Math Behind Roulette

Roulette is one of the most popular casino games worldwide and is often featured in movies due to the glamorous associations it has come to enjoy. The spinning wheel, and the ball bobbing around before coming to rest on one of 38 spaces, generates a unique sense of anticipation among betters. Behind all the fun is a complex set of mathematics at play, and an understanding some of the mathematics of Roulette could be the difference between that big win and a loss.

Roulette Mathematics principles

MathMath behind roulette

The math underlying odds and gambling can help determine whether a wager is worth pursuing. The first thing to understand is that there are three distinct types of odds: fractional, decimal,. Basic Gambling Mathematics: The Numbers Behind the Neon explains the mathematics involved in analyzing games of chance, including casino games, horse racing, and lotteries. The book helps readers understand the mathematical reasons why some gambling games are better for the player than others. Unlike Blackjack, Roulette is a game involving independent events. When playing Roulette, a large wheel is spun and a small ball is dropped onto it. The ball will eventually fall into one of 38 spaces. The spaces are alternately colored black and red and numbered 1 – 36, with two additional green spaces marked with 0 and 00. The roulette game is as popular today as it was in the past. Gamblers play the game to rest on what number the ball would be after the ball is spun on a wheel on purpose built. There are basically two types of roulette wheel: the European and American. The European wheel has 37 slots numbered 0-36. In this case, the house advantage is 2.7%. Still, a lot of contemporary casino players hardly realize how important the systems of complex mathematics are to gambling. Of course, there are various games that are based on randomness and luck, but a great number of casino offerings are based on pure mathematics, or at least part of the strategies associated with them are.

Roulette is based on independent events, which means that any event (say, the ball landing on a certain numbered slot on the wheel) is not influenced by previous events and does not influence future events. This is in opposition to dependent events, such as in blackjack, where the outcome is affected by previous outcomes.

Roulette odds

The payout ratio for betting on one number in Roulette is 35:1, which means that if you bet £10 that the ball will land on the number 8, for example, you will receive your £10 back plus another £350, if the ball does in fact land on 8. You can also bet on red or black, and the payout ratio for this is 1:1, because the probability of this occurring is much higher, so therefore the payout ratio is lower.

Math Behind Blackjack


Because there are 36 red and black slots on a roulette wheel, and two green slots, the probability of landing on either red or black is slightly less than one in two. The probability of landing on a red slot is the number of red slots (18) divided by the total number of slots (38), which equates to 0.47, or 47%. Therefore, the probability of the ball not landing on red is 0.53, which means the house has the advantage and has a 53% chance of winning every bet on red a player makes. Read our theory of probability page if you’re interested in finding out more about the concept of probability.

Expected Value in Roulette

Math behind blackjack

Math Behind Roulette

The concept of Expected Value is at play in all casino games including Roulette. In short, the Expected Value is what a player can theoretically expect to win or lose if they play repeatedly with the same bet. Using the example of betting £10 on red, you could expect to lose £0.53 for each spin. Read our Expected Value page for an explanation of this.

Math Behind Roulette

Our Gambling Mathematics glossaryshould be of use if you’re interested in a quick overview of the main concepts relating to the mathematics of gambling.