Understanding the Odds of Online Roulette
Having a thorough understanding of the odds is just as important as knowing how to place bets at the table. A combination of both is the key to success. If you're looking to learn more about the odds of roulette bets and how to apply that knowledge to your game, then you're in the right place.
Here, we have detailed information about the probability of each bet to win on an American wheel. If you generally prefer European wheels, the basic principle is the same, however, the house edge is slightly more favorable.
The Basics of American Roulette
Roulette is a game in which players bet on where a ball will land on a spinning wheel. An American wheel is divided into 38 pockets with numbers 1-36 on alternating red and black backgrounds. In addition, two of the pockets are green with a zero or double zero. The green pockets give this variation of roulette a 5.26% house edge directly impacting the potential chance for each bet to win.
Bets are placed on a table layout. It features the numbers with corresponding colors in three columns. Inside bets on individual numbers, or groups of up to 6 numbers, can be found on the inside of the layout. Outside bets covering from a third to almost half of all numbers can be found on the outside of the layout. You can probably guess which type gives the best odds to win already. Let's take a closer look.
What are the Odds for Roulette Bets?
Let's begin with outside bets which offer the highest probability to win. These include even-money bets such as red/black, odd/even and high 18/low 18. These are not dissimilar to flipping a coin, albeit a coin that is slightly in the house's favor, and simply involve picking one of two options. Each option covers 18 numbers out of 38.
The probability for even-money bets to win is 47.37% and each pays 1/1. Why isn't the probability showing an even 50-50 chance to win? This is due to the green 0 pockets. If the ball lands on zero or double-zero, you will lose your bet automatically.
"There's no way to reduce or increase roulette's house edge, meaning inexperienced players have the same odds of hitting a massive win as a seasoned gambling veteran."
Other outside bets include columns and dozens. Each covers 12 numbers in a single wager, giving a 31.58% chance to win each spin. The payout is 2/1. Like even money bets, these will lose if 0 or 00 is chosen.
Inside bets have much longer odds to win but pay out more. The bulk of the wheel is made of the individual numbers 1-36. Placing wagers on these, or various combinations thereof, will yield payouts of 5/1 to 35/1.
American roulette has the unique option to bet on the first five numbers: 0, 00, 1, 2, 3. This is known as the 'basket bet' and has a higher house edge than any other bet: 7.89%. All other inside bets are subject to the same 5.26% house edge.
A Break Down of Inside Bets
How to Work Out the Numbers
To work out the probability of each bet to win for yourself, you can use this equation.
Probability to win (P) = potential ways to win / all potential outcomes x 100.
For a 'straight-up' bet that wagers on a single number, there is only one potential way to win out of 38 potential outcomes. So, the calculation would work out in the following way:
P = (1 / 38) x 100
P = 0.0263 x 100
P = 2.63%
This shows that a straight-up bet has a 2.63% chance to win each spin. It also works for bets on multiple numbers. Have a look at how it works with outside bets.
P = (18 / 38) x 100
P = 0. 4737 x 100
P = 47.37%
|Columns and Dozens||
P = (12 / 38) x 100
P = 0. 3158 x 100
P = 31.58%
Probability for Combination Bets
Calculating the potential for multiple bets to win is a bit different. If you place 1 bet unit on red and another on black, your probability to win is still only 47.37%, because you can't win both in the same round. However, if you place 1 bet unit on black and another on the second column, the probability to win at least one of the two bets each spin must be calculated the following way.
Probability to win (P) = (possible wins for black + possible wins for column 2 – shared wins for both bets) x 100
P = (18/38 + 12/38 - 8/38) x 100
P = 57.89%
Notice how it requires subtracting the 8 black numbers in the second column so that those numbers won't be counted twice. This leaves a probability of 57.89% that at least one bet will win.
Of course, if you're more interested in knowing when both bets will win each spin, then the probability would be calculated as follows.
P = (possible wins for black and column 2 ÷ all possible outcomes) x 100
P = (8/38) x 100
P = 0.2105 x 100
P = 21.05%
As you can see, the probability for both bets to come in on the same spin is 21.05%, because 8 numbers overlap on the layout. So, for this combination, you should expect at least one bet to win 57.89% of the time, and both to win 21.05% of the time.
The equation for determining the probability of combined bets to win also works when placing inside and outside bets together. For example, if you place a bet unit on column 2, a unit on red 3 and a unit on a row containing red 7, black 8 and red 9, the probability to get at least one bet to win each spin would look like this:
P = [(possible wins for column 2 + possible wins for red 3 + possible wins for row 7, 8, 9 – shared wins) ÷ all possible outcomes] x 100
P = [12/38 + 1/38 + 3/38 - 1/38] x 100
P = 39.47%
As there is only a single number shared by all bets, the chance that at least two of the three bets will come in on the same spin is only 2.63%.
