Roulette Odds & Probability

Roulette is one of the oldest casino games, with its origins dating back more than a millennium. Today, gamblers can use dozens of betting systems, strategies, and even cheating devices that promise long-term success if used correctly. Still, there are only two simple concepts they need to grasp in order to improve their play and increase their chances of winning: odds and casino advantage.

One of the differences between games of chance and games of skill is that players’ decisions can significantly affect the outcome in games of skill, but not in games of chance. The game of roulette, for example, is a game of pure chance where the outcome is completely random.

Once you understand how roulette works, you can learn to play the game well. You just need to know the odds and figure out how likely it is that any given bet will win or lose. Casinos make money because they always have more bets that lose than win.

So, what is probability and does it differ from the odds offered to players at the roulette table? These are important questions that any gambler should ask before sitting down to play.

Probability and True Odds

Even though the terms “probability” and “odds” are often used interchangeably by some casino players, there is actually a clear difference between them.

Players should know that roulette wheels produce random results with every spin. They should also know that each number on the wheel has an equal chance of winning or losing. For example, the numbers 0 to 36 only have two possible outcomes – win or lose.


The probability of an event is the likelihood that it will occur compared to all possible outcomes. The probability always falls between 0 and 1, with 0 meaning impossible and 1 meaning certain. For example, if there are 38 numbers on a roulette wheel and we have even chances, this would be expressed as 0.50; if there were 37 numbers on the wheel we would have 37/38ths chance of winning.

The probability of the ball falling on 17 in the next spin is 2.70%. Most people find it easier to understand this as a percentage, so we multiply 0.027 by 100 and get 2.70.

True Odds in Roulette

Now that we have defined probability, let’s see how it compares to the notion of odds. Odds are also used to describe the chance of an event occurring but they compare the number of ways it can occur to the number of ways it cannot occur. So if there are 36 possible outcomes in roulette, then one way to express this is 1/36 or 1%.

Some bets in roulette have odds that are expressed in reverse. For example, the odds against winning a bet on number 17 are 36:1–or 36 to one. These odds are known as “true odds” to distinguish them from what some players refer to as “casino odds,” which do not include any advantage for the casino.

If we bet on red in roulette, the probability of winning is 18 out of 37 (48.65%), while the odds against us are 19:18 because there are 19 ways to lose and only 18 to win.

Casino Odds

When determining whether a roulette bet has good or bad odds, experienced players take into account not only their probability of winning and the true odds but also the potential reward they could bring. Each bet pays out differently, depending on its likelihood of winning – the less likely a given outcome is to occur, the more its potential payout would be.

To match the risk of this bet, the casino would be expected to return the original stake and pay out winnings worth 36 times the amount of the bet.

Casinos give slightly lower payouts than they should on winning straight-up bets. In this case, it’s a 1-unit difference. But over time, the tiny difference adds up to make a large profit for the house and gives casinos a guaranteed income in any possible scenario.

Casino odds are normally expressed in terms of a ratio of two numbers. The advantage that casinos have over players is a little more complicated than this, however; it depends on the bet being made. The better the casino odds are at representing the true chance of winning (or losing) on a given bet, the less of an advantage they have over players.

Roulette House Edge Explained

Casinos pay out less than the odds would suggest. Casinos are in the business of making money and they gain that advantage by paying out less than what is due to players. This difference is called the house advantage and can be demonstrated with the following example: We bet $1 on the number 17, win the bet, and are paid out $35 instead of receiving our original stake back plus $36.

In roulette, the player bets on which slot a ball will land in, and the casino has an edge because the wheel has equal numbers of slots on one side as it does on the other. For example, a single-zero wheel has 36 slots (0 through 35) and two of them are zero slots; whereas a double-zero wheel has 38 slots (0 through 37), with two of them being zero slots. The average house edge for single-zero roulette is 2.70%, and for double-zero roulette it’s 5.26%. There are several formulas for calculating the house edge but probably the simplest one is the following:

The house edge is the amount by which true odds are reduced by the casino’s odds.

If we substitute our earlier numbers for the straight bet, we get the following: 36/1 – 35/1 x 1/37 = 1×1/37 = 0.027, or 0.027%. This means that the house edge is 2.70%. Several other formulas exist for calculating the house edge, but they all lead to the same conclusion about this percentage.

There is a house edge of 2.70% on single-zero roulette and players can expect to lose $2.70 for every $100 wagered. Of course, this is a theoretical ratio between the stake and the expected loss but things could be very different in real life. If we place a $100 chip on red, we can either lose or win its entire value.

