Once players have become acquainted with the different types of bets they can place in roulette, they can turn their attention to the mathematical side of the game. Many casual players ignore this aspect of roulette. However, prior to placing real-money wagers, it is advisable to gain a better idea of the odds and probabilities of winning with the various types of bets. This will enable players to balance the risks against their potential profits and help them implement a suitable betting strategy to minimise their losses.
Many inexperienced roulette players fail to make a distinction between the concepts of odds and probabilities. Yet, there is a clear difference. Read on to gain a better understanding of what the two terms mean and how you can calculate both the odds and the probabilities of winning with each type of bet in roulette.
What Does the Term “Probability” Mean?
Generally speaking, the term “probability” can be defined as the likelihood that a specific event or outcome will occur. In casino games such as roulette, however, the term denotes the likelihood that a given number will come up. When the concept of probability is applied to roulette, it is expressed as “1 out of 37”, for example, or written as 1/37, which means the same thing.
When the probability is expressed as a fraction, the first number stands for the number of ways a given event can occur. The second number, 37 in our example, represents the overall number of possible outcomes. In European roulette, all 37 numbers have an equal chance of appearing. For every straight-up bet, there are two possible outcomes – the player either wins or loses. Thus, in this instance, 1 represents the number of ways to win with a straight-up bet, while 37 stands for the total number of possible outcomes.
The concept of probability can best be explained with a coin-flip example. Ask yourself what the probability is of tails appearing the next time you flip the coin. There are only two possible outcomes of a coin flip – either heads or tails will come up.
In this instance, we are betting that tails will appear, so the probability can be expressed as 1 out of 2, 1 to 2, 1:2 or 1/2. To convert the probability of tails appearing into a percentage, one needs to divide the first number of the fraction by the second. This gives the following result: 1/2 = 0.50 × 100 = 50%. Bear in mind that the total number of outcomes includes both the ways to win and the ways to lose.
Calculating Probability in Roulette
Naturally, this principle can be applied to the game of roulette as well. Let us assume we are playing the European variation of the game, where there are 36 numbered pockets on the wheel plus a single-zero pocket. This makes a total of 37 possible outcomes on any given spin of the wheel. You want to place a straight-up bet on an individual number – number 16, for example. But before you place your wager, you want to figure out the probability of number 16 appearing on the next spin.
A seasoned gambler would say the probability of 16 winning is 1 to 37. Indeed it is, but we want to convert it to a percentage. We divide the number of ways to win by the number of all possible outcomes and obtain the following: 1/37 = 0.0270. Then we multiply the decimal by 100 and the result is: 0.0270 × 100 = 2.70. It turns out the probability of winning with a straight-up bet on number 16 is 2.70%.
The same formula can be used to calculate the probability of winning for all roulette bets. Let us provide another example with an even-money bet. Assume you want to place an even-money bet on Red. As we know, there are 18 red and 18 black pockets on the wheel, plus the single-zero pocket. This means 18 ways to win out of 37 possible outcomes. The calculation is as follows: 18/37 = 0.4864 × 100 = 48.64%. Many inexperienced players wrongly assume they have equal chances of winning and losing with even-money bets, but apparently this is not so. The reason lies in the single-zero pocket, which gives the house its edge.
Let us finish with one last example and assume you wish to place a corner bet covering numbers 7, 8, 10 and 11. This way, you will have 4 ways to win out of 37 possible outcomes. The calculation in this case will be: 4/37 = 0.1081 × 100 = 10.81%. Not too shabby, especially compared with your chances of winning a straight-up bet.
