What are your chances of winning at roulette?
Many players may not believe it, but winning at roulette depends on probability. So, in this article, we will look at the chances of winning for each type of bet based on the number of rounds of play. As complicated as it may seem, it is very simple and you will even be able to calculate the chances of success for your bets favorites.
Roulette and probability theory have a lot in common. First of all, they share the same father: the famous mathematician, physicist and philosopher Blaise Pascal. He invented both roulette and probability in the 17th century, which is why these concepts are in every school textbook.
Although probability theory is extremely interesting in itself, today we will focus on its real-life applications. More specifically, we will look at what all players are primarily interested in: the chances of winning. This is essential information if you want to know how to win at roulette.
First of all, it should be noted that all probability calculations are based on European roulette, which has 18 black boxes, 18 red boxes and 1 green box with a zero. We chose this game because it has half the house edge and is therefore much more profitable to play. Although it is rarely found in land-based casinos, all online casinos offering table games have European roulette in their game portfolio.
You need to know the odds of winning for each type of roulette bet as well as their respective payouts.
Complete
Payment
European
American
Red Black
1:1
48.65%
47.37%
Pair/Impair
1:1
48.65%
47.37%
Miss/Pass
1:1
48.65%
47.37%
Dozen
2:1
32.43%
32.58%
Column
2:1
32.43%
31.58%
Sixain
5:1
16.22%
15.79%
Square
8:1
10.81%
10.63%
Transverse square
11:1
8.11%
7.89%
Simple square
17:1
5.41%
5.26%
Full number
35:1
2.70%
2.63%
Each type of bet covers a certain number of boxes. Logically, the more boxes the bet covers, the higher the chances of winning. The probability is simply calculated according to the following formula:
Number of boxes covered / 37 * 100
Statistically, the best bets in roulette are single bets (flush, even x odd, miss x pass) which cover less than half of the game board. The chances of winning in roulette with these bets are 48.65% (18/37*100). Bets on individual numbers are the least secure. They only have a 2.7% (1/37 * 100) chance of winning.
Calculating the probability of winning for consecutive bets
Now that we have already calculated the odds for each individual bet, we can also calculate the odds of winning in a series of games. For this case, the original formula must be modified:
Q – Number of fields covered
N – Number of rounds played
For our simulation of all individual bets, we have chosen a limit of 50 game rounds, which corresponds on average to an hour of play at a table of 4 or 5 players.
The probability of at least one win in 50 consecutive games
In the graph above you can see how the probability of winning an individual bet increases. At this point, it is very important to say that the odds never reach 100% probability.
De plus, si vous êtes assis à une table, les chances de gagner une seule mise dépendent toujours du calcul de probabilité des mises individuelles. Cela signifie que la chance de gagner une mise sur le rouge sera toujours de 48,65%, indépendamment de la précédente. N’oubliez pas que ce calcul suit l’ensemble de la série de jeux.
Vous pouvez le constater clairement dans le célèbre exemple du Monte Carlo en 19137 lorsque le noir est sorti 26 fois d’affilée. La probabilité de ce phénomène est de 0,000000007%. Si nous convertissons ce chiffre en une valeur significative, il s’avère que vous devriez connaître environ 143 millions de séries de 26 jeux pour le revoir, ce qui prendrait environ 10 000 ans de jeu consécutif.
L’un des facteurs critiques qui rendent la roulette si amusante est simplement la quantité de mises avec différents rapports de paiement et probabilités. Comme le savent les joueurs expérimentés, en principe, les paris peuvent être divisés en deux catégories principales : les paris intérieurs et les paris extérieurs. Les paris intérieurs portent sur des numéros simples ou un petit groupe de numéros. Les paris extérieurs portent sur de grands groupes de numéros tels que les paris rouge-noir, haut-bas ou pair-impair.
Ces paris sont répertoriés sur la table et sont assez familiers pour tout le monde. Les plus couramment utilisés sont les soi-disant paris équitables (rouge-noir, haut-bas, pair et impair).
