These are the values that need to be calculated:

• Since there are 37 spaces, the probability of a ball landing on one of them is 1/37.
• There are 18 red spaces 18, so the chance of a ball landing on a red is 18/37.
• The black or green spaces equal 20, so the probability that the ball will not land on red is 20/37.

If you bet 1€ on red, and the ball lands on red, you will win it back, and the amount is doubled, so you profit 1€. If you bet 2€ on red, but the ball lands on green or black, you will lose your bet (-2).

Here, ”A” is used as the variable for the calculation to represent your winnings in roulette from red that takes the value of 2€. The probability is 18/37 and will take the -2 value with 20/37 probability. Here is how you should do the roulette probability formula:

P(Red) x A (value for red) + P(Not red) x A (value that is not red) = 18/37 + 2 + 20/37x (-1) = 0.4865.

Russian Roulette Probability Calculator

Interpreting the results of the probability roulette calculator:

You must remember that the expected value’s meaning is used to interpret the results. The value you can expect is like the average measurement. It is an indication of what will happen each time you bet 2€.

Even if you win multiple times consecutively, you will averagely lose 5 cents in the long run while you play. The house advantage comes from the 0 and 00. This is a very small advantage, making it hard to detect, but the house will always win at the end of your game.

You must know that the true odds represent the probability of roulette outcome, rather than the possibility. However, the casino is not going to pay out winnings based on true odds. The winning bets are paid using the 1:35 odds, and the even money wagers have a 1:1 payout. This is because of that one zero pocket.

What is the Probability of Winning at a Roulette Wheel?

These bets are quite different, and they are exclusive to French/European roulette only. The numbers in this wheel are combined based on the roulette wheel’s position instead of the table. There are two kinds – fixed and variable.

Zero’s neighbours – These are bets that cover 17 numbers, and all of those are near green zero. You would have to put at least nine chips so that all those numbers are covered, and you will have winning odds of 45.9%. There is no fixed payout, and it can be as high as 24:1, which depends on the number that wins. This is also called “the grand series.”

Wheel thirds – These are the 12 numbers that are directly situated from across neighbours of Zero. This has a probability of 32.4%, with a payout that is set at 17:1. This is quite like dozen/column bets when it comes to the odd terms and payout.

Zero Game – This is a smaller version of neighbours of Zero. It covers only seven numbers that are closest to slot green zero. There is an 18.9% bet winning odds here, and the payout could be up to 26:1.

The Orphans – The bet that covers the remaining numbers that were not yet mentioned. There is a 21.6% chance of winning this bet, and payouts can be 35:1 or 17:1.

These are fixed call bets. Your variables here are the neighbours where you will place bets on five neighbouring numbers, and your winnings are at 13.5%. The remaining variable is called the ‘finals’ where your bet is on the last digit. Based on the numbers, there is an 8.1% and 10.8% probability.

The European table only contains one zero, and this is a big difference to players. European roulette odds have better odds since there is only one pocket that could make the round fail. That also means there is a smaller house edge in a European roulette compared to American roulette that has 0 and 00.

Roulette Probability Example

Some roulette games in Europe have more rules that are more helpful to the player in beating the house edge. If a casino is offering a la partage, that means you are only using half of your even money bet in case the ball lands in zero. The probability of winning a roulette wheel cannot really be predicted because the previous sequences do not impact the current one.

What is the Highest Roulette Odds Probability?

You only have one chance of winning and 37 ways of losing the bet. That means your probabilities in roulette odds are 37 to one, and this makes it a thrill. Calculate odds with roulette odds calculator online.

In order to understand this in terms of money, you must realize that the winner’s payoff is not 36:1 roulette odds because it will be a fair game. It is rather 35:1. The casino will short you out by two units because the casino will not make a profit if it pays odds fairly. Thirty-six will be divided into two and times 100 to reveal a house edge of 5.26%. Hence, roulette odds do not reflect actual roulette payouts. If you check a roulette probability chart, you will see the probability for each set of numbers.

Odds for Success:

Roulette Wheel Probability

–Even, odd, black, red, 1-18, and 19-36 all have a probability of 48.6% if the payout is 1:1.

–1-12, 13-24, and 25-36 have a probability of 32.4% if the payout is 2:1.

–Single number with a payout of 35:1 have a probability of 2.7%.

–Two numbers with a 17:1 payout have a 5.4% probability.

–Three-number combo with an 11:1 payout has an 8.1% probability.

–Four-number combo with an 8:1 payout has a 10.8% probability.

–Six-number combo with a 5:1 payout has a probability of 16.2%.

