Roulette is a casino game built around randomness. On each spin, a ball lands in one of a fixed number of equal-size pockets; probability describes the chance it settles in any given pocket or group of pockets. House edge is the long-run average percentage of each stake the casino expects to keep; expected value is the average outcome per unit staked over many spins. This article is informational for adults. It does not recommend gambling, offer betting strategy, or suggest where to play roulette.
The two main wheel types are European roulette (37 pockets: numbers 1 to 36 plus a single zero) and American roulette (38 pockets: numbers 1 to 36, 0, and 00). European roulette has 37 pockets while American has 38; that single extra pocket drives most of the probability and house edge contrasts between them. Examples use fair wheels and the payment assumptions stated in each calculation.
Wheel structures and basic outcome probabilities
On a fair roulette wheel, every pocket is equally likely on each spin. The total number of outcomes is fixed, so probability for any bet covering n numbers is n divided by total pockets.
On the European roulette wheel, the probability of hitting a single specific pocket is 1/37, approximately 2.70%. On an American roulette wheel, it is 1/38, approximately 2.63%. The Massachusetts Gaming Commission equipment regulations describe the 37-compartment single-zero structure. Roulette probabilities depend on the wheel layout. These figures assume the roulette wheel is mechanically fair and ball motion is random.
Expected value and the origin of the house edge
House edge depends on both outcome probabilities and payment rules. Consider a mathematical example in which a £1 stake produces £35 profit on one pocket and a £1 loss on every other pocket. This example describes the calculation, not a recommendation to place a bet.
With 37 equally likely pockets, expected net value is (1/37 × £35) + (36/37 × −£1) = −£1/37. The corresponding theoretical house edge is about 2.70%. With 38 pockets and the same payment assumption, it is −£2/38, corresponding to about 5.26%.
A £35 profit plus the returned £1 stake gives a £36 total return. Profit and total return must not be confused in the calculation. Different payout rules or additional features can change the result, so these figures do not apply automatically to every roulette variant.
Expected loss is not a maximum loss
Expected value is a mathematical average, not a promise about an individual session. A 2.70% house edge does not mean a £100 deposit loses precisely £2.70. It applies to aggregate stakes, which can exceed the initial deposit if returned funds are used again. A session can lose the full amount committed.
The law of large numbers concerns averages under the stated assumptions. It does not promise that an individual’s losses will be recovered by continuing.
Consecutive colours, streaks, and gambler’s fallacy
Sequences of the same colour appearing several times in a row are consistent with basic probability. On a European wheel, the probability of k consecutive reds is (18/37)^k:
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2 times in a row: about 23.67%
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4 times in a row: about 5.60%
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6 times in a row: about 1.33%
On an American wheel, the corresponding expression is (18/38)^k because the additional zero outcome reduces the per-spin probability of one colour.
Each spin in roulette is an independent event. The probability of red on the next spin remains 18/37 on a European wheel regardless of previous spins. After ten consecutive blacks, the chance of red is still 18/37, approximately 48.6% regardless of past results. Believing a colour is “due” after a streak is the gambler’s fallacy, the mistaken belief that past results influence future outcomes. Gambler’s fallacy leads to poor betting decisions in roulette because it confuses cumulative probability (the chance of a streak starting fresh) with conditional probability (the chance of the next spin given a specific number or colour has just appeared).
Same number twice or more in a row
On a fair European wheel, the probability that a specific number appears on two consecutive spins, predicted in advance, is (1/37) × (1/37) = 1/1,369, roughly 0.073%. For three consecutive hits: (1/37)^3 ≈ 1 in 50,653. Observing such a streak provides no exploitable prediction advantage; each spin remains independent.
Formats for expressing roulette probability and odds
The same probability can appear as a fraction, a decimal, or a percentage. Take the chance of red on a European wheel: 18/37 as a fraction, approximately 0.4865 as a decimal, and about 48.65% as a percentage.
Odds against notation expresses losing outcomes to winning outcomes. For red on the European roulette wheel: 19 losing outcomes (18 blacks + one zero) against 18 winning, so odds against are 19:18 or roughly 1.06:1. On an American wheel: 20:18, roughly 1.11:1 against.
Probability and payment are different measurements. A quoted payout should not be mistaken for the chance of receiving it.
Randomness and published information
The Gambling Commission’s RTS 7 standard addresses acceptable randomness for products within scope. Its RTS 3 standard addresses clear rules, prizes and relevant probability information. A fair random process can still have a mathematical house advantage.
Gambling protection and support
Probability does not remove the risk of financial harm. GAMSTOP provides online self-exclusion, and GamCare provides information and support. Self-exclusion protections should be maintained. Seeking a different game or software provider is not a substitute for them.
Reviewed 22 October 2026. Calculations assume fair, independent outcomes and the specified payment rules.