Probability and Payout for Inside and Outside Roulette Bets
Stratégies de roulette pour augmenter vos chances de gagner en 2023 | AnyGamble
Les paris à la roulette et leurs probabilités de gain :
– Red/Black: 1 chance in 48.6%
– Pair/Impair : 1 chance sur 48,6%
– Haut/Bas : 1 chance sur 48,6%
– Douzaine : 2 chances sur 32,4%
– Ligne de pari : 5 chances sur 16,2%
– Square: 8 chances out of 10.8%
– Street: 11 chances out of 8.1%
– Split: 17 chances out of 5.4%
– Full: 35 chances out of 2.7%
This table only includes numbers for European roulette, which is the type of online roulette with a single zero. This variant generally offers better chances of winning. If possible, avoid playing American roulette (double zero).
The Best Bets in Roulette
To win at roulette, you need to know more than probability and payout to find the best roulette bets. The key factor is also what is called the “House Edge” or “expected return” as economists would say. House Edge represents the amount that casinos earn in the long term from a particular game or bet. With this logic, the goal is to find a bet with the lowest House Edge.
Complete
House Edge
Red Black
2.7%
Pair/Impair
2.7%
Miss/Pass
2.7%
Dozen
2.7%
Bet line
2.7%
Square
2.7%
Corner square
2.7%
Transverse
2.7%
Full number
2.7%
As you can see, every roulette bet has the same house edge. This means that in the long run it doesn’t matter which bet you choose to use. Most players bet on even bets because of the almost 50/50 probability.
La plupart des joueurs ne savent pas qu’il existe un sous-type de roulette européenne qui propose des paris encore meilleurs. Sur certaines roulettes françaises, il y a deux règles spécifiques :
En Prison house edge – 1,35%
La Partage house edge – 1,35%
En Prison et La Partage sont les meilleurs paris à la roulette. Il n’y a pas d’autre combinaison ou de pari unique avec de meilleures chances.
En Prison and La Partage Bet Explained
La Partage and En Prison bets are the most popular bets in roulette. But it is not easy to find them. Both bets have one thing in common. They only apply to even bets (red/black, even/odd, high/low). Let’s start first with the La Partage rule.
La Partage is a French word that means “to share or divide.” Every time a ball lands on zero, all even bets are split in half. The first half goes to the casino and the other half goes to the player.
En Prison means “in prison,” and the rule works in a similar way. Each time a ball lands on zero, all active bets are marked and kept on the table. If the second roulette spin wins the original bet, the entire amount goes to the player.
What is the best roulette strategy?
Betting strategies are very popular among roulette players. And not just among gamers. Many mathematicians and enthusiasts try to invent new systems. In the past, there was also very often software designed to predict online roulette results. Which was, of course, absurd.
One of the first and best roulette strategies is the Martingale strategy. The Martingale system is very simple.
You choose the Base Bet
You bet on what are called outside bets (red or black, even or odd, high or low)
After each losing hand, you double the previous bet
After each game won, you return to the Base Bet
Let’s take an example.
Let’s say the Base Bet is €5. So, in the first round, we bet €5 and lose. In the second round, the stake is doubled, or €10. We also lose this round. In the third round, the stake is already €20. We win the third round. In the fourth round, the stake is again €5.
And where is the profit? Let’s look at the numbers from our example. A gaming session in the best Martingale roulette system begins in the first round with the Base Bet and ends with the last win.
First round bet – bet €5, win 0
Second round bet – bet €10, win 0
Third round bet – bet €20, win €40
In total, we bet €35 for the game session and won €40. We therefore have a profit of €5. It turns out that for each gaming session, the player makes a profit equal to the Base Bet.
Problem with the Martingale system
Sounds like the best roulette strategy, doesn’t it? However, the problem comes with the maximum bet amount. Even if you start with a relatively small stake, a series of losses can quickly bring you to that limit. And once you can no longer afford to double your bet, this whole roulette strategy falls apart.
Nous traitons du sujet des systèmes de mise dans l’article Top 10 des systèmes de mise à la roulette. De plus, nous avons publié une série d’articles analysant les stratégies de mise à la roulette. Vous pouvez trouver la liste complète dans notre catégorie Testing Roulette Systems.
Biased Roulette is another chance how to win at roulette
Comme son nom l’indique, une roulette biaisée produit des résultats différents de ce que prévoit la théorie des probabilités. Cela peut se produire de deux manières. Soit la roue est déjà défectueuse lors de sa fabrication, ce qui entraîne des résultats non aléatoires, soit la roulette s’use pendant le jeu au point que ces dommages la rendent biaisée.
