Probabilities at roulette


When playing roulette games, probabilities allow you to understand the logical structure governing the bets placed by players, but also game strategies. Finally, they allow you to understand why bets on simple chances present greater chances to win in the long run and are therefore preferable to other types of bets.

Probabilities to win at European roulette

In order to evaluate the probability to get a number on the wheel when betting on simple chances, here is a mathematical formula that is easy to apply: it allows you to determine the percentage of chances for a number to be winning.

E = N/37x100

In this formula, E represents the expectation for the number to be winning and N is the quantity of said number, while 37 is the number of boxes present on a French roulette cylinder.

Let's take a concrete example to better understand this theoretical formula that proves to be very useful.

  • To calculate the probability for number 2 to be winning during a round of French roulette, let's apply the formula presented above and replace N by 1, since in this case a single number is concerned: number 2. The formula therefore gives an expectation of 1/37x100, i.e. 2.7% chances for number 2 to be winning.
  • As for the chances for the colour black to be winning, this probability can also be calculated thanks to the previous formula: let's replace N by 18, since there are 18 black boxes on the French roulette wheel. We then get an expectation of 18/37x100, i.e. 48.65%.

Don't be surprised if you do not get 100% when you add up the probability for the colour black to be winning and for the colour red to be winning: this is due to the fact that the zero box is neither red nor black.

Table of probabilities at European roulette
Type of betProfitsProbability
Red 1 to 1 48.65%
Black 1 to 1 48.65%
Even 1 to 1 48.65%
Odd 1 to 1 48.65%
1 to 18 1 to 1 48.65%
19 to 36 1 to 1 48.65%
1 to 12 2 to 1 32,43%
13 to 24 2 to 1 32,43%
25 to 36 2 to 1 32,43%
One number 35 to 1 2,70%
Split 17 to 1 5,40%
Street 11 to 1 8.11%
Corner 8 to 1 10,80%
Line - Six-number 5 to 1 16,20%

Probabilities at American roulette

The formulas described previously must be adapted when you want to calculate the probabilities of profits at the other variation of roulette: American roulette.

Indeed, the latter is made of a 38-box wheel, instead of 37 at European roulette. Therefore, you need to replace 37 by 38 in each of the formulas presented above, and that's all there is to it!

Similarly, you need to take into account the fact that two boxes are neither red nor black, i.e. boxes numbered 0 and 00: this has an impact on probabilities for the colour red or black to be winning during a round of American roulette.

Table of probabilities at American roulette
Type of betProfitsProbability
Red 1 to 1 46.37%
Black 1 to 1 46.37%
Even 1 to 1 46.37%
Odd 1 to 1 46.37%
1 to 18 1 to 1 46.37%
19 to 36 1 to 1 46.37%
1 to 12 2 to 1 31,58%
13 to 24 2 to 1 31,58%
25 to 36 2 to 1 31,58%
One number 35 to 1 2,63%
Split 17 to 1 5,26%
Street 11 to 1 7.89%
Corner 8 to 1 10,53%
Line - Six-number 5 to 1 15,79%
Combination of 0, 00, 1, 2, 3 6 to 1 13.16%

Place your bets and do not believe the saying “as luck would have it”. True laws of probabilities exist and they are at the root of your victories and your losses, but also your foolproof game strategies!

Become a master of the game and a fine strategist by relying on true probabilistic theories...