To understand your odds at roulette it is crucial to accept the fact that all results of each spin in roulette are completely random and depend on mere chance as far as each spin is actually an independent trial.

The factors that influence the odds at roulette are:

• Bets in roulette,
• Roulette payouts and
• Roulette house advantage.

Odds at roulette vary depending on the number of zero slots on European and American roulette wheels. European roulette wheel has a single zero slot, while American roulette introduces a second slot for zero, reducing the American roulette odds. The house edge in the two roulette variants is thus different and makes 2.63% for European roulette and 5.26% for the American variant. For this reason it is usually recommended to avoid playing roulette with American wheel.

House edge is seen as the mathematical difference between the true odds at roulette and actual roulette payout which is made possible due to the presence of the zero slot and brings a long term profit to a casino.

Roulette betting probabilities and payouts

Roulette offers a variety of inside and outside bets the player can make. The payouts for the bets may differ, but in fact the house edge basically remains the same for each bet.

• Even money bets in roulette (bets on Black-Red, Odd-Even and Low-High (1-18 and 19-36)) are paid out at 1 to 1, but the probabilities are different for American and European roulette - 46.37% and 48.6% respectively.
• Straight bets - bets on any certain number on the layout - pay 35 to 1. The probabilities for hitting a straight bet are 2.63% for American and 2.7% for European roulette. Straight bets are the most risky as the probability of hitting a certain number is very low. But in fact these bets offer the highest odds at roulette as far as they pay the most.
• Columns and Dozens pay 2 to 1 and have a 31.58% or 32.4% probability.
• Line bets on 6 adjacent numbers pay 5 to 1. The probabilities are 15.79% in American or 16.2% in European roulette.
• Corner bets on 4 numbers pay 8 to 1 and have a 10.53% or 10.8% probability for being hit.
• Street bets on 3 numbers pay 11 to 1. The probabilities are 7.89% or 8.1%.
• Split bets on 2 adjacent numbers pay 17 to 1 with the probabilities of 5.26% or 5.4%.

As it was mentioned, the roulette house edge remains unchanged for all types of bets - all but one. There is an additional bet available at American roulette known as the five-number or basket bet on numbers 1, 2, 3 and both zeros, '0' and '00'. The house edge for this bet is actually bigger - about 7.9%. It is recommended to avoid making this bet ever.

Romanian mathematician Catalin Barboianu in the book Roulette Odds and Profits: The mathematics of Complex Bets introduces additional type of bets - complex or improved bets that are mathematically proven to increase the player's odds at roulette:

• Bets on Red-Black and on any numbers of opposite colors
• Bets on Columns and outside numbers
• Bets on the 3rd Column and on Black
• Street bets plus bets on the opposites of predominant color
• Corner bets plus bets on the opposites of predominant color
• Line bets plus bets on the opposites of predominant color
• Bets on Red-Black and on opposite color split numbers
• Bets on High-Low plus Split bets of Low-High numbers
• Bets on 1st and 3rd Columns and on Black