The probabilities listed above all account for the house edge. Even though there are 1-36 majority numbers on the layout, the 0 and 00 pockets give the house an advantage. To calculate the house edge for an American wheel, you must use the equation below. This example uses the probability attached to a straight-up bet.
House Edge (HE) = (probability to win – probability to lose) x 100
HE = (1/38) - (3/38) x 100
HE = -0.0526 x 100
E = -5.26%
For the same bet on a European wheel, the equation work would work out something like this:
E = (1/37) - (2/37) x 100
E = -0.0270 x 100
E = -2.70%
Calculating the house edge proves that over time you are more likely to lose than win. In other words, for every hundred dollars you spend at an American wheel, you can expect to lose $5.26. The key to succeeding at roulette is to take advantage of short-term variances such as winning streaks by pocketing your profit and walking away from the table.
Probability vs Odds Formats
You may have seen other formats to communicate your chances to win. Odds plainly show a comparison between the potential to win against the potential to lose in the form of ratios. Probabilities are expressed as percentages showing the expected occurrence of winning compared to all possibilities. Both give you an idea as to the expected likelihood that your chosen bet or bet combination will succeed each spin.
Have a look at some of the different formats measuring your likelihood to win with basic roulette bets at an American table.
|Bet||Odds For||Odds Against||Prob. to Win||Prob. To Lose|
|Straight-up||1:37, 1/37, or 1 to 37||37/1, 37:1 or 37 to 1||2.63%||97.37%|
|Even-money||0.9:1, 0.9/1, or 0.9 to 1||1.11:1, 1.11/1 or 1.11 to 1||47.37%||52.63%|
Notice how the even-money odds are a bit uneven. In a game of chance without any house edge, these types of bets would have odds of 1 to 1. However, there is a slight imbalance due to those extra 0 pockets. The 'odds for' have a slightly less than 50% chance to win, and the 'odds against' have a slightly higher chance.
To switch from odds to probability, you must use this conversion equation. The example below uses the 'odds for' of 0.9 given by even-money bets.
Odds = probability an event will occur (P) / probability an event will not occur (1-P)
(9/10) = P / 1 - P
9 (1-P) = 10 (1 P)
9 - 9P = 10 P
9 = 10P + 9P
9 = 19P
0.4737 = P
P = 47.37%
To switch from probability back to odds format, you need this equation.
Probability an event will occur / probability an event will not occur
P / 1 - P = Odds
(18/38) ÷ (20/38) = 9/10 = 0.9
Placing the Same Bets
Probability never changes from one spin to the next. Each spin has the same chance to win or lose independently from the spins that came before and the spins that will come after. However, the likelihood of winning or losing streaks over a series of multiple spins can be estimated and used as a general guideline for how often you may or may not hit a streak during your gameplay.
This example uses odds for getting a win on a straight-up bet.
Of course, this is merely theoretical. However, you can see that it is incredibly unlikely to get the exact same number 7 times in a row at the table.
|Getting a winning streak of 5 red numbers||0.59 to 1||2.38%|
|Winning both red and even||8 to 37||21.05%|
|Winning both black and even||10 to 37||26.32%|
|Winning both a color and hi/low||9 to 37||23.68%|
|Getting 0 or 00||2 to 37||5.26%|
|Winning both 2nd column and red||4 to 37||10.53%|
|Winning both 2nd column and black||8 to 37||21.05%|
|Winning both a columns bet with a dozens bet||4 to 37||10.53%|
Your Best Bets
Choosing which bets or combination of bets are best depends on your style of gameplay and preferred level of action. Obviously, if you like to win frequently and don't mind small payouts, outside bets are best. If you prefer higher payouts and don't mind winning infrequently, then inside bets are best. Want a bit of both? Try some combinations.
Keep in mind that, even when combined bets give expanded coverage of the wheel, you won't necessarily be more likely to profit. Be sure to consider the likelihood that all of your bets will come in on the same spin. That way, you won't be disappointed if you don't 'get rich quick' off of your chosen combinations.
The Best Way to Use Odds
If nothing else, the best way to use probabilities/odds is to consider each spin to be independent from the last. Even if red turns up 10 rounds in a row, it doesn't mean that the next spin will be more likely to produce a black number. Even the best laid plans can fail without a bit of luck. That's why we recommend quitting while you're ahead, as your luck may change at any given moment.