Let’s start with the table itself. On a roulette wheel there are either 37 or 38 numbers depending on whether you’re playing American or European Roulette. The numbers range from zero to 36, with a 00 on the American wheel. The American Wheel has an extra edge to the casino so it’s always worth playing European. Additional Rule for American Roulette. Some casinos have the Surrender rule in American Roulette. According to the Surrender rule, a gambler lose only half of the even money bet if the ball stops on 0 or 00. The rule makes the house edge as 2.63% which is much better than the usual 5.26% for American Roulette. A powerful Tracker to find the outliers and biased roulette tables (Fox Roulette can log up to 100,000 numbers for each table) Fox Roulette will keep the numbers you have entered to factor into future probability calculations. After 20,000 entries for a given table Fox Roulette will identify if the wheel is bias.

1. American Roulette Probability Calculator Formula
2. American Roulette Probability Calculator Present Value
3. American Roulette Probability Calculator Cheat
4. American Roulette Probability Calculator Solver

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In any case, such skills require lots of time and knowledge. Alternatively, a player should have a brilliant mind. Not every player is able to calculate the odds of hitting the target. It is not so easy to calculate which the sequence of cards will be on the table. Still, many players believe the theory of probability works and can influence the course of a roulette session. In this article, we are going to consider the main roulette probability problems.

Frankly speaking, it is impossible to predict how the ball will behave in roulette. Intuition and inner voice are the only things that can guide the player. There are no other forces that can help in the struggle against a roulette ball. Why? Everything is rather clear. The player should track and remember each move during the whole session. And if players were able to do this, then casinos would immediately go bankrupt.

Yet, players seek new ways to submit a roulette ball and tame it. Many players calculate odds using the theory of probability. Below, let’s find out whether it is reasonable.

The Concept of Probability in the Game

To begin with, let’s recall what the probability theory is. The notion studies random events. The concept arose as a science from the belief that certain patterns lie at the heart of random mass events. The notion studies these patterns. The probability theory deals with the study of events, the occurrence of which is not known for sure. It allows judging the degree of probability of occurrence of some events in comparison with others.

For example, it is impossible to determine unambiguously the result of getting 'heads' or 'tails' as a result of a coin toss. Yet, with repeated tossing, approximately the same number of 'heads' and 'tails' comes up. It means that the probability that 'heads' or 'tails' drop out is equal to 50%.

A test, in this case, is the implementation of a certain set of conditions. That is, in this case, tossing a coin. The challenge can be played an unlimited number of times. In this case, the complex of conditions includes random factors. An event is the result of the test. The event happens:

• Real (always happens as a result of a test)
• Unreal (never happens)
• Accidental (may or may not happen as a result of the test)

For example, when a coin is tossed, an impossible event is that the coin will be on the edge; a random event is 'heads' or 'tails'. The particular test result is called an atomic event. As a result of the test, only elementary events occur. The collection of all possible, different, specific test outcomes is called the space of elementary events.

Probability is the degree to which an event may occur. When the grounds for some possible event outweigh the opposite grounds, then the event is called probable, otherwise unlikely, or improbable.

The same rule applies to roulette. Many players try to predict the outcome of a roulette spin with the help of the concept. Let's study this point on an example and find out what happens when using the formula. No, we are to calculate the probability of getting 5 simple odds in a row (for instance, 5 BLACK in a row).

Do not forget that a roulette ball lacks any memory. Thus, there are 5 independent events. Divide 18 by 37 to find out the probability of each of them. We get 0.49. Multiply 0.49 five times to find out the probability of a series of 5 BLACK. We get 0.03. As you see, odds are rather small. So, you need to play against such a probability to win. But how to play? Bet on RED five times? Keep in mind that the probability of five RED has no difference. The result will be the same.

Okay, let's wait for a series of four shots on BLACK, and then put on RED. Do not forget that the probability of 5 BLACK in a row is very small. We spin the roulette and finally see 4 BLACK. Now, the moment has come when you need to bet on RED. Yet, the probability of getting RED hasn't changed, as the ball lacks any experience.

Now, I would like to draw a clear analogy. Let’s say you want to pull clothes out of a wardrobe with your eyes closed. Moreover, the wardrobe is directly roulette. There are a lot of clothes in it. Your eyes are shut. When you stick your hand up a pile of clothes, you cannot know which one you will get out.

No matter how hard you try, the chances of finding the desired garment are small. But still, there are few of them. For example, you know the material by touch and perhaps remember the approximate arrangement of things in the wardrobe. Therefore, it can be said that there are certain changes, but they are small.

