What are your Chances of Winning at Roulette

Roulette and probability theory have a lot in common. First of all, they share the same father. None other than the famous mathematician, physicist, and philosopher Blaise Pascal. He invented both roulette and probability in the 17th century and, thanks in part to this, it has made its way into every primary school textbook.

Although probability theory is extremely interesting as such, today we will focus more on its real-life applications. Specifically, then, we will look at what all gamblers are primarily interested in, namely the chances of winning. It is the first to know if you know how to win at roulette.

To begin with, it should be noted that all probability calculations are derived from the European roulette wheel, which has 18 black squares, 18 red squares, and 1 green square with zero. We have chosen this game because it has half the house edge and is thus much more profitable to play on in the first place. Although you won't often find it in brick-and-mortar casinos, every online casino that offers table and card games has European roulette in its portfolio of games.

You should know the chances of winning for every roulette bet and their respective payouts.

Every basic bet covers a certain number of playing fields. Logically, then, the more fields the single bet covers, the higher the chances of winning. The probability is simply calculated by the formula:

Number of covered fields / 37 * 100

Statistically, the best bets at roulette are even bets (colour, even x, odd, high x low) which cover less than half of the gaming area. The chances of winning in the roulette with them are 48.65% (18/37 * 100). The least sure is betting on individual numbers. These bets have only a 2.7% (1/37 * 100) chance to win.

Calculating the probability of winning for consecutive bets

Now that we already have calculated the odds for individual bets, we can further calculate the chances of winning in the series of games. For this case, the original formula has to be modified:

Q - Number of covered fields

N - Number of played rounds

For our simulation of all individual bets, we have chosen a limit of 50 game rounds, which corresponds, on average, to one hour of playing at a table of 4 or 5 players.

The probability of at least one win in 50 consecutive games

In the chart above you can see how the probability of winning an individual bet increases. At this point, it is very important to say that the chances never reach 100% probability.

In addition, if you are actually sitting at a table, the chances of winning a single bet always depend on the probability calculation of individual bets. This means that the chance of winning a red bet will always be 48.65%, regardless of the previous one. Do not forget that this calculation tracks the game series as a whole.

You can see it clearly in the famous Monte Carlo example in 19137 when black hit 26 times in a row. The probability of this phenomenon is 0.000000007%. If we convert this number into a meaningful figure, it turns out that you would have to experience about 143 million series of 26 games to see it again, which would take about 10 000 years of consecutive play.