You can use these statistics when you try the roulette wheel probability calculator, but it does not guarantee anything.

How to Use Probability When Playing Roulette?

You can beat roulette by improving the probability of your odds. Roulette is famous for being a tricky game, and that is because of the huge house edge it has. There is no solution to how you can win roulette each time it spins. However, if you want to maximize your winning potential, you would have to use the odds wisely. Even if it is really based on luck, you can do a couple of things to increase your chances of winning a nice payout.

You must know your odds

The odds that are placed in bets vary greatly, so if you want to maximize your bankroll, you need to know your odds.

If you use a probability roulette wheel in a game, you can find out if you can beat the math in your game.

A system could combine the playing and money management strategy. If you have enough bankroll, you can increase your chance of winning by doubling your bet after each loss, and you will not reach the table limit, which you can easily do. However, this is not really a guarantee.

Whatever your strategy is, they could suffer in the same way. Assuming all wheel numbers have the same probability, which means there is no bias. The math would mean the casino always wins. The system might look great, and it works short term, but if it lands on a number you did not bet on, you are going to lose. The casino will move to winning with a house edge of 2.7% or 5.26%.

There are systems that involve betting on a lot of numbers, like 20. If this is the case, you will win more often because you are betting on most of the numbers. However, if none of them turn up, you will lose all bets. This could wipe out your wins.

What is the Probability of Red in Roulette?

If the ball lands on red, you win 1€. Then, the next step is to bet 1€ on black. Always change the colour when you win. If it’s black, you will lose the first 1€. Then bet 2€ on red. If you lose, you stay in red and double your bet until you win. For instance, losing 1€, you must bet 2€ on red; if you lose again, bet 4€; another loss, bet 8€ on red. When you win, change to black and bet 1€.

If zero comes up, which rarely happens, you lose your 1€. Then, bet 2€ on red again, and keep doing this until you win before you can change colour.

There are 37 numbers on the wheel. There are 18 blacks and 18 reds. Therefore, the winning odds of red are 18/37, which is 0.4865. The odds of black are the same. The same goes for any “even chance” bet that includes highs and lows, and evens and odds. The odds are not changing, no matter how many times red or black have appeared in a row. Consider your loss when you bet on black. What you do not realize is that the odds of red or black coming up is not affected by any sequence. This is the case in all losing roulette online game.

The calculation is very simple. There are no changes except for the amount that you made a bet on. You are either lucky, and you could win back what you lost, or lose it all. The casino owner does not care if you win because they know there is always a loser in every win. If you think about it, there are more losses than wins.

What is the Probability of Black in Roulette?

Since each spin is a new event, black can come up with the same probability as red anytime during the play, no matter how many times each colour wins. Particularly with European roulette where there are 18 blacks, 18 reds, one zero.American roulette has two zeros, which is not good for your winning chances. Hence, the probability of black is 18/37 = 0.4765 or 48.65%.

Black and red have the same probability, which seems paradoxical, and it is expected that the colour changes fast. It could be from a probability point that it is senseless to assume the colour that has not won for a long time could most likely appear now.

American vs. European Roulette

Anyone who is trying to figure out the difference between American and European roulette must understand the double and single zeros, watch roulette rules in 6 min video. The American version has double zeros. In the European roulette, the croupier spins the reel with 37 pockets, and the small ball falls into one when the spinning stops. Any number on the wheel has an odds of 35/1, and if you succeed, you earn your bet back. That means the house edge is 2.7% and the RTP rate is 97.3%

The American roulette wheel is the same, but it has an extra pocket – double zero. The same principle is applicable when you bet on a pocket the ball falls into, and each number has an odds of 35/1. Your stake is given back to you if your bet succeeds. However, even if the odds are the same, your chance of succeeding becomes less because of the extra pocket. Hence, the house edge is 5.26%, and the RTP is 94.74%. Therefore, you have a bigger chance of winning if you play European roulette.

The House Edge Difference

Even if there is only a subtle difference, and it may look irrelevant, it has a huge impact on how your games will turn out.

When there are lower odds, there are bigger payouts. However, as logical as it may be, it is not the same with American roulette. Even if the odds are lower, if you bet on a winning number, you will also get paid 35:1, which is the same in European roulette.

The Return to Player (RTP) Percentage

In roulette, it is essential to take note that this is theoretical because it is based on what is returned to a player on hundreds of spins, and all kinds of bets are available.

You could get great results by just spinning a few lucky spins, or you might not win at all. Players who focus on making Even Money bets such as Black or Red receive more winning bets compared to players who just choose their favourites. However, the odds are only suggesting that.

