Roulette Odds and Probability: Charts and Percentages for Different Events

Basics of Roulette Table Odds

Before clicking the spin roulette button, it's a good idea to have basic information about odds and probabilities. Some casino games involve a limited number of outcomes, while others have a theoretically unlimited number of possibilities to choose from. Online slot machines are a good example of the latter. Card and table games fall into the first category. For example, if you are playing blackjack with a single deck, you are playing a game limited to 52 outcomes, as this is the total number of cards in a deck.

The same is true when it comes to roulette. As we will explain in more detail below, there are 37 or 38 numbers on the wheel, depending on the variant you play. That is, the outcome of the game will always be only one of 37 or 38 possibilities. As long as there is a limit to the possibilities and it is known in advance what that limit is, it is possible to calculate what the probability of each occurring is.

Odds on roulette table can, therefore, be calculated in detail for each outcome. The best part about this is that the results will be constant: so, whether you spin the wheel for the first time or the thousandth time, the odds will not change at all. It is important for you to learn and remember this: roulette wheel odds never change, that is, they do not decrease or increase over time. We will explain why this is important below, but for now let's point out that forgetting this fact causes the mistake called “gambler's fallacy”.

The Correlation Between Odds on Roulette and Payouts

We will explain with examples how to calculate probability for roulette wheel numbers, but first let's briefly talk about the difference between odds and payouts, as we will use both of these terms frequently.

• Odds: Shows how likely you are to win any bet in roulette. For example, “green roulette odds” means the probability of pockets of green color on the wheel.
• Payouts: Shows what the payout is for each bet in roulette. For example, a 1:2 payout means that 2 units will be paid for each unit of wager, i.e., if you make a 10 CAD wager and win, you will get a 20 CAD payout. Payouts can be small or large depending on probability.

After this preliminary information, we can start explaining how roulette wheel odds calculations are made. First, let's remember that there are 37 numbers in European roulette and 38 in American roulette: the difference will change the result of the calculations. In other words, American roulette odds are different from European roulette.

In this example, we'll assume you're playing European roulette and placing a straight bet on green to try your luck.

• This simply means that you are betting on only 1 of 37 possibilities.
• This situation can be expressed mathematically as follows: 1/37.
• The result of this math operation is 0.0270.
• We can simply express this as 2.70%.
• So, your chance of winning a straight bet (roulette odds green) in European roulette is 2.70%.

And, for the same reason, this is the highest paying bet in all variants of roulette – 1:35. This is simply because it has the lowest odds in the game. Basically, the payouts increase as probability decreases and decrease as probability increases. So, the lower your chances of winning, the larger the payout becomes.

American and European Roulette Wheel Layouts & Their Probabilities

We know the total number of outcomes on a European roulette wheel: 37. And, how many numbers on a roulette wheel if you are playing the American variant? 38, because of the extra “00” pocket. By dividing these numbers by the total number covered by our bet, we can find out what the odds will be for each variant, and we can do this for any bet type. For example, when you choose the red/black bet (or any bet that pays even money) in European roulette, you bet on a total of 18 numbers. So:

• 18/37
• 0.4864
• 48.64%

But why are American roulette odds different? This version of the game uses the same formula, but having an extra pocket on the wheel changes the results. For example, let's say you place a straight bet again:

• There are 38 numbers on the wheel, so the formula would be 1/38.
• The result of this is 0.0263.
• This is expressed as 2.63%.

Note that the same formula will apply for other bets too, the only difference is that you divide by 38 instead of 37. But this one digit can cause a big difference in terms of odds & probabilities. Generally speaking, the American roulette (double zero roulette variants) always offers lower odds. And, for the same reason, it has a higher house edge – the casino gets more from your bets in the long run.

Detailed Probability Charts & Roulette Bet Percentages

We explained how to calculate the odds of winning roulette, but let’s also share a roulette payout chart with detailed probabilities, so you can understand the correlation between the odds and payouts. The table below includes data for both variants of the game:

So, why do outside bets offer higher odds? As we explained above, this is because they cover more numbers (outcomes). For example, the column and dozen bets involve 12 numbers. Others allow you to cover 18 numbers at once. When playing European roulette, being able to cover 18 of the 37 outcomes naturally increases the chance of winning.

For the same reason, they are also called “safe bets”. This doesn't mean they offer a “guarantee”, of course, but 48.65% is a significant chance of winning and is certainly "safe" compared to others. However, as we mentioned above, as the odds increase, the payout decreases: outside bets pay either 1:2 or 1:1.

Impact of Roulette Variants on Probability

Above we have discussed probability calculations in the two basic variants of the game and helped you understand how they relate to the numbers on roulette wheel. However, roulette is not just about European and American: there are many different variants of this game, and we need to touch on them too. Depending on the features they have (or don't have), the odds on roulette table calculation will vary.

French Roulette

This variant uses the same wheel as European roulette, meaning it is played with a total of 37 numbers. Therefore, its odds do not change: the payout values and probabilities are exactly the same. However, due to the “La Partage” rule, French roulette offers a lower house edge.

Lar Partage is a simple but useful rule: if the player tries his luck on a bet that pays even money (1:1) and loses because the ball stops on 0, he gets half his bet back. So, for example, if you made a wager of 50 CAD, you would get a refund of 25 CAD even if you lost. In the long run, as you will be able to recover more of your losses, the money the casino earns from your bets (house edge) will also decrease. So, although it is no different from European roulette in terms of odds and probabilities, the French variant allows you to get back more of your investment.

