Roulette Odds & Probability
Are you ready to bet at a table of roulette with real money? Then you need to understand the principles and concepts of roulette odds and payouts. In this finely diced article, we will take you through all odds and payout involved in roulette and various rules you can find in the European roulette version.
It is not just about playing with real money, but about understanding your chances of winning the game, which largely depends on mathematical probability (odds), house advantage, the type of roulette wheel you are playing on, and additional rules.
Even though roulette is based on chance, you can be at an advantage if you understand the odds, probability, and payouts methods of the game; this will ensure that you win big.
Table of content:
- Roulette odds & probability
- American wheel probability of success
- European wheel probability of success
- Probability Table
- Payouts
- What will happen if a ball stops at number 3?
- Types of Bets
- Inside Bets
- Outside Bets
- Extra Roulette Bet Types
- European roulette table rules
Roulette Odds & Probability
Probability is the chance that a particular event will happen and not all other likely outcome. Probability exists between 0 and 1 where 0 means something is impossible to occur, while 1 means something is absolutely possible to happen.
A roulette wheel has either 37 (European roulette wheel) or 38 (American roulette wheel) numbers in total; therefore these are all the possible outcomes for an event to occur.
In a European roulette wheel for example, for specific numbers, there is only one means to win and 36 means to lose. Therefore, the probability or probability of success of putting a bet on a single number, e.g. 17 is calculated by dividing the number of possible ways to win by the addition of all possible ways to win and all possible ways to lose.
Probability of success, therefore, is 1/1+36 = 1/37 = 0.027 = 2.70%, implying that you have 2.70% chance to win on the number 17 or any other single number for every 100 spins.
American wheel probability of success
On an American wheel, the probability of success for putting your bet on a single number is 1/1+37 = 1/38 = 0.026 = 2.60%, which means that for every 100 spins you have a 2.60% chance to win on any single number.
The European roulette offers a 97.3% average payout for every $100 while the American roulette offers a 94.74% average payout for every $100.
The probability to win is higher in the European roulette than the American roulette that is why we recommend betting at a European roulette table.
European wheel probability of success
On the European roulette wheel, if you place bets on three numbers, then you have three chances to win and thirty-four chances to lose. Therefore, the probability of success, which is the probability for one of the three numbers to win, will be 3 / 3 + 34 = 3 / 37 = 0.0810, or 8.10%.
Similarly, if we place bet on 12 numbers, then we have 12 ways to win and 25 ways to lose. Probability of success will be 12/12+25 = 12/37 = 0.3243 = 32.43%
The table below gives a summary of all probability of success, payout on various bets using either the European or the American roulette version.
Roulette Probability Table
| Bet | Payout | Probability in % (American) | Probability in % (European) |
| Straight (single number | 35 to 1 | 2.63 | 2.7 |
| Split (2 Number Combination) | 17 to 1 | 5.26 | 5.41 |
| Street (3 Number Combination) | 11 to 1 | 7.89 | 8.1 |
| Corner (4 Number Combination) | 8 to 1 | 10.53 | 10.81 |
| 5 Number Combination | 6 to 1 | 15.8 | 16.2 |
| Line (6 Number Combination) | 5 to 1 | 15.79 | 16.22 |
| Numbers 1-12 | 2 to 1 | 31.58 | 32.43 |
| Numbers 13-24 | 2 to 1 | 31.58 | 32.43 |
| Numbers 25-36 | 2 to 1 | 31.58 | 32.43 |
| Red/Black | 1 to 1 | 47.37 | 48.65 |
| Even/Odd | 1 to 1 | 47.37 | 48.65 |
| Numbers 1-18 | 1 to 1 | 47.37 | 48.65 |
| Numbers 19-36 | 1 to 1 | 47.37 | 48.65 |
Odds
Odds also describes the possibility of an event happening; it makes comparison between the numbers of ways an event can happen with the number of ways it cannot occur. 1 to 37 or 37 to 1 is the odds of any particular number to win in roulette.
For example, if a single bet of $5 is placed on the number 3 on a European roulette wheel. The probability of success will be 1/37 = 0.027 = 2.70% while the odds will be 36 to 1, 36 ways to lose against one way to win.
Another example, if you place a $10 bet on red on a European roulette wheel. There are 18 red pockets on the roulette wheel. The probability of success will be 18/37 = 0.4865 = 48.65% while the odds will be 19 to 18, 19 ways to lose against 18 ways to win.
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Roulette Payouts
House odds (odds paid or payouts) represent the odds of failure or the opposite of odds for success. The lower the possibility of success, the higher the odds and the higher the payout. The odds paid by the house is the number of ways the event cannot occur; this is if the house does not take a cut out of the odds against success.