These days, misaligned or damaged casters are uncommon. This may be the only way to legally beat roulette. Casinos are well aware of this and regularly examine and maintain new and used machines. However, it is possible to encounter a distorted roulette wheel in some of the smaller casinos where roulette inspections are not really on the agenda.
Another reason why you will rarely encounter a warped roulette wheel in today’s casinos is the way it is made. In the past, casters were most often made of wood and laminate, materials more likely to warp over time. Today’s casters are increasingly made of metal. However, even on these there are still parts that can be damaged.
How to recognize and use a biased roulette wheel
Finding a game that gives you an edge over the casino can be harder than it seems. After all, if the roulette is too damaged and after a few dozen spins it is visible that the results are not random, the owner of the roulette will notice this very quickly and simply replace the wheel or the entire table.
However, given the low house edge in roulette, even a small imperfection is enough to make the bettor win in the long run. However, the smaller the flaw in the roulette, the more difficult it will be to detect. It may take days or weeks in this case.
Tracking down such a roulette wheel is quite tedious. First of all, it is necessary to observe and write down the fallen numbers. Here, the more numbers you get, the better. We would like to remind you that there is no need to save. You certainly won’t be able to tell a biased roulette wheel from a dozen spins. Here, observation may involve several hundred or thousands of rounds. However, once you have established that the numbers fall in a particular sector more often than the odds indicate, it is time to bet on them.
Famous cases of biased roulettes from the past
A more obscure case where a player took advantage of an imperfection on a roulette wheel and won a larger sum of money is, strangely, even a first time. This happened in 1873 at the Monte Carlo Casino, where Joseph Jagger managed to win 65,000 pounds sterling at roulette. Allowing for inflation, that sum would be around £3 million today. Perhaps no one has won this amount of money at roulette in modern times.
Joseph Jagger, often called the Man Who Broke the Bank in Monte Carlo, noticed that some roulette cylinders were slightly damaged or had a misaligned spindle. So he hired several people to monitor all the roulette tables in a selected casino and note the results. After a few days, he was able to find the roulette wheel biased and Jagger started cashing out.
However, the casino soon discovered his trick and began changing the roulette reels. Jagger lost some of his money, but when he realized that his advantage was irretrievably lost, he left Monte Carlo with the rest of his winnings.
Another case occurred more than a century later when Spanish entrepreneur Gonzalo Garcia-Pelayo discovered a deviated roulette wheel at the Madrid Casino and managed to win more than a million euros with it.
The Most Famous Cheaters in Roulette
Since the beginning of gambling, people have tried to cheat in these games. That’s why we present to you the best roulette scams and cheats throughout history. Every player wants to know how to win roulette legally, but these guys are so determined that they decided to break the law.
Roulette is one of the most popular gambling games today and in history. According to some sources, it was created by the famous mathematician Blaise Pascal, who tried to invent a device called Perpetuum Mobile. Whether this is true is not yet confirmed, but it’s a cute story. Pascal himself is also the father of probability theory, which he defined when he tried to help a player beat a game similar to today’s dice.
Regardless, the first mention of roulette dates back to the 17th century. At this time, the first roulette betting system – Martingale – was created. It is the Martingale that could be considered a precursor to attempts to beat roulette. And it certainly wasn’t the last.
The Man Who Broke the Bank in Monte Carlo
Joseph Jagger was a British textile businessman. Until 1871, it had nothing special. But then he had the idea that some roulette wheels might be slightly deviated from the axis and lean sideways. Let’s not forget that at that time, production was not as perfect as it is today.
Jagger decided to test his theory and went to the famous Monte Carlo, where he studied the local roulette table for more than a month. After analyzing thousands of games, he was able to see that the roulette wheel was indeed tilted and that the ball fell more often in the chosen places than the probability indicated. Jagger reportedly earned over two million francs, which would be equivalent to around £7.5 million at the current exchange rate.