| European Roulette House Edge and Payout | |||
|---|---|---|---|
| Bet Type | Bet Payout | Bet Probability | House Edge |
| Straight | 35/1 | 2.70% | 2.70% |
| Split | 17/1 | 5.41% | 2.70% |
| Street | 11/1 | 8.11% | 2.70% |
| Square or Corner | 8/1 | 10.81% | 2.70% |
| Six Line | 5/1 | 16.2% | 2.70% |
| Column | 2/1 | 32.4% | 2.70% |
| Dozen | 2/1 | 32.4% | 2.70% |
| Red / Black | 1/1 | 48.64% | 2.70% |
| Odd / Even | 1/1 | 48.64% | 2.70% |
| High / Low | 1/1 | 48.64% | 2.70% |
| American Roulette House Edge and Payout | |||
|---|---|---|---|
| Bet Type | Bet Payout | Bet Probability | House Edge |
| Straight | 35/1 | 2.63% | 5.26% |
| Split | 17/1 | 5.26% | 5.26% |
| Street | 11/1 | 7.89% | 5.26% |
| Square or Corner | 8/1 | 10.53% | 5.26% |
| Five Line | 6/1 | 13.16% | 7.89% |
| Six Line | 5/1 | 15.79% | 5.26% |
| Column | 2/1 | 31.58% | 5.26% |
| Dozen | 2/1 | 31.58% | 5.26% |
| Red / Black | 1/1 | 46.37% | 5.26% |
| Odd / Even | 1/1 | 46.37% | 5.26% |
| High / Low | 1/1 | 46.37% | 5.26% |
| French Roulette House Edge and Payout * | |||
|---|---|---|---|
| Bet Type | Bet Payout | Bet Probability | House Edge |
| Straight | 35/1 | 2.70% | 2.70% |
| Split | 17/1 | 5.41% | 2.70% |
| Street | 11/1 | 8.11% | 2.70% |
| Trio (0,1,2 / 0,2,3) | 11/1 | 8.11% | 2.70% |
| Four-Number (0,1,2,3) | 8/1 | 10.81% | 2.70% |
| Square or Corner | 8/1 | 10.81% | 2.70% |
| Six Line | 5/1 | 16.2% | 2.70% |
| Column | 2/1 | 32.4% | 2.70% |
| Dozen (P12, M12, D12) | 2/1 | 32.4% | 2.70% |
| Red / Black | 1/1 | 48.64% | 2.70% |
| Impair (Odd) / Pair (Even) | 1/1 | 48.64% | 2.70% |
| Manque (Low) / Passe (High) | 1/1 | 48.64% | 2.70% |
* In French roulette, when even-money bets are placed and the ball ends up in the zero pocket, only half of the bet is returned to the player. This is known as the “half-back” or “en prison” rule and reduces the house edge for even-money bets to 1.35%.
Odds and Probabilities
Low Limits Roulette
High Stakes Roulette
American Roulette
European Roulette
What Does the Term “Odds” Mean?
Casual players often assume “odds” and “probabilities” are interchangeable terms. They are not. The term “odds” refers to the likelihood of a specific outcome occurring compared with the likelihood of the same outcome not occurring.
Similar to probabilities, odds can also be expressed as two numbers in a specific ratio. In this case, the first number stands for the expected frequency of a given outcome, while the second represents the number of remaining possible outcomes and excludes the chosen event.
Let us now return to our coin-flip example. This time, you decide to bet on heads, and tails is the only other option. The odds of heads appearing the next time you flip the coin can be expressed as 1 to 1, 1:1 or 1/1. One important thing to remember is that probabilities can be expressed as both percentages and ratios, whereas odds are expressed only as ratios.
Calculating the Odds
Now, let us return to the game of European roulette. You are still considering placing a straight-up bet on the number 16 and are wondering what the odds are of this particular number showing up when the ball loses momentum and comes to a stop.
With straight-up bets there is only 1 way to win and 36 ways to lose. So, the odds of your number appearing can be expressed as 1 to 36 or 1:36. It is worth mentioning that the odds can be represented in reverse, for example, 36:1, which some find confusing. Nevertheless, the ratio still indicates there are 36 ways to lose with a straight-up bet and only one way to win. Similarly, the odds of winning with an even-money bet are represented by the ratio 18:19, while the odds of losing can be shown as 19:18.
It is important to note that these are the true odds, representing the actual likelihood of winning or losing with your bets in roulette. However, the casino will not pay your winnings on the basis of the true odds. Winning straight-up bets are paid at odds of 1:35, while even-money wagers are paid at odds of 1:1, even though players’ chances of winning and losing are not 100% equal because of the single-zero pocket on the European roulette wheel. To calculate the house edge, players can divide the number of ways to win by the overall number of possible outcomes. In this case the result will be: 1/37 = 0.0270 × 100 = 2.70%.
In European roulette, the house gains one unit of profit, while in American roulette, where there are 38 pockets, the casino collects two units of profit per winning straight-up bet.
True Odds and House Odds
The calculations we have already made help gambling enthusiasts figure out their actual chances of winning or losing. As it seems, many players, including some experienced ones, are not aware that house odds are the inverse of winning odds.
It is important to note that if you are looking to enjoy a fruitful roulette session, the true casino odds and the probability of winning should not be the only information to consider.
While deciding on a wager, casino enthusiasts should also be guided by the rewards they can potentially collect if their wager is settled as a winner.
Remember that the higher the chances of winning, the smaller the pay-offs will be and vice versa – the lower the chances of winning, the larger the payouts.
The pay-offs awarded on winning stakes are reduced and are not based on the true odds against winning. In other words, casinos guarantee themselves consistent profit by paying players less than they should.
Let us focus on Straight bets, for which the odds against winning are 36 to 1, while casino odds are 35 to 1. Many may think that the difference is negligible, but if you intend to spend more time betting on roulette, the disparity will become much more pronounced. What players should remember is that casinos, whether land-based or online, will invariably bet against you and will always take their cut.
