Anyone who runs a casino or makes online casino games knows the probability theory very well. It is directly linked to its profits. And thanks to it, the casino always wins over the long run. Everything in a casino is related to the probability and house edge.
Note: All numbers in the article refer to European Roulette – so we count on 37 numbers.
Percentages vs. Fractions and Odds
There are several ways to write down a probability. Perhaps the best known are percentages. We can also use fractions or ratios.
Expression as a percentage (%) – Probability is calculated as (Event / Outcomes) * 100. E.g. probability that the single number on the roulette (Straight) will fall: 1/37 * 100 = 2.7%
Expression using fractions (1 / x) – If we express the probability using a fraction, we say that the phenomenon occurs 1 time from X attempts. In numerical terms, we use the calculation of percentages. Using the example above 1/37, this means that the single number on the roulette will hit one time out of 37 spins.
Expression by the odds (x to 1) – Each time X occurs, the chosen phenomenon happens one time. Here, too, we will remain at the probability for the single number at roulette. In this case, the odds will be written as 36 to 1. This means that for every 36 spins when the number does not fall, there will be one case when the selected number falls.
Note: The higher the number of attempts, you get closer and closer to the calculated result.
As you can see, expressions by fractions and by odds are very similar. The only difference is that the fractions work with all possible outcomes, while the ratio splits the total spins into two categories.
Table of Probabilities for Single Roulette Bets
|Even bet||1/2.055||1,055 in 1||48,6 %|
|Sloupec||1/3.08||2,08 in 1||32,4 %|
|Dozen||1/3.08||2,08 in 1||32,4 %|
|Six Line||1/6.17||5,17 in 1||16,2 %|
|Corner||1/9.25||8,25 in 1||10,8 %|
|Street||1/12.33||11,33 in 1||8,1 %|
|Split||1/19.5||18,5 in 1||5,4 %|
|Straight||1/37||36 in 1||2,7 %|
Probability for a straight bet
Probability of repetitive phenomenon is also very interesting. For this case, we have chosen an even bet, precisely a red bet. So, for example, what is the probability of red hitting five times in a row?
|Number of Spins||Odds||Percentages|
|1||1.06 in 1||48.6 %|
|2||3.23 in 1||23.7 %|
|3||7.69 in 1||11.5 %|
|4||16.9 in 1||5.6 %|
|5||35.7 in 1||2.73 %|
|6||74.4 in 1||1.33 %|
|7||154 in 1||0.65 %|
|8||318 in 1||0.31 %|
|9||654 in 1||0.15 %|
|10||1 346 in 1||0.074 %|
|15||49 423 in 1||0.002 %|
|20||1 813 778 in 1||0.000055 %|
As you can see with the increasing number of spins, the probability of this phenomenon decreases rapidly. However, remember that these probabilities describe the event as a whole. The Random Number Generator does not take into account the previous results, so even though a 20 red game series occurs once in 1,813 million games, the 21st game round will have the same probability (48.6%) as any other game round.
Often, in this case, you may encounter the myth called Gamblers Fallacy, where a player believes that if one colour hits several times in a row, there is a higher probability that the other colour will hit in the next spin. In fact, it is not true, as we explained earlier. The most well-known case of this fallacy was observed in 1913 at the Monte Carlo casino when black roulette fell 26 times in a row, and for almost the entire time of this incredible series, and even after it ended, people were betting on red.
Note: The probability that one colour hit 26 times in a row is 0.000000730870%.
How to Calculate a Probability for Roulette Bets
Do you want to know more about roulette probability? Generally, the easiest way is to start with fractions. For example, if you want to quantify the probability in a fraction for a situation where red wins, do the following:
Total reds cells on roulette / Total cells on roulette = 18/37
Probability for one roulette spin
Again, a simple rule applies. Just calculate the number of cells that will win and divide them by the total number of fields.
- Colour – 18/37
- Even / Odd – 18/37
- Dozen – 12/37
- Number 0 – 1/37
Black and Even bet – 9/37 (there are only nine numbers, which are both black and even)
Dozen and Column – 4/37 (there are only four numbers in one dozen and in one column at the same time)
As well as the probability of winning, you can calculate the probability of losing. All you have to do is count the number of non-winning cells and divide them again by the total number of cells. For example, the probability of losing when you bet on red is 19/37. (18 black numbers + green zero).
Note: You can convert a fraction to 1 / x with a simple adjustment by dividing the numerator and denominator by the numerator. E.g. 18/37 (you divide both numbers by 18) will be 1 / 2.055. It means that every 2.055 turns one time red or black hit.
Probability for multiple spins
Once you have mastered the calculation for individual spins, calculating the probability for many spins is very simple. All you have to do is multiply the individual fractions between itself.
- First spin – bet on red = 18/37
- Second spin – bet on dozen = 12/37
Probability of winning both rounds = (18/37) * (12/37) = 1 / 6.34 or 15.77% or 5.34 to 1
- First spin – straight bet – 1/37
- Second spin – straight bet – 1/37
Probability of winning both rounds = (1/37) * (1 * 37) = 1/1369 or 0.073% or 1368 to 1
- First spin – bet on black and odd 9/37
- Second spin – bet on even 18/37
- Third spin – bet on column 12/37
Probability of winning all 3 rounds = (9/37) * (18/37) * (12/37) = 1 / 26.06 or 3.84% or 25.06 to 1
Conversion between results is effortless again. To get a percentage divide the 1 / x fraction and then multiply it by 100. To get the x-to-1 ratio, subtract one from the denominator.
You subtract the X-to-1 ratio by subtracting one from the denominator. See the examples above.
And that is how you calculate the probability and odds for every possible roulette bet.