Most times the house pays out a unit or two less than the odds against success. This difference in the odds is called the house advantage; it causes an increase in the profit margin of the house.
What will happen if a ball stops at number 3?
From our first example above, if the ball eventually stops at number 3 and you win the bet. The house returns the original stake, which in this case is $5, but if the house pays out a unit less than the odds against success, you will be paid 35 times of the original stake instead of 36 times. Thirty-five times of our original stake is $175, in the end, you make a gain of $175.
From the second example above, If the ball eventually stops on a red pocket and you win the bet, the house returns the original stake, which in this case is $10 and pay out 18 times instead of 19 times of the original stake. Eighteen times of our original stake is $180, in the end, you make a gain of $180 excluding your initial bet.
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Types of Bets
Whether you play the European version or the American version, there are several betting options in roulette. There are even more options in the European version where the chances of players to win are increased.
We will explain the numerous options and explain your chances of winning on each option. Roulette bets are divided into two; inside bets and outside bets based on the position of the bet on the table.
Additional betting option in the European version is not categorized into these two, and they are sometimes called traditional rules.
Inside Bets
Inside bets has large payouts because the chances of them occurring are slim. We, therefore, recommend starting with inside bets for newbies. This type of bet will allow them to try their luck and earn big payouts. Examples of inside bets include:
Straight, single-number bet
This type of betting involves betting on a single number of your choice. Implying that of all the 37 numbers in the European roulette, you are betting that the ball will land on the number you have chosen. This bet has a low winning probability of 2.7% and 2.63% and a high payout of 35:1 and 36:1 for European and American roulette respectively
Split bet
A split bet is when you bet on two neighboring or adjacent numbers out of the 37 available on the wheel. This bet has a low winning probability of 5.41% and 5.26% and a high payout of 17:1 and 18:1 for European and American roulette respectively.
Street bet
This is when you bet on a row of three numbers. For example, you place a street bet when you bet on 14, 15, 16, or 34, 35, 36. The probability of winning a street bet is 8.11% and 7.89% and payout 11:1 and 12:1 for European and American roulette respectively
Corner bet
When you place a bet on four number that makes a square on the roulette layout, you are making a corner bet. For example, 1, 2, 4, and 5. This bet pays out 8:1 and 9:1 and has a winning probability of 10.81% and 10.53% for European and American roulette respectively.
First four bet
The first four are only used on European roulette tables. You bet on the First four when you bet on 0, 1, 2, and 3. This bet payouts 8:1 and has a winning probability of 10.81%.
Trio bet
This bet is similar to a street bet, but you must include one of the zeros in the row of three numbers you choose. For example, 0, 1, and 2 or 00, 31, and 32. The winning probability of this bet is 8.1% and 7.89% and has a payout of 11:1 and 12:1 for European and American roulette respectively.
Outside Bets
Outside bets give you a better chance of winning with little payouts. It covers the more extensive section of the wheel and sometimes involves higher maximum bets than inside bets. Examples are as follows;
Double street bet/ six line bet
This is betting on two successive rows, covering six numbers in total. For instance, placing bets on 8, 9, 10 and 20, 21, 22. This bet payout 5:1 and 6:1 and has a winning probability of 16.22% and 15.79% for European and American roulette respectively.
Basket, or a five number or top line bet
Topline bet is used only on American roulette tables. It involves placing bets on five constant numbers, these numbers are, 0, 00, 1, 2, and 3. This bet payout 6:1 odds, and has a winning probability of 15.8%.
Column bets
This is placing your bet on one of the three columns laid out on the roulette table; each of these columns contains 12 numbers. The winning probability of this bet is 32.43% and 31.58% and has a payout of 2:1 and 3:1 odds for European and American roulette respectively.
Dozens bet
This type of bet involves placing your bet on 12 consecutive numbers. For example 1-12, 13-24, or 25-36. The winning probability of this bet is 32.43% and 31.58% and has a payout of 2:1
Odd bet
This is placing your bets on all odd numbers on the wheel starting from 1-36. There are 18 odd numbers between 1 and 36. The winning probability of this bet is 47.37% and 48.65% for European and American roulette respectively and has a payout of 1:1.
Even bet
This is placing your bets on all even numbers on the wheel starting from 1-36. Eighteen even numbers are between 1 and 36. The winning probability of this bet is 47.37% and 48.65% for European and American roulette respectively and has a payout of 1:1.