An interesting fact is the following. Odds in American roulette are estimated at 5.26%. The same indicator is 2.7% in European roulette. The difference is due to the fact that the first one has two Zeros. Actually, roulette is purely a game of luck. The gambler has odds either to win or to lose.

Precise Analysis of a Roulette Session

Let's start with the fact that in the probability theory, the concept of probability is formalized as a numerical characteristic of an event. Recall once again that it is a probabilistic measure that takes a value from 0 to 1. Value 1 corresponds to a reliable/real event. An impossible/unreal event has a probability of 0. If the probability of an event occurring is x, then the probability of its non-occurrence is 1 – x.

Let’s apply the theory to roulette. As a real event, we take the fact that the ball will stop at any number. In other words, the probability that any number will play is 1. In our case, an unreal event means that no numbers have been played. Theoretically, this is possible if the ball flies out of the wheel, or an electronic roulette freezes. Yet, in this case, the casino usually returns bets, and this happens quite rarely.

Since there are 37 numbers on the wheel and each of them can appear with the same probability, the probability of a particular number being drawn is 1/37. One should add the corresponding probabilities to determine the probability that one of several numbers will play. For example, the probability of hitting a split or one of two specific numbers is 2/37. For equal chances, the probability of falling out will be 18/37.

Use the formula 1 - 1/37 to calculate the probability that a specific number won’t play. We get that the probability of not drawing a specific number is 36/37. Still, non-hitting a number means that any of the remaining 36 numbers will play in any case. The probability of this event is just 36/37. As you can see, everything is logical.

American Roulette Probability Calculator Formula

Having calculated roulette probabilities per spin, it is interesting to look further. To calculate the probability of the same number drawing, one should multiply the corresponding probabilities. Thus, the probability that the same specific number will play twice is calculated using the formula (1/37)*(1/37). By analogy, the repetition probability for equal chances is calculated by (18/37)*(18/37). For another repetition, simply add a new multiplier. So, the likelihood of an equal chance for three times is (18/37)*(18/37)*(18/37), etc.

And finally, if the chosen number does not play during the first spin. How to calculate the probability of getting the number on the second, third, etc. spin? No way! The probability is always the same and does not depend on all previous spins. For any number, the probability of falling out is always 1/37. For an equal chance, the indicator is 18/37.

Yet, every one counts and somehow shows that with each next spin the probability of getting a specific number is constantly increasing... Here is the trick — in fact, each roulette probability chart shows the probability with which the required bet will drop out at least once during the specified number of spins.

To calculate this probability, you’re welcome to use a roulette odds calculator. It calculates the probability of not hitting the desired number in a row for a certain number of spins. The opposite of this value will be the required probability. Let’s examine this rule using the following instances.

The first one is the following: find out the probability that a particular number will appear at least once in 5 spins.

• Players’ odds of hitting a number is 1/37 or 0.027;
• The probability of missing a number is 1-1/37 = 36/37;
• The odds of not hitting a specific number 5 times in a row is (36/37) * (36/37) * (36/37) * (36/37) * (36/37) or if shorter than (36/37)^5. Numerically, it will be 0.8719;
• Thus, the probability that a specific number will not play 5 times in a row is 0.8719. The probability that the required number will play at least once in 5 spins is 1-0.8719 = 0.1281.

Let's proceed to another one: calculate the probability that RED will drop out at least once in 5 spins.

• The probability that RED drops out is 18/37 or 0.4864;
• The probability of missing RED is 1-18/37 = 19/37;
• The probability of not hitting of RED 5 times in a row is (19/37)^5 = 0.0357;
• The probability that RED will play at least once in 5 spins is 1-0.0357 = 0.9643;
• The final touch. Ordinary people are not used to dealing with a roulette probability distribution. They easier perceive information in the form of percentages. Therefore, we take the value of 100% as a real event; an impossible event corresponds to 0%. Thus, to convert to percentages, it is enough to multiply the obtained probabilities by 100.

Things to Remember Before Sitting at a Roulette Table

It is worth mentioning that an attempt to find a correct winning combination or strategy for playing roulette always fails. Remember how the story of a successful combination of cards in Pushkin's “Queen of Spades” ended. Try not to repeat such mistakes, and do not hope for a miracle.

With such a strategy, you can only change dispersion. Still, you cannot influence the mathematical expectation. Players spend much time to develop the right working strategy. Yet, keep in mind that the more bets you make, the fewer chances to win at least something in a casino you have. This rule is applied to online casinos as well.

Just think for yourself the following fact. When you visit a casino, all players and the system itself hope to get as much benefit from you as possible. Thus, you are playing the game not only according to the theory of probability and against it. You also compete with the casino itself, which is practically a separate organism. It craves benefits and large profits, which appear only in case of your loss.

