Roulette Odds & Probability

Roulette is one of the oldest casino games and its origins can be traced back more than a millennium, when various simplified versions existed as a form of entertainment. Today, gamblers have access to dozens of betting systems, strategies, and even cheating devices that promise long-term success to those who dare use them. Still, there are only two simple concepts they need to grasp to improve their play and chances of winning: the odds and the casino advantage built into every roulette game.

Knowing the odds is essential when playing roulette or any other game of chance in which players’ decisions have no impact on the outcome of the round. Games of skill, in contrast, typically require at least basic knowledge of the rules and give skilled players the opportunity to improve their chances of winning. Unlike classic casino games such as blackjack or poker where individual actions can significantly change the outcome, roulette is a game of pure chance where the outcome is completely random.

Once players recognize this fact, they can truly understand the nature of roulette and learn how to optimize their play to avoid significant losses on the roulette table. Those who want to be successful in the long term need to learn the basic probabilities in this game and determine how likely any given bet is to win or lose. Moreover, all roulette fans should bear in mind that every bet they place is more likely to lose than to win. This is how casinos manage to always make a profit, even with the occasional big wins they have to pay out.

So, what is probability and is there a difference between the true odds in roulette and the casino odds offered to players? These are fundamental questions that need to be answered honestly before gamblers sit at the roulette table.

Probability and True Odds

Even professional casino players can confuse the terms “probability” and “odds”. Although they are indeed very similar in their usefulness and relevance to evaluating different roulette bets, the two are quite different, at least theoretically.

First of all, players should know that, if fair and unbiased, roulette wheels produce random results with every spin. Each number is equally likely to win or, rather, equally likely to lose. At the same time, for each number from 0 to 36, there are only two possible outcomes: a win or a loss.

Probability

Probability is the likelihood of any given outcome compared with all outcomes that are possible. Expressed as a number, probability always falls between 0 and 1. A value of 0 indicates that something is impossible, while 1 means absolute certainty for the outcome. Even chances, for example, would be expressed as a 0.50 probability. In roulette, we have either 37 or 38 numbers in total, so these are all the possible outcomes.

Let us take a single-zero roulette wheel, where for each number there is only one way to win and 36 ways to lose. So what is the probability that the ball will fall on 17 in the next spin, for example? We can calculate it by dividing the number of ways to win by all possible ways: 1/37, which is 0.027. For most people, the probability is easier to understand as a percentage, so we simply multiply the decimal by 100 and we get 2.70%.

True Odds in Roulette

Now that we have established what probability is and how it is determined in roulette, we can compare it with 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 with the number of ways it cannot occur. The odds of any particular number winning in roulette could be simply displayed as 1:36 or 1/36 where 36 is, once again, the number of ways to lose.

Sometimes the odds are expressed in reverse, indicating the odds against winning. Using the same example, the odds of the number 17 against winning would be 36:1, or 36 to 1. These are known as “true odds” as compared to what some players refer to as “casino odds”. There is a huge difference between the two terms, but it will be explained in detail in the following section.

To make this even clearer, let us see the odds for probably the most commonly placed bet in roulette, red/black. If we place our chips on red, the probability would be 18 out of 37, while the odds would be 19:18 against us because there would be 19 ways to lose against 18 ways to win. Expressed as a percentage, 18/37 equals 0.48648648648, or 48.65%.

Casino Odds

When determining whether a roulette bet has good or bad odds, experienced players consider not only the probability of winning and the true odds, but also the potential reward. Each bet pays out differently, depending on its likelihood of winning. The less likely a given outcome is to occur, the higher its potential payout will be. There is a sound logic behind this and in a perfect world where casinos would not have to make a profit, the payout of every bet would be equal to the odds against winning.

Let us take a look at the straight bet in European roulette: the odds against the player here are 36 to 1 (36:1) because, as we have already shown above, there are 36 ways for this bet to lose and only one way to win. In order to offer a reward that would match the risk, the casino would be expected to pay players 36 to 1. In other words, it would be expected to return the original stake and to pay out winnings that are worth 36 times the amount of the bet.

Roulette House Edge Explained

Clearly, the payout does not correspond to the true odds of roulette bets. This advantage of the casino over its patrons is called house advantage and can be easily demonstrated with the following example. We bet $1 on the number 17 and win. If given the true odds for this bet (36:1), we would receive our initial $1 stake back plus $36 as a payout. Instead, casinos pay us $35 and the original $1 bet, but they keep the $1 difference.