The house edge, or the advantage that a casino has over its players, can be calculated based on the expected return of a game. A roulette wheel has a 1.35% advantage for the house. In practice, this means that if you play roulette long enough and bet exclusively on even money bets (red or black, odd or even), you can expect to lose 1.35% of your bankroll per spin of the wheel. You might win or lose hundreds of dollars during one gaming session – but if you stick to these kinds of bets, you are less likely to lose your entire bankroll over time.

Beating the Odds in Roulette

The belief that there is a guaranteed method of winning at roulette is common and equally misleading. There are countless guides, books, and websites dedicated to convincing people that there is a guaranteed way to beat the odds. In fact, various betting systems have been developed over the years, some of which are inaccurate and claim to help players exploit imperfections in physical roulette wheels.

Over the years, casinos have used a variety of methods to try to ensure that their house wins in the long run. However, these techniques have proven inefficient at best and misleading at worst; they are not as effective as many gamblers believe them to be. The reason for this is simple: Roulette is a game of chance with fixed odds that cannot be changed by even the most advanced strategies. As explained above, every spin of the wheel is random, so the casino’s edge will remain the same almost as proof that it will always win in the end.

Roulette Strategies

Roulette strategies are betting systems that revolve around the idea of gradually increasing or decreasing the amount wagered after a certain outcome. One famous example is the Martingale, which suggests that you increase your bet after every loss, hoping that one winning bet will compensate for all of your previous losses. There are also roulette strategies where the amount wagered remains constant throughout the entire game session.

While betting progressions do not guarantee you will win, certain strategies claim to improve your chances of winning. One such method involves covering much of the table. However, this strategy will be too costly for most players, especially after a few losing spins.

If you are not prepared to lose your entire bankroll, then you should avoid placing neighbor bets or any other type of announced bet. In addition, even the best betting systems and roulette strategies cannot aid you in overcoming the built-in casino advantage. In conclusion, betting systems and roulette strategies will not help you beat the odds.

Advantage Play

Some roulette players rely on different methods for securing winnings. These methods, known as advantage play strategies, give players either an edge over the casino or a mathematical advantage. If used successfully, they can beat the house odds and even if it is just by a little, it should be enough to provide players with long-term winnings. Unlike betting strategies and systems described above, advantage play does not revolve around the betting layout but rather, around the wheel.

Land-based and online casinos offer roulette games based on random number generators (RNGs). Advantage players use special software to record the results of hundreds of spins in order to find patterns, such as repeating sequences of winning numbers. These patterns may be used to predict future outcomes. However, most modern casinos offer RNG-based roulette games so finding these patterns would be impossible.

However, advantage play in a physical roulette game is much different than that of an online roulette game. Physical roulette players typically stand beside the roulette table for at least 40-50 spins and write down all the winning numbers in the hope that they would be able to spot numbers that come out more frequently than others. In fact, sometimes they observe the wheel for hundreds of spins before they can notice repeating numbers, patterns or some irregularities.

Advantage play, a method of exploiting the imperfections in roulette wheels and other gaming equipment, was mostly used in the past when casinos did not have such strict maintenance rules and protocols. Today, players who wish to turn the odds in their favor need to be extremely discreet if they plan to observe the wheels before security become aware of them. Exploiting roulette wheels’ bias and imperfections for one’s profit is not usually met with understanding from casinos.

How to Enhance a Player’s Chances of Winning

There are no sure bets when playing roulette, but players can increase their chances of winning by following a few simple guidelines.

It is important to choose a good roulette table and obviously single-zero games are much better than double-zero ones. The house edge in American-style roulette is twice as high due to the additional sector on the wheel, which is green 00. But picking French or European-style roulette variations is just the first step in learning how to maximize players’ expected value.

While the game of roulette offers several betting options, players should concentrate on wagers with the lowest possible house edge. For example, outside bets cover large portions of the wheel and require just one chip to be wagered. These include black/red, even/odd, and low/high where the casino’s advantage is 2.70% but the player’s odds of winning are highest. While payout is not particularly attractive, these are less risky options in the game.

When choosing a bet, players must compare the casino’s payout odds to true odds and find a bet where these two numbers are as close to each other as possible. Generally speaking, the most attractive payouts are offered for bets with bad odds, but because these bets carry more risk than others, players should remember that they can’t expect to win much. Good payouts come with exceptionally high risks, so gamblers need a great tolerance for risk in order to win big.

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