If you play in an online casino, then you play against a program that is a set of letters and numbers. Simply put, your main competitor is a code.

A computer is a machine that has no intelligence, even artificial. Yet, players who expect you to fail do have intelligence. Remember that everyone starting from the owner of the casino up to its employees and visitors can’t wait to see your losses. Players should leave as much money as possible there. Then a disappointed player comes back for revenge with another big sum in a pocket. It has always been this way, and it is now.

The machine does not think and does not know how to do this. So, it simply executes commands. In other words, it carries out the programmed line code. No one needs to write any variations or tricky combinations. There is no need to create traps in the program. Simplicity and triviality are important for any computer program.

All computers in the world, no matter what they are (old or new, simple or advanced, for work or home), are equipped with random number generators. It is this generator that is considered the very heart of the computer. These generators are exactly the same. They don't have any trickery.

How to Increase Roulette Winning Odds

Every player dreams of increasing roulette odds of winning. To play roulette, you do not need to have any special knowledge. It all depends on chance. Yet, despite this fact, each player thinks about the way to increase the odds of winning the game. Thus, consider the following points to improve your odds.

• 1. It is worth paying attention to the type of roulette. Each roulette wheel has various odds of winning due to a different number of slots. For example, it is much easier to win in European roulette than in American one. Since European roulette leaves the casino with an advantage of only 2.7%, and American roulette has 5.3%.
• 2. Play on proven systems. Players are divided into 2 types: those who play relying only on their minds, and those who play according to different systems. Surely, it is more profitable to play by systems. But, in this case, choose only approved algorithms. For example, Martingale, Lucky 7, etc.
• 3. Use bonuses. Do not neglect the bonuses that a casino offers. When using them, you also increase your odds of winning. Before playing at any casino, look at a few more options and choose the one in which the wagering coefficient is minimal.
• 4. Bankroll management. If you want to win frequently, you need to follow Bankroll Management. Its essence is as follows: you need to learn how to choose the size of bets so that you can make another 150 to 300 bets with the remaining money. This strategy will help improve the roulette odds payout.

Roulette Strategies that Help to Win

Systems for playing simple roulette odds:

• Martingale strategy
• Anti-Martingale System (Parlay Strategy)
• D’Alembert system
• Anti-D’Alembert algorithm
• Labouchere method
• Anti-Labouchere systems
• Donald's strategy with Nathanson's changes
• Fibonacci strategy

Systems for playing in the main playing field:

• System of two thirds (Law of distribution)
• Biarritz System (Makarov Strategy)
• Counter-Biarritz system

How to Win at Casino Roulette

Is it possible to win at the casino by playing roulette according to the rules of the listed strategies and systems? This is how beginners usually formulate the question, without specifying other important and significant conditions of the game. Thus, roulette odds are explained by many factors.

There is no purely mathematical roulette strategy that would allow the player to completely eliminate losses. Also, no single gambling strategy can affect the mathematical profitability of a game.

In extremely rare cases, and purely due to technical reasons, roulette wheels in certain casinos may deviate from the uniform distribution of the numbers drawn.
This phenomenon is called roulette wheel addiction. Counter-Biarritz system is designed for playing against casinos in which addictive wheel roulette has been identified. Yet, even this strategy, like all others, does not exclude the factor of luck in the game.

Every single launch of the ball is luck. The player constantly runs the risk of both winning and losing. That is why the game is called roulette.

It should be noted that all mathematical systems and strategies for playing roulette were developed by the players themselves. The main idea and advantage of using a certain strategy during the game are that the player can control it and his/her deposit.

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KNOW YOUR ROULETTE ODDS

Roulette odds provide you with the information you need to know how likely you are to win any bet. There are many different bets available on a roulette table, and each one has its own odds. These range from even money bets that pay off nearly half the time, to single number bets that are hard to hit, but which will earn you a lot of money when they do.

Before diving deeper into roulette odds, however, it’s important that you understand the basics of how to play roulette. Before every spin, you will have the opportunity to place as many bets as you like all around the roulette table. Each of these bets covers one or more of the numbered pockets on the roulette wheel, and comes with its own specific odds of winning.

When the croupier spins the ball around the wheel, it will eventually fall into one of these pockets. The number and color of that pocket will determine which bets win on that spin. At this point, the croupier will mark the winning number, losing bets are taken off the table, and roulette payouts are made for the remaining winning bets before the next spin.

AMERICAN VS. EUROPEAN ROULETTE PROBABILITIES

While the American and European games may seem similar at first glance, the two games actually use different roulette wheels. The American wheel has both a zero (0) and a double zero (00) on it, while the European wheel only has the single zero.