Triple Zero

This is an exotic variant and, as the name suggests, it has three house pockets (0 – 00 – casino logo). Therefore, there are a total of 39 numbers on the wheel. It has appeared in US land-based casinos and can also be found in some online casino sites. In terms of odds, it is even worse than American roulette because this time you will have to use the formula we mentioned above with 39 numbers. So, assuming you place a straight bet:

• 1/39
• 0.0256
• 2,56%

Triple zero offers some side bets where the third additional pocket can be used and these can have high payouts, but the payouts for other types of bets are the same. Generally speaking, it is not a recommended variant as it offers an even higher house edge than the American roulette.

Mini Roulette

This is a game designed to be played on the small screens of smartphones and has only 13 numbers on its wheel (0 – 12). Therefore, it has its own completely unique rules and payouts. It is more advantageous in terms of odds, because this time only 13 numbers will have to be considered. So, for example, the straight bet calculation is done like this:

• 1/13
• 0.0769
• 7,69%

A much higher rate than other variants, right? The problem is that payouts have been reduced to offset this. Straight bet pays 1:11, not 1:35. And all other bets pay 1:1 – there is no other option. These values cause the RTP of the game in the long run to be slightly below European roulette (around 96.00%).

Advanced Probability Concepts for Roulette Winnings

Before we talk about advanced probability concepts, we need to talk a little more about the concept of house edge, as we will touch on it often when talking about strategies. Each casino game has a different RTP (return to player) and house edge value. The first determines how much of the money you invest in a game you can get back. The second will determine what profit the casino will make from your bets. For example, let's say you play a game with an RTP of 95.00% and a house edge of 5%, and you deposit a total of 100 CAD.

• After approximately 1,000 rounds, you can earn 95 CAD back (RTP).
• After approximately 1,000 rounds, the casino will earn a profit of 5 CAD from your bets (house edge).

European and American roulette have different RTP – house edge values, because they have different wheel designs and therefore different odds. And sometimes, as in French roulette, special betting rules affect these values even if the odds do not change. Below, you can see the RTP and house edge values of three important variants of roulette:

• European roulette: 97.30% RTP – 2.70% house edge.
• American roulette: 94.74% RTP – 5.26 house edge.
• French roulette: 98.65% RTP - 1.35% house edge.

Don't forget these values because we'll mention them in the section where we talk about strategies. For now, let's note that it is not possible to change the RTP and house edge, that is, increase or decrease them.

The Law of Large Numbers also confirms this. If you run a simulation and complete, say, 5,000 spins, you may find that at certain intervals, some results repeat more frequently than others. So, for example, betting on black may seem like a better option than red. However, it is natural for statistical deviations to appear in large groups of numbers, and these do not mean that there is a "pattern". In the long run, the RTP and house edge percentages will not change in any way.

Strategies Based on Odds on a Roulette Table

There are many strategies developed for roulette, some of which focus on betting management and others on increasing your chances of winning. Martingale, D'Alembert, and Fibonacci are the most well-known strategies developed for bet management: they ask you to increase or decrease the wager amount according to certain rules. For example, you double the wager after each loss. James Bond is the most famous strategy that focus on the chance of winning: at each round, it allows you to cover a total of 25 numbers.

So, do these strategies affect the odds of the game in any way?

The answer is no. Neither strategy changes the RTP and house edge values of roulette. Likewise, they do not decrease or increase your chances of winning a particular bet. In the long run, the casino always wins. However, betting strategies can help you manage your budget more efficiently, and mathematically they have a certain validity: if you play with a large bankroll and do not reach the table limits until a win occurs, they can allow you to make a small profit. However, using a strategy does not guarantee you a win or in any way reduce the edge the casino has on you.

In this regard, the only thing we can say for sure is what the best and worst bets will be according to mathematical odds. Inside bets have lower odds and straight bet is the worst among them. Outside bets have higher odds, and those that pay even money (red/black, odd/even, low/high) are the best ones. But of course, the risk/reward balance must also be taken into account: inside bets will always pay out higher.

Using Probability on a Roulette Strategy Chart

Therefore, it would be best to focus mainly on odds and budget management when determining your strategy. Now you know which bet offers which odds: for most players, focusing on outside bets, specifically even money bets, will be the most ideal option. In this way, and as long as you play European roulette, you can get a 48.64% chance of winning on each spin.

In addition, you should manage your budget wisely, for example by dividing it into groups of ten, aiming to both extend your playing time and place more bets. Let's say you have a budget of 100 CAD: placing a straight bet with all of it to win 35x may seem like an attractive idea, but your chances of winning won't even be 3%. Instead, you can divide that budget into groups of 10 CAD and place even money bets ten times: in the long run, this will be much more effective.

The Importance of Probability on Roulette Numbers

Learning the odds allows you to understand what your chances are of winning each bet and lets you use your money more efficiently. You can see which bet would be a better choice depending on the money you have left and calculate the risk/reward more accurately. In other words, you still have to rely on your luck, but at least you know what your chances will be. Focus on the fun when playing roulette and remember that you cannot change the RTP-house edge values: you should always keep this in mind when deciding on a strategy or playing for casual fun.