If you want to consistently win in roulette, you must not base your chances on the sequences and patterns. It is sensible to see 1,2,3 spinning patterns, but that is not different from 31,8,15 spinning. The betting progression does not change except for the amount. You can only beat roulette if you can change the winning odds. You must also take note of the differences between American and European roulette because it can greatly affect your winning chances. Therefore, it is important to know how the Roulette probability calculator works.

Roulette wheel has 37 fields (American one – 38). So, the probability of hitting one of them is 1/37 or 2.7%.

Drinking Roulette Questions

Your winning probability may vary depending on your chosen bet type. If you would decide to pick only one number then you would have 2.7% chance of winning. However, if you would go for a Red/Black bet then you would have a 48.6% chance of winning and so on.

If you would go for Even/Odd, Red/Black or Low/High bets then a probability of hitting is – 48.6%, Column and Dozen bets has a 32.4% probability of winning and a bet on a Single Number has a 2.7% chance of winning.

American roulette has 38 fields instead of 37 (additional 00). As a result, your chances of winning become lower.

Roulette is a game of luck after all and in the end casino will win. Always be aware and gamble only with money you can afford to lose.

Red/Black, Even/Odd and Low/High bets has a highest chance of winning – 48.6%.

A bet on a single number has the lowest chance of winning – 2.7%. However, it has the highest payout – 35 to 1.

Roulette is one of oldest casino games and its origins could easily be traced to more than a millennium ago when various simplified versions of it 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 in order to improve their play and their chances of winning and that is the odds and the casino advantage that is built-in in every roulette game.

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Knowing the odds is essential in playing roulette or any other game of chance where 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 to win or lose any given bet is. 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 around the roulette table.

Probability and True Odds

Often, the terms “probability” and “odds” can be confused by even professional casino players. Although they are, indeed, very similar in terms of 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 of the numbers 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

The probability is the likelihood of any given outcome compared to all outcomes that are possible. Expressed as a number, the probability always exists between 0 and 1 – 0 would indicate that something is impossible to occur, while 1 would mean 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 the single-zero roulette wheel where for each number, there is only 1 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%.

Blackjack Probability Questions

True Odds in Roulette

Now that we have established what probability is and how it is determined in roulette, we can compare it 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. 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, when it comes to expressing the odds of a particular bet in roulette, they would be 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. In percentages, the probability would be 18/37 = 0.48648648648, 48.65%.

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. 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 1 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.

Casino Odds Additional TipsIn reality, this does not happen, however, and the house gives a slightly lower payout of 35:1 on winning straight-up bets. The idea is that on every winning wager, players pay a small fee to the casino and in this case, it is one unit. The difference does not seem significant but it is how casinos gain their advantage over players – by paying every winner just slightly less than they should have. Over time, this tiny difference makes a large profit for the house and provides a guaranteed income in any possible scenario.

These payouts offered by casinos are sometimes referred to as “casino odds” due to their visible similarity. And while both are expressed as ratios of two numbers, they are never equal – the odds against winning are always slightly higher than the casino odds. The closer the casino odds get to the true odds of any given bet, the lower the advantage of the casino.

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, to multiply that by the probability of success. So, the formula will look like this:

Probability Roulette Wheel Math

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

When we substitute with the numbers we have already used for the straight bet, we get – (36/1 – 35/1) x 1/37 = 1×1/37 = 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.

Roulette House Edge Additional TipsWhat this means for the players is that they can expect to lose 2.70% of their wager when playing a single-zero roulette. For every $100 they bet, they would lose on $2.70 on average. 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 win or lose its entire value. But we cannot win the bet and lose $2.70 at the same time.

So, the house edge can only get closer to reality with hundreds or even hundreds of thousands spins of the roulette wheel. It is a theoretical concept and while this may sound too vague to players, it is a good indicator of how much money they can expect to lose over time. Of course, they might win hundreds of dollars by the end of one gaming session or lose hundreds more in the next one. Still, they are less likely to lose their bankroll if they stick to specific games and bets where the casino has the lowest advantage.

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 is random and based on probability. The house edge, therefore, also remains the same almost as a proof for 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 fool-proof way to win, another type of strategies comes with 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 it is just by a little, it should be enough to 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 and 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 much more 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.

Advantage Play Additional TipsThis method was mostly used in the past when casinos did not have such strict maintenance rules and protocols, while the wheels and other gaming equipment were manufactured in a manner that today would be deemed unacceptable. Players who wish to turn the odds in their favor these days need to be extremely discreet if they plan to observe the wheels before the casino 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 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 the 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 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.