This actually makes a major difference to players. European roulette odds are much better for players, because there is one less pocket on the wheel for the ball to fall into. Since both versions offer the same roulette payouts, this means that the odds and house edge are smaller in European roulette.

Some European roulette games offer additional rules that further help the player cut into the house edge. When a casino offers la partage, that means that you will only lose half of an even money bet (meaning bets like odd/even or red/black) if the ball lands on zero.

En prison is a variation of the la partage rule. Rather than getting half of your bet back, the money will instead be put “in prison”. after which you can win it all back If the next spin results in a win for that bet. In either case, these options offer the best odds in roulette, as they cut the house edge roughly in half.

ROULETTE ODDS AND PAYOUTS EXPLAINED

While there are a wide array of roulette bet types to choose from, these options can mainly be divided into two types: inside bets and outside bets. These categories get their names based on where these bets occur on the roulette table layout. Inside bets are placed on the numbers at the center of the table, while outside bets have special betting areas on the outer portion of the board.

Inside Bets

Inside bets tend to have a lower probability of winning, but they offer the biggest roulette payouts. For this reason, they are often the best way to start playing for those who are new to the game, as they give you a chance to earn a big payout on any given spin without having to risk much money on each bet.

Straight: A bet on a single number. If the ball lands on that number, the bet pays 35-1.

Split: A bet on two adjacent numbers on the roulette table. If either of those numbers hits, the bet pays 17-1.

Street: A bet on a row of three numbers on the roulette layout. If any of those numbers wins, your bet pays out at 11-1 odds.

Corner: A bet on a “square” of four numbers on the roulette betting layout. If any of these numbers wins, the bet pays 8-1.

Six Line: A bet on two consecutive rows, covering six numbers in total. If the ball lands on any of those numbers, you’ll win at 5-1 odds.

First Four: This bet is only available on European roulette tables, and covers the zero along with 1, 2, and 3. If any of those four numbers wins, the bet pays 8-1.

Trio: Like a street bet, this bet covers three numbers, but it includes one of the zeros. For instance, a player can make a trio bet covering 0, 1, and 2. If any of those numbers wins, the bet pays 11-1.

Top Line: This bet is only available on American roulette tables and covers five numbers in total: the zero, double zero, 1, 2, and 3. If the ball lands on any of those numbers, your bet pays out at 6-1 odds.

Outside Bets

Outside bets cover large sections of the wheel, giving you a better chance of winning your bet. However, they also come with smaller payouts, and may require higher minimum wagers than inside bets.

Columns: A column bet covers one of the three columns on the roulette table layout, each of which contains 12 numbers. If any of those 12 numbers wins, your bet pays 2-1 odds.

Dozens: These bets cover sets of 12 consecutive numbers: 1-12, 13-24, or 25-36. If a number in the range you bet on wins, the bet pays 2-1.

Odd/Even: These bets cover all of the odd or even numbers on the table (note that zeros do not count as either odd or even). If a matching number wins, then your bet pays out even money.

Red/Black: These bets cover all pockets – 18 each – of that color. If the ball lands on that color, you win at even money odds.

High/Low: These bets cover the range of 1-18 and 19-36. Should the ball land on a number in the range you’ve chosen, the bet pays even money.

Called & Announced Bets

Called and announced bets are roulette bet types that may not be familiar even to many experienced players. These are more frequently seen in European casinos, and they allow players to make bets by announcing them to the croupier. Called bets can be made on credit, while announced bets require a player to actually have the money on the table in order to make them.Typically, such bets are only offered to known players, usually high rollers. In modern roulette, announced bets are far more common than called bets, as most casinos cannot or will not allow their players to wager on credit.

While any bet can be an announced bet, this option is typically only used for complex wagers, most of which are known as the French bets. These bets cover specific portions of the roulette wheel, which takes several chips to accomplish and can be unwieldy to manage on the standard roulette betting layout. Instead, the croupier can manage those bets for players, sometimes by using the “racetrack” layout seen on some European roulette tables.

Common announced bets include:Voisins du Zero: This bet covers 17 numbers using nine chips. Your payout will be determined by the type of bet covering the winning number: 16 chips on the corner bet, 22 on the trio, or 17 chips if one of the splits wins.

Jeu Zero: The “zero game” covers just seven numbers using four chips. If a split wins, the bet will pay out 17 chips. If the number 26 hits, you win 35 chips.

Tiers du Cylindre: This bet covers 12 numbers that lie far away from the zero. It takes six split bets to cover these numbers, and you get a payout of 17 chips if any of them wins.