He used the money to purchase real estate for himself and his family members, and in 1892 he died of diabetes. He is also often nicknamed « the man who ruined the bank of Monte Carlo. »
Pierre Dugal and Biased Roulette
In the 18th century, Pierre Dugal also exploited the construction errors of roulette. A better expression would be “caused”. Dugal was a gifted carpenter who hid in a casino bathroom and waited. Once all the employees had left, he would take the tools and adjust the roulette wheel so that the ball fell often in the selected sector. Then he and his wife would return to the casino and win big.
But everything doesn’t always end well. Dugal’s wife discovered his belongings and reported her husband to the police. He went to prison for a while, then after his release he found a new wife.
Dugal repeated the same roulette scam three more times. Each time with another woman, each time unfaithful and he always ended up in prison. His last stay in a detention center was also the last for Dugal.
Cheating in Roulette with Mobile
Enough of scams with rigged roulettes. Now let’s look at the more recent case, specifically 2004. Two men and a woman entered the Ritz casino in London and headed straight for the roulette wheel. That same evening, the three walked away with £100,000. They returned the next day and won an incredible £2.1 million. As such winnings are not common in roulette, the casino called the police, who then arrested the group.
Investigators said the gang successfully put into practice the theory known as « area targeting. » Players were able to use a laser to capture the entry point of the ball into the roulette wheel. Then, they use the laser to measure its speed and finally, use specialized software on cell phones to estimate its decreasing orbit. Just out of curiosity, similar software is also used in the analysis of objects descending into the atmosphere.
But the story didn’t end there. Due to the imprecise wording of the law, these cheaters were never charged with fraud. Their device did not affect the roulette or its elements. And 18th-century British law did not directly prohibit the use of lasers and predictive software. In conclusion, the case is 15 years old and something like this wouldn’t work today, simply because casinos use cell signal jammers.
The Big Cigarette Scam
We’re going to stick with high-tech gear for a while. In 1973, Monique Laurent became the face of this roulette fraud. Along with her husband and brother, they managed to cheat the Deauville Casino in France out of more than $1 million. In just a week.
At the time, Laurent’s brother worked as a roulette dealer in the casino and since the beginning of his career, he wondered how to beat roulette. Eventually, he and his step sister came up with a near-perfect plan. They implanted a radio receiver in a ball and hid a transmitter in a cigarette box. Once the device was activated, the modified ball would end up in a six-digit sector. While her husband was betting, Monique controlled the device in the cigarette box.
All the action was revealed by accident. The attractive Monique caught the attention of the casino owner and he started propositioning her. For obvious reasons, Monique stubbornly refused these proposals. The owner noticed that Monique herself practically did not play, but on the contrary, often moved suspiciously at a very losing roulette.
The casino eventually had to hire detectives to reveal the details of this roulette-specific cheating. Monique herself was not imprisoned for fraud.
How Magnets Beat Roulette
This incident occurred in 2003 in Austria. According to all reports, the roulette fraudsters consisted of four Germans and one Austrian. The gang won tens of thousands of euros in a casino in Vienna, thanks to the fact that they managed to get a specially modified ball with a magnet from the roulette table.
According to police, this group of five people created an electromagnetic field using a remote electronic device, probably a watch. The ball then fell in a specific sector. The unknown scammers did not win every game, but they managed to take around €200,000 from the casino.
It is interesting how the casino discovered their roulette fraud. When the dealer picked up the ball, it stuck to the metal button on his jacket. After the incident, the group quickly left the casino and did not appear again. All that remains is the mystery of how they managed to modify the ball.
Richard Marcus and his Quick Hands
Richard Marcus is probably the most famous casino cheater of all time. He operated with his group in the United States for over 20 years and earned millions of dollars.
Marcus seemed to have a feel for the game since his youth. He moved to Sin City from New York in 1976 with $30,000 won at the races. However, he soon lost all his money. Marcus then lived as a homeless person for a time and got a job as a dealer at a casino.
While he was dealing the cards, a certain Joe Classon approached him and suggested that they cheat together at the casino. Using a pre-shuffled deck of cards, they won over $20,000. It was also Classon who introduced him to the technique of late placement of tokens.
The trick was that Marcus always placed a few low value chips and placed a high value chip at the very bottom of the pile. If the bet won, it left a high chip on the table. If, on the other hand, the situation was losing, Marcus discreetly removed the token from the bottom of the pile. In this way he operated with his group for more than 20 years until 1999, when he decided to retire and write his memoirs.