The same concept applies to all bets in the game, which results in an average house edge of 2.70% for single-zero roulette and 5.26% for double-zero roulette. There are several formulas for calculating the house edge, but probably the simplest one is the following. We need to subtract the casino odds from the true odds against success and then multiply that by the probability of success. So, the formula will look like this:

House Edge = (True Odds – Casino Odds) x Probability

When we substitute the numbers we have already used for the straight bet, we get (36/1 – 35/1) x 1/37 = 1 x 1/37 = 0.02702702702, or 0.027. To express it as a percentage, we multiply by 100 and get 2.70%. Several other formulas exist, but they all eventually come to the same conclusion and percentage for the house edge.

Beating the Odds in Roulette

The idea that by using a complex strategy one could beat the odds in roulette is very popular but equally misleading. There are countless guides, books, and websites dedicated to convincing people that there is a guaranteed method of winning in this game. In fact, various betting systems, often inaccurately called “strategies”, have been developed over the years, as well as ways that would supposedly help players exploit the imperfections of physical roulette wheels and overcome the house edge.

Unfortunately, these methodologies have been repeatedly proven to be inefficient in securing winnings over the long term. Moreover, their short-term usefulness is doubtful and the reason is obvious to most expert-level players: roulette is a game with fixed odds that cannot be changed, even with the best strategy. As explained above, the outcome of every spin of the roulette wheel is random and based on probability. The house edge, therefore, also remains the same, reinforcing the popular saying that the house always wins.

Roulette Strategies

The so-called roulette strategies are, in their essence, betting systems based on a progression where the amount of the stake changes after a certain outcome. Famous methods such as the Martingale or the D’Alembert suggest that you increase your bet after every loss, hoping that, in the end, one winning bet will compensate for all the losses. There are also systems where the bet is decreased, while in others, it remains the same throughout the entire game session. Overall, the idea is to help players minimize their losses or even generate some decent winnings over the long term.

While none of these betting progressions provides a foolproof way to win, another type of strategy makes exactly this claim. These strategies are based on the notion that you can increase your chances of winning by covering a large part of the table. Indeed, this sounds logical at first and certain methods even suggest that you should cover much more than 50% of the table. This strategy, however, will be too costly for most players, especially after a few losing spins.

If not used carefully, both betting systems and roulette strategies may “eat up” players’ entire bankroll within a short period of time. Placing neighbor bets or any other type of announced bets could be detrimental to those who are not well prepared to suffer serious losses. In conclusion, even the best methods and combinations of bets cannot aid you in beating the odds and overcoming the built-in casino advantage.

Advantage Play

Some roulette players rely on quite different methods for securing winnings. Known as advantage play methods, these include any strategies that give players either a statistical or a mathematical advantage over the casino. If employed successfully, they can beat the standard roulette odds and, even if only by a little, provide players with long-term winnings. Unlike the betting strategies and systems described above, advantage play does not revolve around the betting layout but rather, around the wheel.

It can be used in both online and land-based casinos. Online, advantage players would try to use special software that records and analyzes the results of hundreds of spins. The aim is to find a pattern in the winning numbers (such as repeating sequences of winning numbers) and then, to use it to make predictions. However, most online casinos nowadays offer roulette games based on RNG (random number generator), so finding patterns would be impossible as the outcome of every spin is random.

When it comes to playing a roulette game with a physical roulette wheel, however, advantage play is quite different. Players who try to use this technique would typically stand by 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.

How to Increase Player’s Chances of Winning

There are no reliable ways to actually beat the odds when playing roulette and even if such methods exist, they are neither simple nor acceptable by casino standards. Yet, players can increase their chances of winning by following several basic principles that can be applied to both online and brick-and-mortar casinos.

First of all, choosing a good roulette table is essential and obviously, single-zero roulette games are a much better option than double-zero games, which are mostly offered in casinos across the United States. The house edge in American-style roulette is twice as high due to the additional sector on the wheel, the green 00. But picking French or European-style roulette variations is just the first step in learning how to maximize players’ expected value.

Second, players should always base their play around wagers with the lowest possible house edge. Of course, the best bets in roulette are the outside bets, which cover large portions of the wheel and require a single chip to be wagered. These include black/red, even/odd, and low/high, where the advantage of the casino is 2.70% while the player’s odds of winning are the highest. It is true that the payouts are not particularly attractive, but these bets are less risky options in the game.

When choosing a bet, players need to compare the casino odds to the true odds and find the type of bet where these two are as close to each other as possible. Often, the most attractive payouts are offered for bets which the casino pays much less than their actual worth. As a general rule of thumb, players should remember that the less risk they take, the less they can expect to win. All the good payouts, however, come with exceptionally bad odds and require a great tolerance for risk.