Roulette Probabilities: Betting Combinations and Their Payouts
Winning probabilities are by far the most important factor for any player of casino or card games, or any games of luck in general. We’re talking, of course, about the mathematical chances players have at winning. Roulette is one of the games that have specific winning probabilities for specific bets. Generally, the probabilities depend on the type of roulette you’re playing. People who are into roulette are aware of the fact that, for example, European roulette has better probabilities compared to American and that a game of European roulette played with the “la Partage” or “en Prison” rule has a lower house edge compared to a game where these roulette rules aren’t enforced and that means higher winning probabilities.
Winning Probabilities of Outside Bets
The winning probabilities could be compared to an easy thing – the rolling of the dice. Dice have six fields and it is comparatively simple to calculate what the chances are of one or another number to be rolled. Here are some of the apparent principles.
.What is the chance to roll a 6 on a dice?
A: It’s exactly 1/6 or 16.7%, as the 6 is placed on one of six sides of the dice.
.And how high is the probability of rolling a number lower than 4?
A: In this case, the odds are 50%, because all 1,2 and 3 are winning. These three numbers take three of the six fields of the dice and that is exactly half of it. Therefore, we have 50% winning chances.
The outside bets in roulette are the ones that have higher winning odds and lower payouts. Speaking in terms of odds, the probability of winning an outside bet is higher than that of winning an inside bet. The bets that cover 18 numbers, or half the table, if we exclude the zero, have the highest winning probability. The payout for those is 1:1, i.e. you’ll get £10 for a £10 bet and the winning odds are 47.37% in American and 48.65% in European roulette.
- 1. Red or Black
- 2. Even or Odd
- 3. Low (1-18) or High (19-36)
Another type of outside bets are the Column and the Dozen bets. With each of these bets you cover 12 numbers on the table, or almost one third, again if we exclude the zero(s). You can bet on the first, second or third dozen (1-12, 13-24, 25-36), or on the first, second or third column (the first starts with 1, then 4, the second with 2 then 5, etc.). The winning probability of each such bet is 31.58% in American and 32.43% in European roulette. The payout is 2:1 and your £10 bet will turn into a £20 winning. If you would like to learn more about the two types of roulette game, American and European, we can suggest this article on the topic.
Winning Odds of Inside Bets
The inside bets would the second category of bets, different from the outside bets, as the name suggest. An inside bet is a bet placed on an individual number, inside the margins of the table where the numbers are placed, or a smaller group of numbers. The numbers can be grouped differently, but always according to their position on the table. The inside bets have much lower winning probabilities, but the possible amount of money that could be won is much higher, of course.
“Straight”
The inside bet with the lowest winning probability is the straight bet – i.e. the single-number bet. Clearly, here a player puts his or her chip(s) on an individual number- 1, 24, 15, 0, etc. The bet is a win only if the ball lands on that number. The payout is 35:1 and the winning probability is 2.63% in American and 2.70% in European roulette.
Winning probability: 1/37 or 2.70%.
“Split”
The second bet is the split, or the two-numbers bet, where the player bets on two neighbouring numbers, such as 1 and 2, or 1 and 4, or 5 and 8. This bet is a win if either of these numbers comes up and the payout is 17:1. The probability is 5.26% in American roulette and 5.41% in European.
Winning probability: 2/37 or 5.41%.
“Street”
Then we have the street, or the three-number bet. Here, the player bets on a row of numbers, such as 4, 5 and 6, or 10, 11 and 12. The payout for a street bet is 11:1, and the probabilities are 7.89% and 8.11% in American and European respectively.
Winning probability: 3/37 or 8.11%.
| Differences in European and American Roulette | |||
|---|---|---|---|
| Bet placement | Payout | Winning odds European Roulette | Winning odds American Roulette |
| Straight | 35:1 | 2.8% | 2.6% |
| Split | 17:1 | 5.4% | 5.3% |
| Street | 11:1 | 8.1% | 7.9% |
| Corner | 8:1 | 10.8% | 10.5% |
| Dozen | 2:1 | 32.4% | 31.6% |
| Column | 2:1 | 32.4% | 31.6% |
| Red / Black | 1:1 | 48.6% | 47.4% |
| Even / Odd | 1:1 | 48.6% | 47.4% |
| Low 18 | 1:1 | 48.6% | 47.4% |
| High 18 | 1:1 | 48.6% | 47.4% |
“Corner”
A bet where the chip(s) cover(s) four numbers is called a corner bet, and here the player bets on four numbers which form a square on the table, like 1, 2, 4 and 5. The payout for a corner bet is 8:1 and the winning probability in European roulette is 10.81%, whereas in American it is 10.53%.
Winning probability: 4/37 or 10.53%.
“Double Street”
The double street bet covers two rows, i.e. six numbers and the probability is 16.22% in European and 15.79% in American roulette, with the payout set at 5:1.
Winning probability: 6/37 or 8.1% in European and 7.9% in American roulette.
“Five Number Bet”
The five number bet is only available in American roulette. This bet is also called basket bet or first five. This bet covers the zero, the double zero and the first three numbers, 1, 2 and 3. This bet is considered to be the worst bet in roulette, knowing that the house edge is quite high – 7.89%, compared to the regular house edge of 5.26% in American roulette.
Winning probability: 5/37 or 13.16%.
Infographics: Comparison of winning odds American/European roulette
Probabilities of Called Bets
The called, or announced, bets are different, because the numbers are combined according to their position on the wheel and they are only available in European roulette. There are two sub-categories of called bets – fixed and variable called bets. There are three fixed called bets and two types of variable bets.
“Neighbours of Zero” – Now, neighbours of zero, or “the grand series” covers 17 numbers on the wheel which are in the proximity of the position of the zero. A player has to place at least 9 chips to cover all the numbers included in the neighbours of zero. The probability of winning is 45.9% and the payout is not fixed, or to be precise it can be 24:1, 17:1, 11:1 and 8:1 depending on the winning number.
“Zero Game” The zero game is a smaller version of the neighbours of zero. It has a winning probability of 18.9% and 7 numbers are covered in this bet.
“Thirds of the Wheel The third of the wheel, sometimes called “the small series” are the 12 numbers which are across the neighbours of zero (respectively sometimes called “the grand series”). The probability is 32.4% and the payout rate is set at 17:1. In terms of probability and payout rate this bet is the same as the dozen and column bets.
“The Orphans” The orphans bet has a probability of 21.6% and the payout can be either 35:1 or 17:1.
There are two types of variable bets. The first are called “the neighbours” where the player bets on 5 neighbouring numbers and the probability here is 13.5%. Then, we have “the finals”, where the player bets on the last digit. Since the finals bet can cover either three or four numbers, the probability is either 8.1% or 10.8%.