge What to know
European1 (0)2.70% on all betsThe standard single-zero game.
French1 (0)1.35% on even-money bets with la partage or en prison; 2.70% on other betsLa partage returns half of an even-money stake when zero lands; en prison holds the stake for the next spin. The rule must appear in the game's rules – not every table called "French" applies it.
American2 (0 and 00)5.26%; 7.89% on the five-number betSame payouts as European on a bigger wheel, so roughly double the cost.
Lightning Roulette (Evolution)1 (0)About 2.7% (Evolution states an RTP of about 97.3% for most bets)Straight-up wins on ordinary numbers pay 29:1; random lucky numbers get 50x–500x multipliers.

Names are not a guarantee of rules. Before playing any table, open its information or help panel and check the number of zeros, the payouts, whether la partage or en prison applies, and the RTP the game states.

Lightning Roulette in more detail

Lightning Roulette is a live game made by Evolution on a standard single-zero wheel. In each round, 1 to 5 random "lucky numbers" receive a multiplier between 50x and 500x (Evolution's published range). A straight-up win on a lucky number pays the multiplier; a straight-up win on any other number pays only 29:1 instead of the usual 35:1. The reduced payout funds the multipliers. According to Evolution the return to player is about 97.3% for most bets, close to European roulette, but the distribution is very different: most straight-up wins are smaller and a few are much larger. Higher variance means a bankroll can run down faster between big hits. RTP can differ between game versions, so the figure in the game's own info panel is the one that counts.

What the edge means in money: a worked example

Assumptions (for illustration only): a stake of €5 per spin, 50 spins per hour and one hour of play, so €250 staked in total. Real pace varies widely: live tables are slower, automatic RNG roulette can be much faster.

  • European roulette: €250 × 2.70% ≈ €6.76 expected loss
  • American roulette: €250 × 5.26% ≈ €13.16 expected loss
  • French even-money bets with la partage: €250 × 1.35% ≈ €3.38 expected loss

Expected loss is a long-run average. In any single hour the real result can be much better or much worse; the edge only shows reliably over many spins. The useful formula is: cost per hour = stake × spins per hour × house edge. Speed is the factor people tend to overlook – auto-play, quick RNG games or several tables at once multiply the number of spins and with it the expected loss.

Why betting systems cannot beat the zero

Each spin is independent. The wheel has no memory, so after five reds in a row the chance of red on a single-zero wheel is still 18/37. Believing that a colour or number is "due" is the gambler's fallacy, and the history boards shown at many tables do not change it.

The Martingale system – double the stake after every loss on an even-money bet – shows the problem clearly. Assumptions: €5 starting stake on red, a single-zero wheel and a table maximum of €500. The sequence 5, 10, 20, 40, 80, 160, 320 adds up to €635; the next doubling (€640) is above the limit. The chance of losing seven spins in a row is (19/37)7 ≈ 0.94%, about once in 106 series. Most series end €5 up; the rare failed series costs €635. Averaged out, each series loses about €1.03 – exactly 2.70% of the roughly €38 staked on average per series. Fibonacci, D'Alembert and Labouchère behave the same way: they rearrange when wins and losses happen, not how much is lost on average. Any system sold as a "guaranteed" roulette method is not one.

Roulette at AzimutBet: what could be checked (2 October 2026)

  • AzimutBet's home-page FAQ describes one account combining sports betting, live betting, casino games, slots, live casino tables and esports, so a live casino section exists.
  • Which roulette variants are offered, their rules (for example la partage) and their RTPs are not published on the operator pages that could be checked.
  • Only the operator's affiliate programme (Azimut Partners) names Evolution among its providers, alongside Pragmatic Play, NetEnt and Spribe. That is a marketing statement, not a verified game list, so it is not confirmed that Lightning Roulette or any particular Evolution table is available.
  • The operator's terms and conditions and bonus rules could not be read on 2 October 2026, so it is unknown whether roulette counts towards bonus wagering and at what rate. Many casinos exclude roulette or count it at a reduced rate; see the bonuses page and the specific offer's terms.
  • Licence: Anjouan, licensee Tetaron Limited, licence ALSI-202411073-FI2, valid until 21 November 2026 according to the Vantegris mirror of the Anjouan register (fetched 27 September 2026). Details and how to verify it are on the licensing page.
  • The operator's own FAQ asks "Is sports betting a guaranteed way to make money?" and answers "No." The same is true of roulette.

Using the maths sensibly

  • Prefer single-zero tables; on French tables with la partage or en prison the even-money bets carry the lowest edge.
  • Avoid double-zero wheels when a single-zero table is available, and skip the five-number bet.
  • Set a budget and a time limit before playing, and work out the expected cost per hour with the formula above.
  • Treat any money spent as the price of entertainment and do not chase losses. More practical advice is on the tips page; the site's terms explain how this site works.
  • If gambling stops being fun, take a break and contact a gambling support service in your country.

The same logic applies to slots, where theme and presentation do not change the payout maths – see ancient-themed slots: myths vs maths. Big roulette wins in the news are a classic case of survivorship bias, covered in celebrity casino stories: what the headlines leave out, and VR casinos: what exists today and what is still speculation looks at whether new formats change anything (the wheel's maths stays the same).

Frequently Asked Questions

What is the house edge in European vs American roulette?

European roulette has one zero and a house edge of 2.70% (1/37) on every standard bet. American roulette adds a double zero, which raises the edge to 5.26% (2/38), and the five-number bet on 0, 00, 1, 2 and 3 costs even more at 7.89%. French rules with la partage or en prison cut the edge on even-money bets to about 1.35%.

How does Lightning Roulette change the mathematics?

In Evolution's Lightning Roulette a straight-up win on an ordinary number pays only 29:1 instead of 35:1, while 1 to 5 random lucky numbers per round get multipliers of 50x to 500x. Evolution states an RTP of about 97.3% for most bets, so the average cost is close to European roulette, but results swing much more. The game's info panel shows the RTP that applies.

Can understanding probability improve long-term results?

No. Every roulette bet has a negative expected value and no knowledge, pattern or system can overcome the house edge. What the maths does help with is choosing lower-edge variants and bets, seeing how fast losses add up with stake and speed, and setting a budget and time limit before playing.

Does a betting system like Martingale change the house edge?

No. Martingale and similar progressions change the pattern of results, with many small wins and occasional large losses, but the expected loss stays equal to the total amount staked multiplied by the house edge. Table limits and a finite bankroll end the doubling long before it can recover a long losing run.

About the Author

This article explains roulette probability and house edge across the main variants. Game maths are calculated from the standard pocket counts and payouts, with the assumptions stated in each example; Lightning Roulette figures are those Evolution publishes for the game. Brand facts come from the operator's own pages and the Vantegris mirror of the Anjouan licence register, checked on 2 October 2026. azimutbet.net is an independent information site, not the operator.

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