Although the values of the true and casino odds come very close, they will never coincide, as casino odds will always be lower. Perhaps most people are familiar with the expression that “the house always wins”; now you know why this is true.
Therefore, players should keep their eyes open for wagers where the casino odds come as close to the true odds as possible, because in such cases, the casino advantage will be lower.
We needed to draw a distinction between true and casino odds to ensure that players can understand how casinos gain their edge over their customers.
Roulette and Randomness
While polishing their knowledge of the game of roulette, gambling enthusiasts should also become acquainted with the concept of randomness. In a perfect world, roulette wheels are designed so that the outcome of the next spin cannot be influenced in any way, thus remaining unforeseeable and entirely random.
Apparently, many roulette players do not have a proper understanding of randomness, which helps explain why they struggle to determine the probability of a specific outcome. One of the clearest descriptions of randomness is that the outcomes will be unpredictable provided that one item of a set is just as likely to be chosen as any other item in that set.
When roulette is concerned, it is impossible for gambling enthusiasts to know for sure which of the numbers 0 through 36 will be the next winner when the wheel is spun.
Therefore, a process – or any spin of the roulette wheel – will be truly random provided that the outcomes of previous spins do not influence upcoming spins. Although this is exactly what casino operators strive to guarantee, some wheels might occasionally show a bias.
This means that the outcomes deviate from truly random results. Sometimes, such deviation might be because casino operators want to rig the wheel, but on other occasions, the bias of the roulette wheel may be caused by certain physical imperfections that make it favour specific sectors or numbers.
Single- and Double-Zero Roulette Odds and Payouts Comparison
There is no denying that roulette is one of the most enthralling casino games for players with years of experience as well as for complete novices.
What seems slightly challenging for players at first is the extensive variety of betting options they can choose from. As gambling aficionados may already be aware, there are wager types that allow them to bet on one specific number, a set of numbers, or on red, black, even and odd numbers, among others.
In this section, we will draw a distinction between the wager types players can opt for when betting on European and American roulette and will elaborate on what the odds and payouts are.
Straight Bets
First off, regardless of whether the roulette variant you have chosen is a single-zero version or it has an additional zero pocket, you will be allowed to opt for a Straight bet. This is a bet that can be placed on any individual number, and, as players might expect, the odds will vary across the different roulette variants.
With European roulette, the odds are 2.70%, while in American roulette they are 2.63%. Another vital point that deserves players’ attention is that the true odds for such bets are 36:1 and 37:1 respectively, yet winning Straight bets pay 35:1, regardless of the variation.
Split Bets
Split bets are wagers that are placed on two numbers simultaneously. Winning Split bets pay 17:1. The American roulette odds are 5.26%, while the European odds are 5.40%. In the first case, the true casino odds are 18:1, while in the second they are 17.5:1.
Street Bets
Street bets are laid on three numbers simultaneously. Winning Street bets pay 11:1. With American roulette, the odds are 7.89%, while with single-zero variants, the odds are 8.1%. The true casino odds in the first case are 11.67:1, while with single-zero roulette variants, they stand at 11.33:1.
Corner Bets
Corner bets are placed on four numbers simultaneously, and if they win, the pay-off will be 8:1. The odds in European roulette are 10.80%, while in American roulette they are 10.53%. When true casino odds are concerned, in the single-zero variant they are 8.25:1, and in American roulette they are 8.5:1.
Basket Bets
Available solely in American roulette, winning Basket bets pay 6:1. Here, the odds are 13.16%, while the true odds are 6.6:1.
Line Bets
Line bets are roulette wagers placed on a combination of six numbers. If successful, Line bets pay 5:1. For Line bets, the American odds are 15.79%, while the European odds are 16.2%. The true odds are 5.33:1 and 5.167:1 respectively.
Column Bets
When players go for a Column bet, they wager that the winning number will belong to one of the three vertical columns, and a correct pick results in a payout of 2:1. For Column bets, American odds are 31.60%, while the European odds are 32.40%. The true casino odds are 2.167:1 on American roulette and 2.083:1 on European and French roulette.
Dozen Bets
While betting on roulette, players may wager on the numbers 1 through 12, 13 through 24, or 25 through 36. If they make a correct pick, the pay-off is 2:1. With Dozen bets, the American odds are 31.58%, while the European odds are 32.40%. The true casino odds, however, are 2.083:1 for single-zero roulette variants and 2.167:1 for double-zero ones.
Red or Black Bets
As the name suggests, this wager type allows you to guess whether the next winning number will be black or red. Winning Red or Black bets pay even money, and the odds on American roulette are 46.37%, while the odds on European roulette are 48.60%. With single-zero roulette versions, the true casino odds are 1.056:1, while with American roulette they are 1.11:1.
