The Probabilities of Roulette

In the famous game of roulette, probabilities play a vital role, dictating the destinies of the players present. 

This article explores the subtle world of odds and risks that intersect around the gaming table, revealing the mathematical mysteries that govern this iconic game of chance. 

How do roulette odds and odds calculators work? 

Roulette probabilities are determined by the number of slots on the wheel and the type of bet being made. A standard roulette wheel has 37 or 38 squares numbered from 0 to 36 (and sometimes a double zero). 

Bets can be placed on solid numbers, colors (red or black), sets of numbers, and so on. The probability of winning depends on the number of favorable outcomes in relation to the total number of possible outcomes. 

For example, the probability of winning by betting on a single number is 1 in 37 (or 1 in 38), while betting on a color offers a probability of 18/37 (or 18/38) due to the presence of zero boxes. Players can use these probabilities to establish their playing strategies. 

Roulette probability calculator: Table 

It's possible to manually calculate the probability of winning at roulette using a simple formula called the "roulette expectation". 

This method measures the degree of fairness, enabling you to assess the balance between your chances of winning and the profitability of playing at a specific table. 

To help you, we've decided to offer you two tables summarizing the percentage odds for each type of bet. 

The first table applies to European roulette: 

This second table applies to American roulette: 

The odds of American roulette 

American roulette is distinguished by the addition of an extra square, the double zero (00), in addition to the numbers from 1 to 36 and the zero (0). 

This significantly influences the odds. The classic bets remain unchanged, but the addition of the double zero increases the house advantage. 

The probability of winning by betting on a specific number is 1 in 38. Other bets, such as dozens or columns, are also affected by the addition of the double zero. This alters the odds compared with European roulette, which has a single zero box. 

American roulette presents slightly less favorable odds for players due to the presence of the double zero, which increases the house advantage and influences the way playing strategies should be employed. 

The odds of European roulette 

European roulette is one of the most popular versions of the game, featuring a wheel with a total of 37 squares. These include the numbers 1 to 36 and a single zero (0). 

When a player bets on a full number, the probability of winning is 1 in 37. Bets on colors (red or black), odd/even, or misses (1-18) and passes (19-36) have a probability of 18 out of 37. 

Other bets, such as dozens or columns, also have their own probabilities based on the number of corresponding squares on the wheel, namely 12 out of 37. 

The presence of a single zero gives European roulette slightly more favorable odds for players than American roulette, where there is a double zero. 

It also reduces the house edge. 

The odds of French roulette  

French roulette is similar to European roulette in terms of design, with a wheel of 37 slots in total, comprising the numbers 1 to 36 and a single zero (0). 

However, French roulette is distinguished by certain specific betting rules that can affect the odds. 

When betting on simple odds (such as red/black, even/odd, miss/pass), if the ball lands on zero, the player can benefit from the so-called "en prison" or "la partage" rule. 

In this case, the player loses only half his bet, and the rest is put in jail for the next round. If the next round is a winner, the player recovers his or her stake without any additional winnings. 

Such a rule can influence the odds and slightly reduce the house advantage in certain situations. 

The odds of English roulette 

English roulette generally follows the same basic principles as European roulette, with a 37-slot wheel featuring the numbers 1 to 36 and a single zero (0). The odds of English roulette are therefore similar. 

The types of bets and their probabilities remain the same as those mentioned above, with a probability of 1 in 37 for a bet on a full number and a probability of 18 in 37 for bets on single odds. 

As with French roulette, there may be specific rules at certain tables that can influence the odds, but the basic structure of the game remains linked to the European version. 

In short, English roulette shares broadly the same principles of probability as European roulette. 

Pay attention to the house edge 

The house edge in roulette represents the statistical advantage that the casino holds over the players, ensuring its long-term profitability. 

This advantage derives from the presence of the zero (and sometimes the double zero) on the wheel, creating slightly unfavorable odds for players. 

On a standard European wheel with a zero, the house edge is around 2.70%, while it rises to around 5.26% on an American roulette wheel with a double zero. 

This means that, over the long term, the casino can expect to win a small portion of players' total bets. 

How to profit from the odds 

Taking advantage of the odds in roulette involves a strategic approach and a conscious understanding of the game's randomness. 

For this reason, it may be worth opting for bets with higher payout probabilities, such as single odds, which offer a payout probability of 48.64%. 

This means avoiding bets on full numbers. Although the winnings can be substantial, the probability of winning by betting on a single number is low. 

The choice of variant is also important. We advise you to choose European or French roulette rather than American roulette, as the presence of the double zero in the latter increases the house advantage. 

Although players can use strategies to make the most of the odds, it's essential to understand that roulette is first and foremost a game of chance, and that the house advantage persists no matter how you play.