Orphelins: Made with five chips, this bet has varying payouts. The straight bet on 1 pays 35-1, while the split bets would pay 17-1.

Finals: A final bet covers every number that ends in a specific digit. These are all straight bets paying out at 35-1 odds.

Full Completes: A full complete is a true maximum bet on a single number. These bets involve heavy risks to the player, with the exact payouts depending on what number is hit, various table maximums, and which number is being maxed out.

You can find out more details on each of these on our called bets and announced bets page.

THE BEST ROULETTE BETS FOR YOUR BANKROLL

Our team of experts has years of experience playing roulette, meaning we know all the pro tips and tricks that can help you get the best roulette odds possible. One of the most important things we can share is how to make the best bets possible each time you step up to the roulette table. Here are our favorite bets in roulette:

THE WORST ODDS TO WATCH OUT FOR

While we’re happy to give you tips on how to find the best odds in roulette, the best thing we can do for our players is steer them away from bets that aren’t worth their time. By avoiding the worst of the worst options, you’ll improve your roulette odds and have more fun playing knowing you aren’t getting ripped off.

The biggest example is the Top Line or First Five bet on American roulette tables. While the odds in roulette are very consistent across almost all bets, this particular bet is an exception. This is because payouts in roulette are generally designed to be fair for a wheel with 36 pockets, with the house edge coming from the fact that there are actually 37 (European roulette) or 38 (American roulette) pockets for the ball to fall into.

On an American table, that means that whether you make a straight bet at 35-1 payout, or bet on black at even money, the house edge is 2/38, or 5.26%. However, the Top Line bet covers exactly five numbers (0-00-1-2-3), a number that 36 can’t be evenly divided into. Casinos offer 6-1 on this bet, which would only be a fair bet if there were 35 pockets. The result of this is a house edge of 7.89%, which is much higher than on any other bet.

The Top Line isn’t always the only sucker bet on the table. Generally, it’s best to avoid unusual side bets that may be added to the game, especially in online roulette. As in other casino games, these side bets are almost always added to make more money off players and come with extraordinarily high house edges.

HOW TO IMPROVE YOUR ODDS AT ROULETTE

One of the best ways to improve your odds in roulette is by brushing up on your roulette strategy. While the results of each spin are random, roulette strategies can be used to manage your sessions and get the kinds of results you’re looking for.

For instance, let’s say you want to maximize your chances of booking at least a small win at the end of a session. Your best bet may be the Martingale System, which asks you to place even money bets, doubling your bet amount after a loss. On the other hand, a player looking for a huge payday would be better off trying something like the Guetting System. We cover many of these systems as well as other ways to improve your odds on our roulette strategy page.

The most important thing you can do to maximize your roulette odds is to get some practice in before you try playing for real money. If you’re looking to develop your skills or test a new betting strategy, you’ll want to check out the 80+ free online roulette titles which are available for you to try without risking any money.

PLAY AT THE TOP ONLINE ROULETTE SITES

At this point, you should have a strong knowledge of roulette odds and payouts, which bets you want to seek out, and which to avoid. Armed with this information, you should feel confident about playing roulette for real cash at one of our top-rated casinos.

We only recommend the most trustworthy and reputable online casinos for our readers. Any of the sites in the table below will provide you with a safe and secure place to enjoy playing roulette.

FAQ

🎲 Are roulette odds good?

While roulette odds vary depending on the type of table you are playing at, the odds are generally quite good. That’s especially true when compared to other popular gambling options like slot machines, which normally have much higher house edges.

❤️ What is the best bet in roulette?

American Roulette Probability Calculator Present Value

If you want the best odds in roulette, you’ll want to find a European roulette table where you can take advantage of la partage rules on even money bets. Under those conditions, the house edge is just 1.35%.

🎰 What are the best roulette bet combinations?

There are many different roulette bet combinations that are effective, with the best one depending on your goals at the table. Familiarizing yourself with bet systems can help you determine what works for you, and what doesn’t.

💰 How much is a roulette chip worth?

The most common value for a roulette chip in an American casino is one dollar. However, this amount can vary depending on how much you buy in for at the table. When you purchase your chips, your croupier will set a value that leaves you with a reasonable amount of chips to play with: buy in for $100, and you’ll get dollar chips; start with $10,000 on the table, and each chip might be worth $100 instead.

American Roulette Probability Calculator Cheat

❓ Are roulette tables rigged?

American Roulette Probability Calculator Solver

Generally speaking, roulette tables are fair. Casinos have a mathematical advantage and don’t need to cheat to get roulette odds they are happy with. However, there have been plenty of cases where biased wheels have made some numbers appear more often than others – something that attentive players can take advantage of.