Probabilities

Probabilities are essential in order to understand the logic structure behind the bets made by players in roulette, as well as to understand the game strategies. Probabilities also allow to understand why the bets in simple chance give more possibilities to win over the long term and should then be privileged by players.

Probabilities to win in the European Roulette

In order to calculate the probabilities of falling on a number of the wheel in chance simple, we provide you a mathematic formula easy to apply: this gives you the possibility to calculate the chances a number has got to be winning.

Formula : E = N/37 x 100

In the formula E is the expectation of a number to be winning and N is the number concerned. 37 is the number of boxes present on a French roulette.

Let’s make a concrete example to better understand this theoretic formula which can be really useful.

In order to calculate if the number 2 is winning in a specific turn of the French roulette, we apply the mentioned formula and replace N with 1, since in our case we are interested only on one number, the number 2. The formula gives therefore an expectation that the number comes out of the 1/37x100, which means 2,7% chances that number 2 is winning.

For those who are expecting the possibility that the colour-black-is-winning, also these probabilities can be calculated with the aforementioned formula: we replace N with 18 since there are 18 black boxes on the wheel of the French roulette. We have therefore an expectation of the black to come out winning of the 18/37x100 and so of the 48,64%.

Do not be surprise if you never get a 100% when calculating the probabilities of the black to be winning or the red to be winning: that is due to the fact that the box zero is not black nor red.

Probabilities Chart

Type of betGainsProbabilities
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 in the American Roulette

The formulas previously explained must be elaborated in order to calculate the probabilities of gains in another variation of Roulette: the American Roulette.

Indeed, the American roulette has got a wheel of 38 boxes instead of 36 as in the European one. You need to replace 37 with 38 in the formulas previously explained and you are ready to go!

At the same time, you must take into account that there are two boxes neither black or red, the box with number 0 and the one with number 00: this affects the probabilities to see the black or the red coming out winning during a turn of American roulette.

Probabilities Chart

Type of betGainsProbabilities
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%

Play your game and do not believe that fate makes things well anymore, there are real laws of probabilities behind your gains and losses, but also behind your infallible game strategies!

Become masters of the game and clever strategists, basing on real probabilistic theories...