High or Low
This roulette wager allows gambling enthusiasts to bet whether the next winning number will be low (between 1 and 18) or high (between 19 and 36). Naturally, such bets pay even money, and the odds are once again 46.37% and 48.60%. The true odds are identical to those mentioned above.
Odd or Even Bets
With Odd or Even bets, players try to guess whether the winning number will be odd or even. The American odds are 46.37%, while the European odds are 48.60%. As with the wagers mentioned above, Odd or Even bets also pay 1:1. The true chances of making a winning Odd or Even bet are 1.056:1 when single-zero roulette variations are concerned and 1.11:1 for double-zero roulette variants.
Probabilities and Payouts of Call Bets
Call bets are another type of roulette wager, but their availability is limited exclusively to single-zero roulette variations. What should be noted about these wagers is that the numbers they comprise are grouped according to their position on the roulette wheel, rather than on the betting layout.
Neighbours of Zero
This is a call bet that comprises all 17 numbers located near the zero. To place this bet, gambling enthusiasts will need a total of 9 chips, and the pay-off granted if the bet wins depends on the number that hits. The odds of the Neighbours of Zero bet are 45.9%.
Third of the Wheel
This wager covers the 12 numbers situated on the opposite side of those included in Neighbours of Zero. This time, the payouts are fixed at 17:1, while the odds of winning are 32.4%.
Zero Game
This bet type bears much resemblance to Neighbours of Zero because it also covers numbers close to zero, but this time there are only 7. While the pay-off for such wagers is 26:1, the odds of winning stand at 18.9%.
Orphelins Bets
Such bets require a total of five chips and cover numbers located on opposite sides of the roulette wheel. With these bets, the odds are 21.6%, while the pay-off will be 35:1 for the wager made on a single number and 17:1 for the splits.
Neighbour Bets
Neighbour bets are placed on one number chosen by the player and four additional numbers that sit on both sides of that number. The odds of winning are 13.50%.
Final Bets
A Final bet is a roulette wager made on all numbers that share the same final digit. The number of chips players need to place such a wager depends on the chosen number and can be three or four. It should be noted that the odds are determined by the chosen digit and will be either 8.10% or 10.80%.
Odds of the Same Number Appearing in Successive Rounds
Often, when roulette variations provide statistics, they show “hot” numbers that have previously won. Although one could base their next bet on the results from preceding roulette spins, it should be noted that the odds of the same number appearing twice in a short period are not exceptionally high, especially if we are talking about landing the same number in two or more consecutive rounds.
The probability of the roulette ball landing on the same number in successive spins also depends on the roulette variation being played. While the odds of a single number appearing in European roulette are 1 to 37, in American roulette the probability is 1 to 38 due to the additional wheel section. When it comes to the same number landing two or more consecutive times, however, the chances are much slimmer.
Back in 1959, a record number of wins with the same number was achieved at the El San Juan hotel in Puerto Rico. During that game of American roulette, the number ten appeared six consecutive times. To calculate the probability of such an event, we simply multiply the probability of each of the six individual events.
In the case of the ball landing on the same number six successive times, we multiply (1/38) × (1/38) × (1/38) × (1/38) × (1/38) × (1/38). The result shows that the probability of that happening is roughly three-billionths.
The example above answers the question about the probability of the same number landing six consecutive times. If we are, however, curious about the probability of the result of the previous spin repeating on the next spin, the answer will be 1/38 for American roulette and 1/37 for European roulette. This is a so-called simple event and expresses the probability of any of the roulette numbers landing twice in a row.
Landing the same colour on successive spins is also possible, with a record of the red colour appearing 32 consecutive times recorded in 1943. Here, we obtain the probability of such an event by multiplying each of the 32 individual probabilities, ending up with a very low probability of (18/37)32 = 0.000000000096886885. If we are playing American roulette, the probability is even lower because of the extra green section on the wheel.
Things to Consider When Picking a Roulette Wager
Once players are aware of the true and casino odds of all roulette bets, it will be much easier for them to find the right approach to betting on the game, which will therefore help them build an effective betting strategy.
One of the most essential things roulette fans should pay attention to is the odds of the chosen bet type. Gambling enthusiasts should be mindful of the fact that the chances of winning a Straight-up bet are the smallest, which is why they should not get carried away by the larger pay-offs such bets provide.
Roulette bets such as Red or Black and Odd or Even award smaller payouts compared with Straight bets, as they offer even money. Yet, gambling enthusiasts will stand a much better chance of collecting a pay-off if they opt for any of these wager types. Although the rewards you collect will not be staggering, choosing wagers that cover larger groups of numbers can be a more advantageous approach because you are likely to turn a profit more often.
One more thing avid casino fans should remember is that opting for single-zero roulette variants is recommended for the simple reason that the odds of winning are slightly better compared with those offered by American roulette.