Red bets
This is placing your bets on all red pockets on the wheel. There are 18 red pockets on the wheel. The winning probability of this bet is 47.37% and 48.65% for European and American roulette respectively and has a payout of 1:1.
Black bets
This is placing your bets on all black pockets on the wheel. There are 18 black pockets on the wheel. The winning probability of this bet is 47.37% and 48.65% for European and American roulette respectively and has a payout of 1:1 odds.
High bets
This is placing your bets on high numbers ranging from 19-36 on the wheel. There are 18 high number slots on the wheel. The winning probability of this bet is 47.37% and 48.65% for European and American roulette respectively and has a payout of 1:1 odds.
Low bets
This is placing your bets on high numbers ranging from 1-18 on the wheel. There are 18 low number slots on the wheel. The winning probability of this bet is 47.37% and 48.65% for European and American roulette respectively and has a payout of 1:1 odds
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Extra Roulette Bet Types
Called bets
Called are only available on the European/French Roulette gaming table. They are used when players cannot place their chips on the table due to crowding or when a player wants to play on credit. He calls out what he wants to play to the croupier and the croupier spots the bet on the table. However, many casinos bans gambling on credit.
The numbers in called bets are series of numbers pooled according to the positions on the roulette wheel and not the table. Each called bet is named according to their positions on the roulette wheel.
Announced Bets
Players can call or announce their bet as far as they still have money on the table. Announced bets are made available to known high stake players. These bets are on precise position on the roulette wheel, and it takes several chips to cover it all.
It can become unmanageable; however, the croupier can help oversee the bets for the players, by sometimes making use of the “racetrack” layout found on few European roulette casinos.
Types of called and announced bets
Neighbors of zero/grand series/ voiusins du zero: This bet uses nine chips to cover the first 17 numbers that are away from the zero. The winning probability is 45.9%. The payout is based on the type of bet the winning number is, for instance, the payout will be 16 chips on the corner bet, 22 on the trio, or 17 chips if one of the splits win. The total payout can be as high as 24:1.
Thirds of the wheel/tiers du cylindre bets
These bets are placed on the 12 numbers that are directly opposite the Neighbours of Zero. Six split bets are needed to cover these numbers. The winning probability is 32.4%, and the payout is 17:1 if the ball lands on any of the 12 numbers. For example, if you spread $1 each on any of these six splits 5-8, 10-11, 13-16, 23-24, 27-30 and 33-36, and the ball lands on any of the splits, you earn $18.
Zero game/ jeu zero bets
This is a miniature form of the Neighbours of Zero. This bet covers only the first seven numbers away from the green zero pockets using four chips. The winning probability is 18.9%, and the payout is determined by the number the ball lands on, for instance, if a split number wins, the bet will payout 17 chips. If the ball falls on a single number, you will be paid 35: 1.
The orphans/ les orphelins bet
This bet uses five chips to cover for numbers outside Third of wheels and Neighbours of Zeros, which are eight numbers. The probability of winning this bet is 21.6%, and the payout can be either 35:1 on single bets or 17:1 on split bets.
The neighbors bet
This is placing bets on five neighboring numbers. The probability of winning is 13.5%, and the payout is 7:1.
The finals bet
This is placing your bets on every number that ends with your chosen number. For instance, if you place your bets on number 3, and the ball lands on, 3, 13, 23, 33, you have to own the bet. Note that setting your chances on numbers ending with 0, 1, 2, 3, 4, 5 and 6, requires four chips while numbers ending with 7, 8 and 9, requires three chips.
Finales a Cheval
Another variation of the final bets is called Finales a Cheval. Here bets are put on split numbers ending with the same digit. For split bets on 0-1, 1-2, 2-3, 4-5, and 5-6, five chips are required, for split bets on 0-3, 1-4, 2-5, 3-6, 7-8 and 8-9 four chips are needed while three chips are necessary for split bets of 4-7, 5-8, 6-9, 7-10, 8-11 and 9-12.
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European roulette table rules
La partage: When this is offered by the house, this implies that you will get back half of the money you placed on an even money bet if the ball stops on zero or double zero. Even money bets are odd/even or red/black bets.
En prison: When the gambling house offers this, it means that you half of an even money bet will be kept “in prison”. You can redeem this money if you win your next spin.
I think we have done excellent job in simplifying roulette odds, probabilities, payouts and winning chances, and we hope you have learned the one or two things about roulette. With all of these, it depends on you to choose how you want to play the game. Some people prefer staking high on large probabilities with small odds.
Others prefer staking small on significant chances with low odds, to keep gathering their earnings, but remember the house in leaning on the winning side, do not overwork it, learn to work away, and ultimately enjoy the game.
Best wishes!
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