The expected value of roulette is a key concept for players who want to understand their long-term odds. It represents the average amount a player can expect to win or lose per bet over time. Because roulette is a game of chance with fixed payouts, calculating expected value helps reveal the house edge behind each type of wager.
Whether you're placing inside bets like straight-ups or outside bets like red/black, every bet on a roulette wheel has a negative expected value in the long run. This means the casino always holds an advantage, but the size of that edge varies depending on the wheel type and bet selection.
Expected value (EV) is calculated by multiplying the probability of winning by the payout, then subtracting the probability of losing multiplied by the bet amount. For example, a $1 bet on red in European roulette has an 18/37 chance of winning $1 and a 19/37 chance of losing $1.
The EV is (18/37 × $1) – (19/37 × $1) = –$0.027. This means you lose, on average, 2.7 cents per dollar bet. This negative EV reflects the house edge and applies to all bets on the wheel.
European roulette has a single zero, giving it 37 pockets. This results in a house edge of 2.7% on most bets. American roulette adds a double zero, creating 38 pockets and increasing the house edge to 5.26%. This nearly doubles the expected loss over time.
For example, a $10 bet on black in American roulette has an EV of –$0.53, compared to –$0.27 in European roulette. Always choose European wheels when available to reduce long-term losses.
All standard roulette bets have the same expected value relative to the house edge. A straight-up bet (single number) pays 35:1, but the odds of winning are 1 in 37 (2.7%). The EV is still –2.7% of the bet amount.
Even-money bets like odd/even or high/low may seem safer, but they also carry the same negative EV. The only exception is the 'top line' bet in American roulette (0, 00, 1, 2, 3), which has a higher house edge of 7.89% and should be avoided.
Is there a roulette bet with positive expected value?
No. All legal roulette bets have negative expected value due to the house edge. No betting system can overcome this over time.
Does the Martingale system beat the expected value?
No. While it can win small amounts in the short term, the negative EV remains. Long losing streaks can lead to massive losses, especially with table limits.
Can biased wheels create positive EV?
Theoretically, yes—if a wheel is physically flawed and certain numbers hit more often. But modern casinos monitor wheels closely, making this extremely rare.
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